# sidk_1986

Brent@GMATPrepNow posted a reply to A certain office supply store stocks 2 sizes of self-stick in the Problem Solving forum
“There are two different cases to consider: 1) All 3 pads the same color 2) The 3 pads are 3 different colors Case 1: All 3 pads the same color Take the task of packaging pads and break it into stages. Stage 1: Select a size There are 2 possible sizes, so we can complete stage 1 in 2 ...”
Yesterday
Brent@GMATPrepNow posted a reply to Byrne and some of his friends go out to dinner and spend in the Data Sufficiency forum
“ Given: Byrne and some of his friends go out to dinner and spend $111, excluding tax and tip. Target question: How many men were in the group? Statement 1: There are a total of five people at the table, including Byrne. No idea how many of these 5 people are men. Statement 1 is NOT ...” Yesterday Brent@GMATPrepNow posted a reply to If xy ≠ 0, and 75 percent of x equals 125 percent of y, in the Problem Solving forum “GIVEN: 75 percent of x equals 125 percent of y Rewrite as: 3/4 of x = 5/4 of y Or we can say: (3/4)(x) = (5/4)( y) Multiply both sides by 4 to get: 3x = 5y Divide both sides by 5 to get: 3x/5 = y Rewrite as: y = (3/5)(x) Or y = 3/5 of x Or y = 60/100 of x Or y = 60% of x Answer: C ...” Yesterday Brent@GMATPrepNow posted a reply to If $$n$$ and $$y$$ are positive integers and $$450y=n^3$$, in the Problem Solving forum “It often helps to find the prime factorization in these question types where we ask whether a certain rational expression is an integer. 450y = n^3 2*3*3*5*5*y = n^3 For 2*3*3*5*5*y to be a cube, we need the number of 2''s, 3''s and 5''s in the prime factorization to each be divisible by 3. ...” July 19, 2019 Ian Stewart posted a reply to Line DB divides Rectangle ABCD into two equal triangles. Is in the Data Sufficiency forum “Even if we had enough information using both Statements to be sure ABD was a 30-60-90 triangle, we still wouldn''t know if angle ABD was 30 degrees or 60 degrees, so the answer must be E (and we can''t even be sure it''s a 30-60-90, because the side of length 2 might not be the hypotenuse of ABD).” July 19, 2019 Ian Stewart posted a reply to If a fair die is rolled three times, what is the probability in the Problem Solving forum “There''s a 5/6 chance we don''t get a ''3'' on one roll, so a (5/6)^3 = 125/216 chance we don''t get a ''3'' on any of our three rolls. So the probability we do get at least one ''3'' is 1 - (125/216) = 91/216.” July 18, 2019 Ian Stewart posted a reply to In a series of four cricket matches, the average number of in the Problem Solving forum “If Jill''s average is the same as Jack''s in 4 games, then their sum is the same. Jill''s sum is 160, so Jack''s sum must be 160. Jack''s median score is the average of his two middle scores, so if his median score is 30, the sum of his two middle scores is 60. His smallest and largest scores ...” July 18, 2019 Brent@GMATPrepNow posted a reply to Set A = {22, 27, 11, 12, 2}, and set B: {14, 19, 3, 4, x} in the Problem Solving forum “The test-makers like to test the following concept: If we take a set of numbers with a Standard Deviation of X and add k to each value in the set, the resulting set will still have a Standard Deviation of X. This should make sense, since Standard Deviation is a measurement of dispersion (i.e., how ...” July 17, 2019 Brent@GMATPrepNow posted a reply to If $$\sqrt{3-2x} = \sqrt{2x} +1$$, then $$4x^2$$ in the Problem Solving forum “GIVEN: √(3-2x) = √(2x) +1 Square both sides to get: [√(3-2x)]² = [√(2x) +1]² Expand and simplify to get: 3 - 2x = 2x + 2√(2x) + 1 Subtract 1 from both sides to get: 1 - 2x = 2x + 2√(2x) Subtract 2x from both sides to get:2 - 4x = 2√(2x) Divide both sides by 2 to ...” July 17, 2019 Brent@GMATPrepNow posted a reply to Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to in the Problem Solving forum “GIVEN: oil: vinegar : water = 3 : 2 : 1 Let''s first try to use ALL 8 cups of oil Take 3 : 2 : 1 and multiply all 3 parts by 8/3 to get the EQUIVALENT ratio 8 : 16/3 : 8/3 Simplify to get: 8 : 5 1/3 : 2 2/3 So, in this case, the dressing is comprised of 8 cups of oil, 5 1/3 cups of vinegar, ...” July 17, 2019 Ian Stewart posted a reply to Is x > y ? in the Data Sufficiency forum “It''s possible to answer a question like this by adding inequalities, but I think it''s a difficult way to solve this type of problem. Neither Statement is sufficient alone (though you need to consider a negative value for x to see that Statement 2 is not sufficient). Using both Statements, we ...” July 16, 2019 Brent@GMATPrepNow posted a new topic called Set A = {22, 27, 11, 12, 2}, and set B: {14, 19, 3, 4, x} in the Problem Solving forum “Set A = {22, 27, 11, 12, 2}, and set B: {14, 19, 3, 4, x} If x < 0, and the standard deviation of set A = the standard deviation of set B, what is the value of x? A) -2 B) -3 C) -4 D) -5 E) -6 Difficulty level: 600-650 Answer: E Source: www.gmatprepnow.com” July 16, 2019 Brent@GMATPrepNow posted a reply to x, y and p are integers, and xyp ≠ 0. in the Problem Solving forum “Two important rules: ODD exponents preserve the sign of the base. So, (NEGATIVE)^(ODD integer) = NEGATIVE and (POSITIVE)^(ODD integer) = POSITIVE An EVEN exponent always yields a positive result (unless the base = 0) So, (NEGATIVE)^(EVEN integer) = POSITIVE and (POSITIVE)^(EVEN integer) ...” July 16, 2019 Brent@GMATPrepNow posted a new topic called x, y and p are integers, and xyp ≠ 0. in the Problem Solving forum “x, y and p are integers, and xyp ≠ 0. If p^x < p^y, which of the following MUST be true? i) x − y < 0 ii) x < 2y iii) x^p < y^p A) i only B) ii only C) iii only D) i and ii only E) none of the above Difficulty level: 650-700 Answer: E Source: ...” July 15, 2019 Brent@GMATPrepNow posted a reply to Five friends play blackjack in Las Vegas and lose an average in the Problem Solving forum “Let A, B, C, D and E represent the LOSSES (in dollars) of the 5 friends Five friends play blackjack in Las Vegas and lose an average of$100 each. So, we can write: (A+B+C+D+E)/5 = 100 Multiply both sides by 5 to get: A+B+C+D+E = 500 If the losses of two of the friends total $380, what is ...” July 15, 2019 Ian Stewart posted a reply to A library bought b books for its collection. What was the in the Data Sufficiency forum “All you know using both Statements is that the books cost at least (40)(12.50) dollars, but we have no way to work out the exact cost, so the answer is E.” July 15, 2019 Ian Stewart posted a reply to A certain shop only sells items for a whole number of dollar in the Data Sufficiency forum “For every additional item she buys, the total price will be one additional cent less than a round number of dollars. So if she buys one item, the total price will end in .99, if she buys two items it will end in .98, and so on. So if the price ended in .72, she must have bought 28 items (she can''t ...” July 15, 2019 Ian Stewart posted a reply to It takes Amy between 6 and 7 minutes to grill a steak, and in the Data Sufficiency forum “Statement 1 is not sufficient because we don''t know how much time she has, and Statement 2 is not sufficient because we don''t know how many steaks she needs. Using both, it will take her at most 4*7 = 28 minutes to grill four steaks, so if she has 30 minutes, she has enough time, and the two ...” July 15, 2019 Ian Stewart posted a reply to If $$x, y$$, and $$z$$ are positive integers such that in the Data Sufficiency forum “The factors of 57 are all odd. If x and y are two different primes, and x+y equals one of those odd factors, one of x or y must be even. But the only even prime is 2, and 2 is the smallest prime, so if x < y, then x = 2 must be true. So x is certainly a factor of the even number z, and Statement ...” July 14, 2019 Brent@GMATPrepNow posted a reply to If k is an integer and 2 < k < 7, for how many differe in the Problem Solving forum “IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . . DIFFERENCE between A and B < length of third side < SUM of A and B We''re told that the two KNOWN sides have lengths 2 and 7 So, we can write: (7 - 2) < k < (7 + 2) Simplify: 5 < k < 9 Since k is an ...” July 14, 2019 Brent@GMATPrepNow posted a reply to For the 5 days shown in the graph, how many kilowatt-hours in the Problem Solving forum “Where''s the graph? Cheers, Brent” July 13, 2019 Ian Stewart posted a reply to A marketer bought $$N$$ crates of empty cardboard gift boxes in the Problem Solving forum “The person bought NQ boxes in total, then packaged sets of J boxes together, so sold a total of NQ/J sets. If those sold for P dollars each, the revenue was PNQ/J dollars. The profit was the revenue minus the expense, W, so the profit Z is given by: Z = PNQ/J - W We need to solve for P: Z+W ...” July 12, 2019 Brent@GMATPrepNow posted a reply to If x and y are both integers greater than 1, is x a multiple in the Data Sufficiency forum “Target question: Is x a multiple of y? Asking whether x is a multiple of y is the same as asking whether x = (y)(some integer) For example, 12 is a multiple of 3 because 12 = (3)(4) So, let''s rephrase the question as... REPHRASED target question: Does x = (y)(some integer)? Statement 1: ...” July 12, 2019 Brent@GMATPrepNow posted a reply to In how many different ways can 3 identical green shirts and in the Problem Solving forum “We can take this question and ask an easier question: In how many ways can we choose 3 of the 6 children to receive a green shirt? Notice that, once we have given a green shirt to each of those 3 chosen children, the remaining children must get red shirts. In other words, once we have given ...” July 12, 2019 Brent@GMATPrepNow posted a reply to Bill took 4 math tests, and each test received a score out in the Data Sufficiency forum “Target question: What was Bill''s average (arithmetic mean) score for all 4 tests? Statement 1: Bill''s first 3 tests received an average score of 50. Since we don''t have any information about the 4th test, statement 1 is NOT SUFFICIENT Statement 2: Bill''s last 2 tests received an ...” July 12, 2019 Brent@GMATPrepNow posted a reply to Did Insurance Company $$K$$ have more than$300 million in in the Data Sufficiency forum
“Target question: Did Insurance Company $$K$$ have more than $300 million in total net profits last year? Jump straight to... . . . Statements 1 and 2 combined Statement 2 tells us about profits from ONE PART of Company K''s business. Statement 1 tells us a tiny bit about Company K''s ...” July 12, 2019 Ian Stewart posted a reply to n points are equally spaced on a circle, where n is an even in the Problem Solving forum “I did this the same way Scott did - with those answer choices, it''s a very fast question. I doubt they meant to make the question so easy to answer. If we had better-chosen answer choices, and needed to actually solve: if you connect three points on a circle, you only get a right triangle if ...” July 11, 2019 Brent@GMATPrepNow posted a reply to a, b, c, d satisfy a-1=b+2=c-3=d+4. Which of a, b, c, d is t in the Problem Solving forum “Rewrite each value in terms of the same variable. Given: a - 1 = b + 3 Subtract 3 from both sides to get: b = a - 4 Given: a - 1 = c - 3 Add 3 to both sides to get: c = a + 2 Given: a - 1 = d + 4 Subtract 4 from both sides to get: d = a - 5 So, a, b, c and d are equal to a, a-4, a+2 ...” July 10, 2019 Ian Stewart posted a reply to At the close of the market on Monday, the price of a certain in the Problem Solving forum “The stock first increases from$100 to $120. This increases a further 10%, so by$12, to $132. This then decreases by 30%, so we''re multiplying it by 0.7, and we get (7/10)(132) =$92.4.”
July 10, 2019
Ian Stewart posted a reply to While making a non-stop trip, a bus averaged m mph for the in the Data Sufficiency forum
“The total distance traveled was 5m + 4n, and the total time was 9 hours, so the average speed we want to find is (5m + 4n)/9. In Statement 1, if we divide by 1.5 on both sides, we get 5m + 4n = 310, so the average speed for the trip was 310/9. From Statement 2 we can''t find 5m + 4n, so we ...”
July 10, 2019
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Data Sufficiency lesson #8: - Choosing Good Numbers Video: https://www.youtube.com/watch?v=bu-WhqM0j1Q Cheers, Brent”
July 9, 2019
Ian Stewart posted a reply to If Anil can finish a job in 4 hours and Gustavo can finish in the Problem Solving forum
“Anil would do 3 jobs in 12 hours, Gustavo 2 jobs in 12 hours, so together 5 jobs in 12 hours, and thus 1 job in 12/5 hours = 2.4 hours = 2 hours and 24 minutes.”
July 9, 2019
Ian Stewart posted a reply to What is the length of line segment $$AB$$ in the figure in the Problem Solving forum
“If we draw a vertical height from A down to BC, that divides the triangle into a 45-45-90 triangle on the left, and a 30-60-90 triangle on the right. The hypotenuse of the 45-45-90 is AC, so is of length 1, and the height we''ve drawn is thus of length 1/√2 = √2/2 (since the sides of a 45-45-90 ...”
July 9, 2019
Ian Stewart posted a reply to If $$A$$ and $$B$$ are consecutive positive integers less in the Data Sufficiency forum
“Clearly neither Statement is sufficient alone. Using both, the only positive cubes less than 100 are 1, 8, 27 and 64, and the only cube that is one away from a positive perfect square is 8 (since it''s one less than 9), so B = 9, and the answer is C.”
July 9, 2019
Ian Stewart posted a reply to For a set $$X$$ containing $$n$$ integers, is the mean even? in the Data Sufficiency forum
“If the set is {2, 4}, the mean is 3, so is odd, and if the set is {2, 6}, the mean is 4, so is even. So using both Statements we cannot answer the question and the answer is E.”
July 9, 2019
Brent@GMATPrepNow posted a reply to A certain candy manufacturer reduced the weight of Candy Bar in the Problem Solving forum
“Let''s assign nice values to the ORIGINAL weight and price of the candy bar. Let''s say it ORIGINALLY weight 100 ounces and cost $100$1 per ounce If we decrease the weight be 20%, the NEW weight is 80 ounces. The price remains at $100 per bar So, the NEW price per ounce =$100/80 ounces = ...”
July 8, 2019
Brent@GMATPrepNow posted a reply to While driving on the expressway, did Robin ever exceed the in the Data Sufficiency forum
“NOTE: There''s nothing here to suggest that Robin''s speed was constant. Sure, she MIGHT have traveled at a constant speed, or her speed may have varied throughout the trip. Target question: Did Robin''s speed ever exceed 55 miles per hour? Statement 1: Robin drove 100 miles No information ...”
July 8, 2019
Brent@GMATPrepNow posted a reply to What is the remainder when positive integer x is divided by in the Data Sufficiency forum
“Target question: What is the remainder when positive integer x is divided by 5? Statement 1: x divided by 10 has a remainder of 7. There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with ...”
July 8, 2019
Brent@GMATPrepNow posted a reply to If x and y are greater than 0, is x = 1 ? in the Data Sufficiency forum
“Target question: Is x = 1 ? Given: x and y are POSITIVE Statement 1: x/y = 1 Let''s TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 1 and y = 1. In this case, the answer to the target question is YES, x DOES equal 1 Case b: ...”
July 8, 2019
Brent@GMATPrepNow posted a reply to The function f(a) is defined for all positive integers a as in the Problem Solving forum
“Since 77 = (11)(7), any positive multiple of 7 or 11 will have a common factor with 77 where that common factor is greater than 1. For example, 77 and 14 share a common factor of 7. And 77 and 35 share a common factor of 7. Likewise, 77 and 55 share a common factor of 11. And 77 and 33 share ...”
July 8, 2019
Brent@GMATPrepNow posted a reply to The table above shows the number of students in a certain in the Data Sufficiency forum
“ASIDE: Since the diagram closely resembles a Double Matrix Method diagram, I''ll treat it as such. Target question: What is the total number of students in the class? Statement 1: Of the boys in the class, 15 are studying biology. Add this information to our diagram to get: ...”
July 8, 2019
Ian Stewart posted a reply to A certain list of 300 test scores has an arithmetic mean of in the Problem Solving forum
“It''s a near-verbatim copy of this GMATPrep question, they just changed a couple of numbers: https://www.beatthegmat.com/standard-deviation-t45521.html”
July 8, 2019
Brent@GMATPrepNow posted a reply to The table above shows the number of students in a certain in the Data Sufficiency forum
“ASIDE: Since the diagram closely resembles a Double Matrix Method diagram, I''ll treat it as such. Target question: What is the total number of students in the class? Statement 1: Of the boys in the class, 15 are studying biology. Add this information to our diagram to get: ...”
July 7, 2019
Brent@GMATPrepNow posted a reply to If x is a positive integer such that x^2 + 5x − 14 = 0, wh in the Problem Solving forum
“GIVEN: x² + 5x − 14 = 0 Factor: (x + 7)(x - 2) = 0 So, EITHER x = -7 OR x = 2 Since we''re told x is POSITIVE, the correct answer is D Cheers, Brent”
July 7, 2019
Ian Stewart posted a reply to If $$m$$ and $$n$$ are positive integers and $$r$$ is the in the Data Sufficiency forum
“If you want a number''s remainder when you divide it by 3, you can sum the digits of the number and take the remainder by 3 of that sum. The sum of the digits of (5)(10^n) is always going to be 5 no matter what n equals, so we only need the value of m. If m = 1, then the digits of (5)(10^n) + m will ...”
July 7, 2019
Ian Stewart posted a reply to A bigger circle (with center A) and a smaller circle (with in the Data Sufficiency forum
“Using Statement 1, there''s only one way to draw the diagram, and we know a length, so from Statement 1 alone it must be possible to find every length - there''s no need to solve anything. If we wanted to actually solve, you could draw the lines AS and BT and notice that the two right triangles ...”
July 7, 2019
Ian Stewart posted a reply to Ann and Bob planted trees on Friday. What is the ratio of in the Data Sufficiency forum
“For Statement 1, if Bob planted 1 tree, then Ann planted 21, and the ratio is 1 to 21. But if Bob planted 1 billion trees, the ratio is very close to 1 to 1, so Statement 1 is not sufficient. For Statement 2, for every 10 trees Bob planted, Ann planted 11, so the ratio is 10 to 11 and Statement 2 ...”
July 7, 2019
Brent@GMATPrepNow posted a reply to What is the value of n in the equation: - 25 + 19 + n = s ? in the Data Sufficiency forum
“ Given: -25 + 19 + n = s Simplify: -6 + n = s Add 6 to both sides to get: n = s + 6 Target question: What is the value of n? Statement 1: s = 2 We already know that n = s + 6 Replace s with 2 to get: n = 2 + 6 = 8 The answer to the target question is n = 8 Since we can answer the ...”
July 6, 2019
Ian Stewart posted a reply to The average American spends y dollars on food per month, in the Problem Solving forum
“Whose food purchases? As the question is written, it''s impossible to tell what they''re asking for. Assuming they mean to ask about the spending of an average American: with no discount, they''d spend $9y in nine months. They save x% in one month, so save (x/100)y = xy/100 dollars in one month. So ...” July 6, 2019 Ian Stewart posted a reply to George bought a large electronic item with a 15% off coupon, in the Problem Solving forum “That''s a lot of words for such a straightforward setup. When he pays back half of the additional 15% discount, he is paying back 7.5% of the original price of the item. So$40.50 is 7.5% of the original price, and doubling everything, $81 is 15% of the original price. Of course we could do algebra ...” July 6, 2019 Ian Stewart posted a reply to Point $$P$$ lies on the equation $$y=x^2−1$$ and Point $$Q in the Problem Solving forum “If y = x^2 - 1, then since x^2 is at least zero, the smallest possible value of y is -1. If y = -x^2 + 1, then since -x^2 is at most zero, the largest possible value of y is 1. So the answer is -1 - 1 = -2.” July 6, 2019 Ian Stewart posted a reply to Line \(k$$ is in the rectangular coordinate system. If line in the Problem Solving forum “If (a, b) is on the x-axis, then b is zero. So the line intersects the x-axis at (a, 0), and if (a, 0) is on the line, that point must ''work'' in the line''s equation. Plugging in x=a and y=0 we get 3(0) = 2(a) + 6 2a = -6 a = -3” July 6, 2019 Ian Stewart posted a reply to What is the probability that the sum of two dice will yield in the Problem Solving forum “If you roll one die, you can always make a sum of 7 if you get the perfect roll on the second die. There''s a 1/6 chance you roll the perfect number, so that''s the probability of getting a sum of 7. The probability we do that twice in a row is (1/6)(1/6) = 1/36. You could get down to A or B ...” July 6, 2019 Ian Stewart posted a reply to Three friends, A, B and C have houses along a straight road, in the Data Sufficiency forum “They''ll travel the minimum combined distance if they meet in the middle house, B. Then person B won''t travel at all, and persons A and C will travel, combined, the total distance between house A and house C (if instead they meet at house A or C, one person travels the total distance from A to C, ...” July 6, 2019 Brent@GMATPrepNow posted a reply to The price of a phone call consists of a standard connection in the Problem Solving forum “BTW, you posted the same question in January: https://www.beatthegmat.com/the-price-of-a-phone-call-consists-of-a-standard-connection-t305974.html Cheers, Brent” July 5, 2019 Brent@GMATPrepNow posted a reply to The price of a phone call consists of a standard connection in the Problem Solving forum “Let C = price of connection fee Let M = the price PER MINUTE A 10-minute call costs$2.90 We can write: C + 10M = 2.90 A 16-minute call costs $4.40. We can write: C + 16M = 4.40 How much does a 13-minute call cost? So far, we have: C + 10M = 2.90 C + 16M = 4.40 ONE (slower) ...” July 5, 2019 Ian Stewart posted a reply to A bag contains ping pong balls, each with a number written in the Data Sufficiency forum “It''s a weighted average -- if 1/3 of the pingpong balls average to 20, and all of them average to 50, the other 2/3 will need to average to 65 (since there are twice as many of them as in the 1/3 group, their average will need to be "twice as close" to the overall average). Statement 2 ...” July 5, 2019 Ian Stewart posted a reply to Q. Is ABC an equilateral triangle? in the Data Sufficiency forum “Statement 1 alone only ensures the triangle is isosceles. From Statement 2, two sides are equal, so two angles must be equal. We also know one angle is 60 degrees. If that''s one of the two equal angles, we have two 60 degree angles, and the third angle then must also be 60 degrees (because a ...” July 5, 2019 Brent@GMATPrepNow posted a reply to A certain family has 3 sons: Richard is 6 years older than in the Problem Solving forum “We can also solve this with 1 variable David is 8 years older than Scott Let x = Scott''s age NOW So, x + 8 = David''s age NOW Richard is 6 years older than David If x + 8 = David''s age NOW, then... (x + 8) + 6 = Richard''s age NOW In other words, x + 14 = Richard''s age NOW In in 8 ...” July 4, 2019 Ian Stewart posted a reply to What is the range of a set consisting of the first 100 multi in the Problem Solving forum “The range of one hundred consecutive multiples of 7 will always be the same no matter what the smallest value in your list is, so we can just find the range of 7, 14, 21..., 693, 700, which is 700-7 =693.” July 4, 2019 Ian Stewart posted a reply to Patrick is cleaning his house in anticipation of the arrival in the Data Sufficiency forum “Statement 1 tells us he can do two of the tasks well before the guests arrive, but we don''t know how long putting the dishes away will take, so Statement 1 is not sufficient. Statement 2 tells us that he''ll need 55+7 = 62 minutes to wash and put away the dishes, so he can''t finish that in less ...” July 4, 2019 Brent@GMATPrepNow posted a reply to When the positive integer x is divided by 11, the quotient in the Problem Solving forum “A fast approach is to find a value of x that meets the given conditions. When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3.... Notice that x = 3 meets the above conditions. 3 divided by 11 = 0 with remainder ...” July 3, 2019 Brent@GMATPrepNow posted a reply to A palindrome, such as 12321, is a number that remains the sa in the Problem Solving forum “If a number is divisible by 4, then the number created by the last 2 digits is divisible by 4. For example, we know that 76512, 311,244 and 2128 are divisible by 4 because 12, 44, and 28 are divisible by 4 So, the last 2 digits of the 4-digit palindromes must be 00, 04, 08, 12, . . . , 92 or ...” July 3, 2019 Ian Stewart posted a reply to When the positive integer x is divided by 11, the quotient in the Problem Solving forum “There''s an old GMATPrep question that is almost identical to this one. Since the value of x can be 3, the quotient can be 0 (when we divide 3 by 11, the quotient is zero and the remainder is 3), so if one of the five answers is right, it has to be E. Or, if one wants a proper ''proof'', then the ...” July 3, 2019 Ian Stewart posted a reply to In 2008, a certain factory produced 25% more widgets than it in the Problem Solving forum “If we start with 100 widgets in 2007, we have 125 in 2008, and then (1.2)(125) = 150 in 2009. For this to decrease to 100, it needs to fall by 50, or by 50/150 = 33 1/3 %.” July 3, 2019 Brent@GMATPrepNow posted a reply to x, y and z are all unique numbers. If x is chosen randomly in the Problem Solving forum “Thanks Ian. Not sure how I missed "unique." Thanks for clarifying. Cheers, Brent” July 2, 2019 Ian Stewart posted a reply to x, y and z are all unique numbers. If x is chosen randomly in the Problem Solving forum “To answer Brent''s question, when they say x, y and z are "unique numbers", I''m guessing they''re trying to say that the selection is being done without replacement. But it''s mathematically wrong to present a probability question this way (and I missed their ''unique'' comment the first ...” July 2, 2019 Brent@GMATPrepNow posted a reply to x, y and z are all unique numbers. If x is chosen randomly in the Problem Solving forum “Are the numbers chosen with or without replacement? For example, can y and z both be 23?” July 2, 2019 Ian Stewart posted a reply to In a group of 100 adults, 75 percent of the women are left- in the Problem Solving forum “The question is unanswerable if some people could be ambidextrous. Assuming everyone is either left or right-handed, we know that among women, the ratio of left to right-handed people is 3 to 1. So if 12 women are right-handed, 36 are left-handed, and there are 48 women in total. There are thus ...” July 2, 2019 Ian Stewart posted a reply to What is the value of y? in the Data Sufficiency forum “Using Statement 1, y can be 29, 31 or 33. Using Statement 2, y can be 32.7 or 33 or 35.419 among other possibilities. Using both Statements, y can only be 33, so the answer is C.” July 2, 2019 Ian Stewart posted a reply to The LCM of three numbers is four times their GCF. Which of in the Problem Solving forum “The numbers could be 2, 4, and 8, so I and II need not be true. That leaves only answer B.” July 1, 2019 Ian Stewart posted a reply to The numbers in which of the following pairs do NOT have a in the Problem Solving forum “32 = 2^5 has only one prime divisor, so it could never have a "pair" of distinct prime divisors in common with any other number. So the answer is C.” July 1, 2019 Ian Stewart posted a reply to Suppose x is a positive even number, all of whose digits in the Problem Solving forum “If the number is even, and its digits are all 3s and 4s, it must end in 4. If the number is divisible by 4, its last two digits must form a multiple of 4, so must be "44" (and not "34"). If the number is divisible by 3, the sum of its digits is a multiple of 3, and we can see ...” July 1, 2019 Ian Stewart posted a reply to a and b are integers such that a/b=3.45. If R is the remaind in the Problem Solving forum “When you divide a by b, the quotient/remainder formula tells us a = Qb + R where Q is the quotient, R the remainder. Divide this by b on both sides and we have a/b = Q + (R/b) Since R < b by the definition of a remainder, on the right side above Q is the integer part of the result of ...” July 1, 2019 Brent@GMATPrepNow posted a reply to How many two-digit whole numbers yield a remainder of 1 when in the Problem Solving forum “...two-digit whole numbers yield a remainder of 1... Possible values are: 11, 21, 31, 41, 51, 61, 71, 81, and 91 ...and also yield a remainder of 1 when divided by 6 Take each value from 11, 21, 31, 41, 51, 61, 71, 81, and 91, and see which ones leave a remainder of 1 when divided by 6 11, 21, ...” July 1, 2019 Ian Stewart posted a reply to Sets R and S each contain three distinct positive integers. in the Data Sufficiency forum “Since r is positive (so since it cannot be zero), we can divide by r in the question "What is the probability that rs = r?" to get the simpler question "What is the probability that s = 1?" So it doesn''t matter what is in set R, since we only care if we pick a "1" ...” July 1, 2019 Ian Stewart posted a reply to Coach Jackson will choose at least two players for his team in the Data Sufficiency forum “I have no idea what this question is even asking. From the stem, the coach is choosing "two players *for* his team", and then Statement 1 talks about the total number of teams he can choose. Is he choosing his complete team on Saturday? Or just part of it? If just part of it, when he ...” July 1, 2019 Ian Stewart posted a reply to A triangle is formed by the x-axis, the y-axis, and Line M. in the Data Sufficiency forum “There''s a reason you never see percentages combined with coordinate geometry in any actual GMAT question: intercepts and slopes can be negative, and the GMAT will never ask you to work out what number is "25% less than" some negative number. It''s also not even clear what Statement 2 is ...” July 1, 2019 Ian Stewart posted a reply to In a group of 80 college students, how many own a car? in the Data Sufficiency forum “From Statement 2, 21 out of 50 car-owners are women. That''s a reduced ratio, so the number of car owners must be a multiple of 50, and the only multiple of 50 less than or equal to 80 is 50 itself, so there must be 50 car owners, and Statement 2 is sufficient. Since Statement 1 only tells us we ...” July 1, 2019 Ian Stewart posted a reply to If $$z$$ is an odd integer, is $$300z > 1500?$$ in the Data Sufficiency forum “It''s also possible that z is negative, so z can also be equal to -3 or -5. That doesn''t change the answer to the question though. I''d find it useful to rephrase the question by dividing by 300 on both sides: we want to know "is z > 5?"” July 1, 2019 Brent@GMATPrepNow posted a reply to Is it true that a > b? in the Data Sufficiency forum “Target question: Is a > b? Statement 1: 2a > 2b Divide both sides by 2 to get: a > b The answer to the target question is YES, a IS greater than b Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: a + c > b + c Subtract b from ...” June 30, 2019 Brent@GMATPrepNow posted a reply to If sequence S has 120 terms, what is the 105th term of S? in the Data Sufficiency forum “Target question: What is the 105th term of S? Given: Sequence S has 120 terms Statement 1: The first term of S is −8. We have no information about the nature of the sequence. So, knowing the value of term 1 won''t help is determine the value of term 105 Since we cannot answer the ...” June 30, 2019 Brent@GMATPrepNow posted a reply to If a certain wheel turns at a constant rate of $$x$$ in the Problem Solving forum “We can solve the question using equivalent ratios Wheel turns at a constant rate of x revolutions per minute We can also say the wheel turns at a constant rate of x revolutions per 60 seconds In other words, # of revolutions/seconds elapsed = x/60 How many revolutions will the wheel make in ...” June 29, 2019 Ian Stewart posted a reply to Sequence A is defined by the equation An = 3n + 7 in the Data Sufficiency forum “I wouldn''t solve this problem by generating a formula -- we know exactly what our sequence is. The sequence is 10, 13, 16, 19, etc. Every term is positive, so as you add more and more terms, the sum gets larger and larger. If we know the sum of the first n terms is 275, there can thus only be one ...” June 29, 2019 Ian Stewart posted a reply to What is the X intercept of non horizontal line m? in the Data Sufficiency forum “Our line has an equation y = mx + b, where m is the slope, b the y-intercept. To find the x-intercept of a line, we find the value of x when y=0. If we plug in y=0 here, we find 0 = mx + b x = -b/m Statement 1 tells us m = 4b, and if we substitute that for m above, we learn that x = ...” June 29, 2019 Ian Stewart posted a reply to Data sufficiency in the GMAT Math forum “If x > 1, then 1/x is between 0 and 1. So 1 + (1/x) will be between 1 and 2, and answers C and E are both possible (for C, x = 7/2, and for E, x = 7). If there''s a typo in D, and instead it''s meant to read "15/11", then D is also possible (x = 11/4). It''s only if the question tells ...” June 28, 2019 Ian Stewart posted a reply to A certain series is defined by the following recursive rule: in the Problem Solving forum “This is not a "series". It is a "sequence". A series is a sum of a sequence, and this question has nothing to do with summing a sequence. It would be understandable for a test taker to be confused by the wording here (I was at first), because test takers aren''t expected to know ...” June 28, 2019 Brent@GMATPrepNow posted a reply to Leona bought a 1-year,$10,000 certificate of deposit that in the Problem Solving forum
“If the interest is at an ANNUAL rate of 8 percent compounded semiannually, then EVERY SIX MONTHS, we add 4% interest to the certificate. No need to apply the compound interest formula. It''s just as fast to make the 2 calculations. After 6 months, the value of the certificate = $10,000 + (4% of ...” June 28, 2019 Ian Stewart posted a reply to Is $$x \geq 0?$$ in the Data Sufficiency forum “Rewriting Statement 1 with zero on one side, x^2 - 9x = 0, so x(x-9) = 0, and x = 0 or x = 9. Either way, x is greater than or equal to zero, so Statement 1 is sufficient. Statement 2 tells us |x| = -x, which only happens when x is less than or equal to zero (when x is positive, the absolute ...” June 27, 2019 Ian Stewart posted a reply to Is the slope of line z positive? in the Data Sufficiency forum “It''s hard to guess which line has the slope of -1/4 in Statement 1. If they''re talking about line z, then the Statement is clearly sufficient. If they''re talking about line m, then since perpendicular lines have slopes that are negative reciprocals of each other, line z would have a slope of 4. ...” June 27, 2019 Ian Stewart posted a reply to S is a set of n consecutive positive integers. Is the mean in the Data Sufficiency forum “A set of consecutive integers is equally spaced, so its mean and median are always equal. So Statement 2 is instantly sufficient. The median will also be halfway between the smallest and largest values in the set, so if S is the smallest value, and R is the range, the median will be S + (R/2). If ...” June 27, 2019 Ian Stewart posted a reply to What is the LCM of the numbers 3, a, and 7, if ‘a’ is an in the Data Sufficiency forum “Statement 1 is not sufficient, because the LCM will be different if a=5 or if a=97. For Statement 2, the GCD of 3 and anything must be a divisor of 3, so it could only be 1 or 3, and will always be a divisor of 30. So Statement 1 only tells us "the LCM of 3 and a is a divisor of 30". ...” June 27, 2019 Ian Stewart posted a reply to A new cell phone plan is offering pricing based on average m in the Data Sufficiency forum “If Brandon averaged q minutes per month, his total usage for the year was 12q minutes. From Statement 1, we know for 8 months Jodie averaged 1.5q minutes per month, so during those 8 months, she used (8)(1.5q) = 12q minutes in total. She might have used zero minutes the rest of the year, in ...” June 27, 2019 Brent@GMATPrepNow posted a reply to A computer routine was developed to generate two numbers, in the Problem Solving forum “Check each answer choice... (A) (99, 10) √100 = 10 So, √99 is LESS THAN 10 In other words, 10 is GREATER THAN √99 So, answer choice A breaks the rule that says the second number must be less than or equal to the square root of the first" Answer: A Cheers, Brent” June 27, 2019 Brent@GMATPrepNow posted a reply to If Lucy walks to work at a rate of 4 miles per hour, but she in the Problem Solving forum “Let d = distance from home to work Average speed = (total distance traveled)/(total travel time) total distance traveled = d + d = 2d total travel time = travel time TO work + travel time FROM work time = distance/speed We get: total travel time = d/4 + d/6 = 3d/12 + 2d/12 = ...” June 26, 2019 Brent@GMATPrepNow posted a reply to Right triangle PQR is to be constructed in the xy-plane so in the Problem Solving forum “Take the task of building triangles and break it into stages. Stage 1: Select any point where the right angle will be (point P). The point can be selected from a 10x11 grid. So, there 110 points to choose from. This means that stage 1 can be completed in 110 ways. Stage 2: Select a point ...” June 26, 2019 Brent@GMATPrepNow posted a reply to If y= 4 + (x - 3)^2, then y is lowest when in the Problem Solving forum “KEY CONCEPT: In order to minimize the value of y, we must minimize the value of (x -3)² We know that (some number)² ≥ 0 So, the SMALLEST possible value of (some number)² is 0 Likewise, the SMALLEST possible value of (x -3)² is 0 (x -3)² = 0 when x = 3 Answer: D Cheers, Brent” June 25, 2019 Brent@GMATPrepNow posted a reply to In the figure shown, what is the value of x? in the Data Sufficiency forum “The diagram (aka figure) is missing.” June 25, 2019 Brent@GMATPrepNow posted a reply to For integers x and y, which of the following MUST be an in the Problem Solving forum “One approach: The question is asking us to determine which expression MUST be an integer for ALL integer values of x and y. So, let''s TEST a pair of values. Let''s plug in x = 1 and y = 1 If an expression evaluates to be a non-integer, we can ELIMINATE that answer choice. We get... ...” June 25, 2019 Brent@GMATPrepNow posted a reply to A certain basketball team that has played 2/3 of its games in the Problem Solving forum “Given: The team has played 2/3 of its games. The team has played 20 games. If 2/3 of the total number of games = 20, then the total number of games = 30. This means that there are 10 games remaining. We want the team to win at least 3/4 of its games. 3/4 of 30 = 22.5 So, in order to ...” June 25, 2019 Brent@GMATPrepNow posted a reply to If 2xy + z = 9, what is the value of the positive integer z? in the Data Sufficiency forum “ Given: 2xy + z = 9 Target question: What is the value of the positive integer z? Statement 1: xyz - z² = 0 Factor to get: z(xy - z) = 0 This means that EITHER z = 0 OR xy - z = 0 HOWEVER, we''re told that z is a POSITIVE integer, which means z ≠0 So, it must be the case that xy - ...” June 22, 2019 Brent@GMATPrepNow posted a reply to What is the perimeter of isosceles triangle MNP? in the Data Sufficiency forum “Target question: What is the perimeter of isosceles triangle MNP? Statement 1: MN = 16 No idea about the other 2 sides Statement 1 is NOT SUFFICIENT Statement 2: NP = 20 No idea about the other 2 sides Statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Since we have an ...” June 22, 2019 Brent@GMATPrepNow posted a reply to f x and y are positive, what is the value of y ? in the Data Sufficiency forum “Target question: What is the value of y? Given: x and y are positive Statement 1: xy is the square of an integer. There are several values of x and y that satisfy this condition. Here are two: Case a: x = 1 and y = 1. Here xy = (1)(1) = 1, which is the square of an integer. In this ...” June 21, 2019 Brent@GMATPrepNow posted a reply to Which of the following is an integer? I. 12! / 6! II. 12! / in the Problem Solving forum “I. 12!/6! = (12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)/(6)(5)(4)(3)(2)(1) = (12)(11)(10)(9)(8)(7) = some integer II. 12!/8! = (12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)/(8)(7)(6)(5)(4)(3)(2)(1) = (12)(11)(10)(9) = some integer III. 12!/7!5! = ...” June 21, 2019 Brent@GMATPrepNow posted a reply to The average salary of 15 people in the shipping department in the Problem Solving forum “]The average salary of 15 people in the shipping department at a certain firm is$20,000 So, (sum of all 15 salaries)/15 = $20,000 Multiply both sides by 15 to get: sum of all 15 salaries =$300,000 The salary of 5 of the employees is $25,000 each and the salary of 4 of the employees is$16,000 ...”
June 20, 2019
Brent@GMATPrepNow posted a reply to In how many different ways can 3 fiction books and 3 in the Problem Solving forum
“Take the task of arranging the 6 books and break it into stages. Stage 1: Arrange the 3 fiction books in a row We can arrange n unique objects in n! ways So, we can arrange the 3 books in 3! ways (= 6 ways) So, we can complete stage 1 in 6 ways Stage 2: Arrange the 3 non-fiction books in ...”
June 20, 2019
Brent@GMATPrepNow posted a reply to Data sufficiency in the GMAT Math forum
“Take: y = 1 + 1/x Rewrite as: y = x/x + 1/x Simplify: y = (x + 1)/x So, we''re looking for an answer choice that can be expressed as a fraction in which the numerator is 1 greater than the denominator. Answer: E Cheers, Brent”
June 19, 2019
Brent@GMATPrepNow posted a reply to If is n is multiple of 5, and n=p^2*q where p and q are prim in the Problem Solving forum
“Let''s test some values that satisfy the given conditions (n is multiple of 5, and n = p²q, where p and q are prime numbers) How about: p = 2 and q = 5. In this case, n = (2²)(5) = 20, and 20 is a multiple of 5, which satisfies the given condition. Now plug p = 2 and q = 5 into the ...”
June 19, 2019
Brent@GMATPrepNow posted a new topic called If 3 different integers are randomly selected from the set { in the Problem Solving forum
“If 3 different integers are randomly selected from the set {1, 2, 3, 4, 5, 6}, what is the probability that a triangle can be constructed so that its 3 sides have the lengths of the 3 selected numbers? A) 0.25 B) 0.3 C) 0.35 D) 0.40 E) 0.45 Source: www.gmatprepnow.com Difficulty level: ...”
June 19, 2019
Brent@GMATPrepNow posted a reply to A certain zoo has mammal and reptiles and birds, and no in the Data Sufficiency forum
“Target question: How many birds are in the zoo? Given: The ratio of mammals to reptiles to birds is 11: 8:5. Given this ratio, we could say that there are: 11x mammals 8x reptiles 5x birds for some value of x. Statement 1: there are twelve more mammals in the zoo than there are ...”
June 19, 2019
Brent@GMATPrepNow posted a reply to If x, y and z are three different non-negative integers, whi in the Problem Solving forum
“Nice work, Mitch! I created this question to illustrate the importance of checking the answer choices each time you analyze one of the statements. Here’s why: Once we know that statement i COULD be true (it''s true when x = 0, y = 1 and z = 2), we should check the answer choices…. ...”
June 18, 2019
Brent@GMATPrepNow posted a reply to A certain machine produces 1,000 units of product P per hour in the Problem Solving forum
“A certain machine produces 1,000 units in 1 hour So, the machine produces 24,000 units in 24 hours In other words, the machine produces 24,000 units in 1 DAY So, the machine produces (24,000)(7) units in 7 DAYS (20,000)(7) = 140,000 So, (24,000)(7) = some number greater than 140,000 ...”
June 18, 2019
Brent@GMATPrepNow posted a new topic called If x, y and z are three different non-negative integers, whi in the Problem Solving forum
“If x, y and z are three different non-negative integers, which of the following COULD be true? i) |x−y| = |x+y| = |y−z| ii) x^y = y^z iii) x³ + y³ = z³ A) i only B) ii only C) iii only D) i and ii E) i and iii Source; www.gmatprepnow.com Difficulty level: 700+ Answer: D”
June 18, 2019
Brent@GMATPrepNow posted a reply to If p is an integer greater than 1, is p a prime number? in the Data Sufficiency forum
“ Given: p is an integer greater than 1 Target question: Is p a prime number? Statement 1: p is a factor of 13 13 has exactly two factors: 1 and 13 Since p > 1, we KNOW that p = 13 (which is prime) The answer to the target question is YES, p IS prime Since we can answer the target ...”
June 17, 2019
Brent@GMATPrepNow posted a reply to How many ways are there to arrange the letters in the word in the Problem Solving forum
“------------ASIDE----------------- When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule. It goes like this: If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, ...”
June 17, 2019
Brent@GMATPrepNow posted a reply to If |2x + 5| = |3x − 2|, which of the following is a possib in the Problem Solving forum
“If |x| = |y|, then either x = y OR x = -y GIVEN: |2x + 5| = |3x − 2| So, EITHER 2x + 5 = 3x − 2 OR 2x + 5 = -(3x − 2) Let''s solve each equation... Take: 2x + 5 = 3x − 2 We get: 5 = x - 2 Solve: x = 7 Check answer choices.....x = 7 is not there. Try the other equation: Take: ...”
June 17, 2019
Brent@GMATPrepNow posted a reply to Is h^2 = h? in the Data Sufficiency forum
“Target question: Is h² = h? Statement 1: h + h = h Subtract h from both sides to get: h = 0 If h = 0, then h² = h becomes 0² = 0 (WORKS!) The answer to the target question is YES, h² = h Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: ...”
June 17, 2019
Brent@GMATPrepNow posted a reply to Is z > 0.5? in the Data Sufficiency forum
“Target question: Is z > 0.5 ? SCAN the statements to see we can jump straight to.... Statements 1 and 2 combined There are infinitely-many values of z that satisfy BOTH statements. . Here are two: Case a: z = 0.6. In this case, the answer to the target question is YES, z IS greater ...”
June 17, 2019
Brent@GMATPrepNow posted a reply to What is the value of x? in the Data Sufficiency forum
“Target question: What is the value of x? Statement 1: 5x + 3y = 15 Since this is a linear equation with infinitely many solutions. Here are two: Case a: x = 3 and y = 0. In this case, the answer to the target question is x = 3 Case b: x = 0 and y = 5. In this case, the answer to the target ...”
June 17, 2019
Brent@GMATPrepNow posted a reply to If the average (arithmetic mean) of seven consecutive in the Problem Solving forum
“Another approach: For any set of consecutive integers, mean = median. So, in this case, mean = median = k + 2 So, the three values that come AFTER k + 2 are k+3, k+4, and k+5 And the three values that come BEFORE k + 2 are k-1, k, k+1, k+2, k+3, k+4, k+5 The product of the greatest and ...”
June 17, 2019
Brent@GMATPrepNow posted a reply to Of the first three dozen cookies baked at a bake shop on a in the Data Sufficiency forum
“ Given: Of the first three dozen (36) cookies baked at a bake shop on a certain day, 1/3 were chocolate chip cookies. 1/2 of the remaining cookies that were baked that day were chocolate chip cookies, 1/3 of 36 = 12. So, 12 chocolate cookies were baked in the first round of baking. Let x = ...”
June 15, 2019
Brent@GMATPrepNow posted a reply to List $$K$$ consists of seven numbers. Is the average in the Data Sufficiency forum
“Target question: Is the average (arithmetic mean) of the seven numbers negative? Statement 1: Four of the seven numbers in list K are negative. There are several scenarios that satisfy statement 1. Here are two: Case a: List K = {-10, -10, -10, -10, 1, 1, 1}. Average = sum/7 = -37/7. The ...”
June 15, 2019
Brent@GMATPrepNow posted a reply to A set of 15 different integers has median of 25 and a range in the Problem Solving forum
“Let''s tackle this one step at a time. First, we have 15 different integers. We can let these 15 spaces represent the 15 numbers written in ascending order: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ If the median is 25, we can add this as the middle value: _ _ _ _ _ _ _ 25 _ _ _ _ _ _ _ Notice that 7 ...”
June 15, 2019
Ian Stewart posted a reply to If x and y are integers, and x + y < 0, is x — y > 0 in the Data Sufficiency forum
“We can rephrase the question "is x > y?" Subtracting |x| on both sides, Statement 1 only tells us that |y| > 0. But that''s always true unless y = 0, so Statement 1 only tells us y is nonzero. Assuming x is nonzero (something the question needs to tell us, so that the left side ...”
June 14, 2019
Ian Stewart posted a reply to In a network of car dealerships, a group of $$d$$ sales in the Data Sufficiency forum
“If we have d directors, and each director has a associates, we have ad associates. If the directors each sell 10 cars, they all sell 10d cars in total, and if the associates each sell 20 cars, they sell 20ad cars in total. So 10d + 20ad = 10d(1 + 2a) is the total number of cars sold. Statement 1 ...”
June 14, 2019
Brent@GMATPrepNow posted a reply to 8, 5, x, 6 The median of the list of positive integers in the Problem Solving forum
“Since there is an even number of values in the list, the median will be the AVERAGE of the two middlemost values (when all values are listed in ASCENDING order) Let''s the answer choices... A) If x = 3, then the values are {3, 5, 6, 8}, which means the median = (5 + 6)/2 = 5.5 NO GOOD. We ...”
June 14, 2019
Brent@GMATPrepNow posted a reply to Will the first 10 volumes of a 20-volume encyclopedia fit in the Data Sufficiency forum
“Target question: Will the first 10 volumes of a 20-volume encyclopedia fit upright in the bookrack shown above? Statement 1: x = 50 centimeters. We have no idea how THICK the first 10 volumes are. They COULD each be 1 mm thick, in which case the 10 volumes will easily fit in the 50 cm ...”
June 14, 2019
Brent@GMATPrepNow posted a reply to For every integer $$k$$ from 1 to 10, inclusive the "k& in the Problem Solving forum
“T = 1/2 - 1/4 + 1/8 - 1/16 + . . . Notice that we can rewrite this as T = (1/2 - 1/4) + (1/8 - 1/16) + . . . When you start simplifying each part in brackets, you''ll see a pattern emerge. We get... T = 1/4 + 1/16 + 1/64 + 1/256 + 1/1024 Now examine the last 4 terms: 1/16 + 1/64 + 1/256 + ...”
June 14, 2019
Brent@GMATPrepNow posted a reply to Jim is twice as old as Fred ... in the Problem Solving forum
“I''ve added the answer choices.... TODAY''S AGES Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Let x = Fred''s age TODAY So, 2x = Jim''s age TODAY And x - 2 = Sam''s age TODAY AGES FOUR YEARS AGO Let''s first determine Jim''s age and Sam''s age FOUR YEARS ...”
June 13, 2019
Brent@GMATPrepNow posted a reply to in terms of k and m in the Problem Solving forum
“One approach is to plug in values. Let $100 be the original price per share of Stock X Choose a "nice" value for k. How about k = 200 So, after a 200% increase, the new price per share =$300 Let $100 be the original earnings per share of Stock X Choose a "nice" ...” June 13, 2019 Brent@GMATPrepNow posted a reply to cd? in the Data Sufficiency forum “Target question: Is the product cd positive? Statement 1: 3c = -8d³ Divide both sides by d to get: 3c/d = -8d² Divide both sides by 3 to get: c/d = -8d²/3 Rewrite as: c/d = (-8/3)(d²) Since d² is greater than or equal to zero for all values of d, and since -8/3 is NEGATIVE, we can ...” June 13, 2019 Brent@GMATPrepNow posted a reply to If f(x) = x^3 + 9, is f(x) positive? in the Data Sufficiency forum “ Given: f(x) = x³ + 9 Target question: Is f(x) positive? Statement 1: x < −1 Let''s TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = -2. In this case, f(-2) = (-2)³ + 9 = (-8) + 9 = 1. So, the answer to the target question is ...” June 13, 2019 Brent@GMATPrepNow posted a reply to In May Mrs Lee's earnings were 60 percent of the Lee family' in the Problem Solving forum “Since we''re asked to find a PERCENT (and not an actual value), we can assign a nice value to the Lee family''s total income. In May Mrs Lee''s earnings were 60 percent of the Lee family''s total income Let''s say$100 = Lee family''s total income IN MAY This means $60 = Mrs Lee''s earnings ...” June 13, 2019 Brent@GMATPrepNow posted a reply to Which of the following could be the median for a set of in the Problem Solving forum “Since 20 < x < 80, we can see that, if we arrange the 5 numbers in ASCENDING order, we get two possible cases: case a: {x, 56, 86, 97, 98} case b: {56, x, 86, 97, 98} In both cases, the median is 86 Answer: B Cheers, Brent” June 13, 2019 Ian Stewart posted a reply to Mixture problem in the Problem Solving forum “The answer needs to be between 25% and 40%, and because we''re using more of the 40% solution, the answer must be closer to 40%, so only one answer makes sense, 37.5%. That''s assuming both vessels are full, something the question needs to mention (but doesn''t). If you want to use alligation, ...” June 12, 2019 Ian Stewart posted a reply to Three gnomes and three elves sit down in a row of six chairs in the Problem Solving forum “If there''s a gnome in the first chair, the arrangement must alternate: GEGEGE. We''ll have 3 choices for the first gnome, 2 for the second, and 1 for the third, and the same for the elves, for 3! * 3! = 36 arrangements in total. But we can also have an elf in the first chair, and the arrangement ...” June 12, 2019 Ian Stewart posted a reply to A state legislator drafts an income tax proposal that in the Data Sufficiency forum “Statement 1 is insufficient, because maybe everyone earns$65,000, and the answer to the question is ''no'', or maybe someone earns $1 trillion, and the percent of income collected is close to 40%. If someone earns$350,000, they pay: 20% on their first $100k 25% on their next$50k 30% on ...”
June 12, 2019
Brent@GMATPrepNow posted a reply to a, b and c are three distinct integers, greater than 1, such in the Problem Solving forum
“150 = (2)(3)(5)(5) There are three sets of 3 values (each greater than 1) that have a product of 150: {2, 3, 25} {3, 5, 50} {2, 5, 15} GIVEN: The greatest common divisor of any two numbers, among the three integers, is 1 The only set that meets this condition is {2, 3, 25} SUM = 2 + 3 + ...”
June 12, 2019
Brent@GMATPrepNow posted a reply to David drove to work at an average (arithmetic mean) speed of in the Problem Solving forum
“Let''s start with a "word equation" We can write: (David''s travel time TO work) + (David''s travel time FROM work) = 2 hours time = distance/speed Let d = the distance each way We can write: d/45 + d/60 = 2 To eliminate the fractions, multiply both sides by 180, the LCM of 45 ...”
June 12, 2019
Brent@GMATPrepNow posted a reply to If x and y are positive integers, are x and y consecutive? in the Data Sufficiency forum
“ Given: x and y are positive integers Target question: Are x and y consecutive? Statement 1: x+y=3 Since x+y=3 are x positive integers, we know that one number must be 1 and the other number must be 2. The answer to the target question is YES, x and y ARE consecutive Since we can ...”
June 12, 2019
Ian Stewart posted a reply to If l1 and l2 are distinct lines in the xy coordinate system in the Data Sufficiency forum
“I''m not sure why they ask "is a^2 = ac", which will be true when a=0 or when a=c, when we can prove the narrower fact that a=c using one of the Statements. Here, a and c are the slopes of the two lines, so if we can be sure the lines have the same slope, we''ll have sufficient ...”
June 11, 2019
Brent@GMATPrepNow posted a reply to How many integers between in the Problem Solving forum
“We want to determine how many integers end in 13 For example, 324713, 324813, 324913, 325013, . . . etc. Recognize that, for every 100 consecutive integers, only 1 will end in 13. There are 133,900 integers between 324,700 and 458,600 (since 458,600 - 324,700 = 133,900) Of those 133,900 ...”
June 11, 2019
Brent@GMATPrepNow posted a reply to sum of these 24 integers? in the Problem Solving forum
“Since we''re adding 24 numbers, we know that: Six numbers will be in the form 1--- Six numbers will be in the form 2--- Six numbers will be in the form 3--- Six numbers will be in the form 4--- Let''s first see what the sum is when we say all 24 numbers are 1000, 2000, 3000 or 4000 The sum = ...”
June 11, 2019
June 11, 2019
Brent@GMATPrepNow posted a reply to A certain library in the Problem Solving forum
“1st day - $0.10 2nd day -$0.20 or $0.40 (double or add$0.30) $0.20 is the lesser amount 3rd day -$0.40 or $0.50 (double or add$0.30) $0.40 is the lesser amount 4th day -$0.80 or $0.70 (double or add$0.30) $0.70 is the lesser amount The correct answer is B Cheers, Brent” June 11, 2019 Brent@GMATPrepNow posted a reply to rates in the Problem Solving forum “Let''s assign a nice value to x (a value that will work well with all of the numbers 3, 4 and 6. Let''s say x = 24 GIVEN: 4 machines make x units in 6 days This means 4 machines make 24 units in 6 days So, 4 machines make 4 units in 1 day So, 1 machine makes 1 unit in 1 day From here, ...” June 11, 2019 Brent@GMATPrepNow posted a reply to DS in the Data Sufficiency forum “Target question: Is b (the y-coordinate of the point on the line) positive? Given: Line k passes through the origin and through the point (a,b) Statement 1: The slope of line k is negative There are several lines and points that satisfy statement 1. Here are two: Case a: ...” June 11, 2019 Brent@GMATPrepNow posted a reply to In a certain pond in the Problem Solving forum “We can use equivalent ratios here. We''re told that the proportion of tagged fish in the 50-fish SAMPLE is equal to the the proportion of tagged fish in the ENTIRE pond. So, (# tagged fish in SAMPLE)/50 = (total # tagged fish)/(total # of fish in POND) Let x = # of fish in the entire ...” June 11, 2019 Brent@GMATPrepNow posted a reply to In the multiplication above, # represents a single digit. in the Problem Solving forum “We''re told that # times 512 equals two thousand and something. Well, 4 times 512 = two thousand and something. And 5 times 512 = two thousand and something. No other digits, when multiplied by 512 will give us two thousand and something So, let''s test 4 and 5 (answer choices C and D) If ...” June 10, 2019 Brent@GMATPrepNow posted a reply to In the xy-plane shown, is the slope of the line L negative ? in the Data Sufficiency forum “Target question: Is the slope of the line L negative ? After scanning the two statement, I see that we can jump straight to . . . Statements 1 and 2 combined The COMBINED statements tell us that line l passes through quadrants III and IV. There are several lines that satisfy BOTH ...” June 10, 2019 Ian Stewart posted a reply to With # and & each representing different digits in the in the Problem Solving forum “We''re subtracting something between 10 and 99, and arriving at 667. So we must be subtracting from a number between 677 and 766, and the digit # could only be 6 or 7. But it can''t be 6, because 6&& - 66 will never be equal to 667 (it could be at most 633), so # must be 7. So we have this ...” June 10, 2019 Ian Stewart posted a reply to In the figure above, equilateral hexagon ABCDEF is in the Problem Solving forum “"Equilateral" means "equal sides". It is not a synonym for "regular", which means "equal sides *and* equal angles". Now, it''s true that an equilateral hexagon that you can inscribe in a circle must be regular, but the GMAT certainly would never expect a test ...” June 10, 2019 Ian Stewart posted a reply to In the figure above, square ABCD has an area of 25. in the Problem Solving forum “The diameter of the circle is the diagonal of the square, and the diagonal of the square is the hypotenuse of a 45-45-90 triangle with legs of length 5. Since sides in a 45-45-90 triangle are in a 1 to 1 to √2 ratio, the diameter of the circle is 5√2, so the radius is (5√2)/2, and the area is ...” June 10, 2019 Brent@GMATPrepNow posted a reply to If x ≠ −2, then 5x+10x+2=5x+10x+2 in the Problem Solving forum “Approach #2: We''re asked to evaluate (find the value of) the given expression. Since all of the answer choices are constants (just numbers), we know that the given expression must evaluate to be ONE of the answer choices FOR ALL VALUES OF X. So, let''s test a value of x Try x = 1 We get: ...” June 10, 2019 Brent@GMATPrepNow posted a reply to If x ≠ −2, then 5x+10x+2=5x+10x+2 in the Problem Solving forum “(5x+10)/(x+2) = (5(x+2))/(x+2) = 5 Answer: D Cheers, Brent” June 10, 2019 Ian Stewart posted a reply to Is Hector taller than Charley? (1) Hector is 5 feet in the Data Sufficiency forum “Statement 1 is useless. Statement 2 tells us Charley is 2 inches taller than Hector, so is sufficient.” June 10, 2019 Ian Stewart posted a reply to What will the ratio of birds to fish in a certain pet store in the Data Sufficiency forum “Statement 1 is clearly insufficient. For Statement 2, imagine we take out 4 fish. Then we know that adding back 4 fish and 7 birds doesn''t change our ratio. That can only happen if the ratio is exactly 4 to 7 (if it weren''t exactly 4 to 7, then adding 4 fish and 7 birds would move the ratio ...” June 10, 2019 Brent@GMATPrepNow posted a reply to For any integers a and b, min(a, b) and max(a, b) denote in the Data Sufficiency forum “Notice that min(3, 4) = 3 Notice that min(2, 2) = 2 Notice that min(1, 11) = 1 KEY PROPERTY: In general, we can say that, if min(a,b) = c, then we know that c ≤ a and c ≤ b Target question: What is max(y, 8)? Statement 1: min(9, x) = y This tells us that y ≤ 9 Let''s test ...” June 10, 2019 Ian Stewart posted a reply to Roger can chop down 4 trees in an hour. How long does it in the Data Sufficiency forum “Statement 1 tells us nothing about how quickly Vincent chops down trees. From Statement 2, it takes Vincent twice as long as Roger to chop down trees, so if Roger chops down four in 1 hour, Vincent chops down four in 2 hours. The answer is B. The wording here is too imprecise for the GMAT, ...” June 10, 2019 Ian Stewart posted a reply to x is a nonzero number. Is xy < 0? in the Data Sufficiency forum “Each Statement is clearly insufficient alone, since if y is nonzero, we''ll get different answers to the question by making x positive or negative. Using both statements, y must be zero, so xy = 0, and the answer to the question "is xy < 0?" is ''no'', so the answer is C.” June 10, 2019 Brent@GMATPrepNow posted a reply to From a group of 10 students, 7 girls and 3 boys, a teacher in the Problem Solving forum “Take the task of arranging students and break it into stages. Stage 1: Select two girls Since the order in which we select the women does not matter, we can use combinations. We can select 2 girls from 7 girls in 11C2 ways (21 ways) So, we can complete stage 1 in 21 ways If anyone is ...” June 10, 2019 Ian Stewart posted a reply to The ratio of red balls to green balls is 4:3. Three green in the Problem Solving forum “Adding 3 balls corresponds to changing one value in the ratio by 1, so our ''multiplier'' must be 3, and we must have 12 and 9 balls of each colour, so the answer is 12.” June 9, 2019 Ian Stewart posted a reply to In how many ways can 10 different paintings be distributed in the Problem Solving forum “Half the time, the first collector gets less than 5 paintings, so 0, 2 or 4 paintings. We can choose those paintings in 10C0 + 10C2 + 10C4 ways, or 1 + (10)(9)/2! + (10)(9)(8)(7)/4! = 1 + 45 + 210 = 256 ways. The other half of the time, or another 256 times, the first collector gets more than ...” June 9, 2019 Ian Stewart posted a reply to Is the product of 3p and 4 greater than 20? in the Data Sufficiency forum “We want to know if 12p > 20, or if p > 5/3, so if p > 1.6666.... Dividing by 5 on both sides in Statement 1, we learn p > 7/5, so p > 1.4, That doesn''t guarantee that p > 1.666..., so Statement 1 is not sufficient. Adding 5 to both sides of Statement 2, we find 3p > 6, ...” June 8, 2019 Ian Stewart posted a reply to A combined of 55 light bulbs are stored in two boxes; of the in the Data Sufficiency forum “We have 2 broken bulbs in the first box, so the rest of the 7 broken bulbs must be in the second box, and we have 5 broken bulbs in the second box. From Statement 1, we have 30 unbroken bulbs in the first box, and thus 32 bulbs in total in that box. The rest of the bulbs are in the other box, so ...” June 7, 2019 Brent@GMATPrepNow posted a reply to If 3 different integers are randomly selected from the integ in the Problem Solving forum “I specifically created this question to illustrate the importance of calculating the denominator first (when using counting techniques to solve a probability question) There are two reasons why you should calculate the denominator first: 1) The denominator is almost always easier to calculate ...” June 7, 2019 Brent@GMATPrepNow posted a reply to Puzzling probability question in the Problem Solving forum “P(selecting a sibling pair) = P(select a business student with a sibling AND select a law student who is that business student''s sibling) = P(select a business student with a sibling) x P(select a law student who is that business student''s sibling) = 30/500 x 1/800 = 30/400,000 = 3/40,000 = ...” June 6, 2019 Brent@GMATPrepNow posted a new topic called If 3 different integers are randomly selected from the integ in the Problem Solving forum “If 3 different integers are randomly selected from the integers from 1 to 12 inclusive, what is the probability that a triangle can be constructed so that its 3 sides are the lengths of the 3 selected numbers? A) 3/8 B) 7/18 C) 19/44 D) 39/88 E) 11/24 Answer: C Source: ...” June 6, 2019 Ian Stewart posted a reply to Find the area of the rectangle ABCD, if the length and bread in the Data Sufficiency forum “From Statement 1, 2L + 2W = 28, so L + W = 14. There are a few pairs of positive odd integers that add to 14, say 9 and 5 or 3 and 11, and these will give us different areas, so this is not sufficient. From Statement 2, the area of an L by L square is 80% bigger than the area of our L by W ...” June 6, 2019 Ian Stewart posted a reply to Hotel California in the Problem Solving forum “We have two groups of lights: lights that should be on, and lights that should be off. Overall, 80% of lights are on. Of lights that should be on, 90% are on (since 10% are off), and of lights that should be off, 40% are on. So we have a standard mixtures situation, which is always a weighted ...” June 5, 2019 Ian Stewart posted a reply to There are 1600 jelly beans divided between two jards, X and in the Problem Solving forum “The wording is awkward, but if we have x beans in jar X, and y beans in jar Y, the question tells us x = 3y - 100. Since x+y = 1600, substituting for ''x'' we get 3y - 100 + y = 1600 4y = 1700 y = 425 and the rest of beans, 1600-425 = 1175 beans, are in jar X.” June 5, 2019 Brent@GMATPrepNow posted a reply to GMAT Prep in the Problem Solving forum “In the 4 months leading up to March, the company PRODUCES 4x rakes (4 months at x/month = 4x) On March 1, x/2 rakes are SHIPPED, leaving 3.5x rakes for which the company must pay storage fees. On April 1, x/2 rakes are SHIPPED, leaving 3x rakes for which the company must pay storage fees. ...” June 5, 2019 Brent@GMATPrepNow posted a reply to VIC question -- picking numbers in the Problem Solving forum “Originally, T people were to pay total cost of x dollars. So, each person pays x/T each. After S people drop out, there are T-S people to pay total cost of x dollars. So, each person pays x/(T-S) each. The additional amount that each must pay = New cost per person - original cost per ...” June 5, 2019 Brent@GMATPrepNow posted a reply to Hotel California in the Problem Solving forum “One option is to use the Double Matrix method. Here, we have a population of lightbulbs, and the two characteristics of each bulb are: - incandescent or fluorescent - on or off Since the questions asks us to find a certain PERCENT, let''s say that there are 100 bulbs altogether. So, we ...” June 5, 2019 Brent@GMATPrepNow posted a reply to Of the 12 temporary employees in a certain company, 4 will in the Problem Solving forum “Take the task of selecting the employees and break it into stages. Stage 1: Select the 3 women The order in which we select the women does not matter, so we can use combinations. We can select 3 women from 5 women in 5C3 ways (= 10 ways) Aside: If anyone is interested, here''s video on ...” June 5, 2019 Brent@GMATPrepNow posted a reply to If k is 96% greater than its reciprocal, which of the follow in the Problem Solving forum “k is 96% greater than its reciprocal The reciprocal of k is 1/k So, we can write: k = (1/k) + (96% of 1/k) In other words: k = (1/k) + 0.96(1/k) Simplify: k = 1.96(1/k) Simplify: k = 1.96/k Multiply both sides by k to get: k² = 1.96 Solve: k = 1.4 of k = -1.4 Rewrite as follows: k = 7/5 of ...” June 5, 2019 Brent@GMATPrepNow posted a new topic called If k is 96% greater than its reciprocal, which of the follow in the Problem Solving forum “If k is 96% greater than its reciprocal, which of the following is an integer? A) 3k/7 B) 3k/5 C) 5k/7 D) 5k/3 E) 7k/5 Source: www.gmatprepnow.com Difficulty level: 600-650 Answer: C” June 4, 2019 Ian Stewart posted a reply to Pat has a pocket full of quarters, dimes, and nickels. He in the Problem Solving forum “He has 6 coins, and he has two types of coins, including nickels. If he has only nickels and dimes, he could have at most 60 cents. But he has 70 cents, so he must have nickels and quarters. Since he must have at least 1 quarter, and can''t have 3 or more (then he''d have more than 70 cents), ...” June 4, 2019 Ian Stewart posted a reply to The length of one of the sides of an acute angled triangle in the Problem Solving forum “Take the side of length 15 as the base. If we draw a height from that base, then since the area is 90, that height must be 12. When we draw that height, we divide the triangle into two smaller right triangles, each of which has, as its hypotenuse, one of the other two sides of the big triangle. ...” June 4, 2019 Brent@GMATPrepNow posted a reply to Which of the following sets contains only factors of 45? in the Problem Solving forum “Scan the answer choices....(C and D)..... 13 is NOT a factor of 45. ELIMINATE C By the process of elimination, the correct answer is D Cheers, Brent Scan the two remaining answer choices.... 7 is NOT a factor of 45. ELIMINATE A, B and E” June 3, 2019 Brent@GMATPrepNow posted a reply to A company has two types of machines, type R and type S. in the Problem Solving forum “Here''s another approach . . . When it comes to questions where we must complete an entire job, I often (not always) like to know what can be accomplished in 1 unit of time (in this case, 1 hour). Machine R can complete 1/36 of the job in 1 hour. Machine S can complete 1/18 of the job in 1 ...” June 3, 2019 Brent@GMATPrepNow posted a reply to A company has two types of machines, type R and type S. in the Problem Solving forum “One approach is to assign a "nice" value to the job. Say, the job is to make 36 widgets. R does a certain job in 36 hours This means that machine R''s rate is 1 widget/hour S does the job in 18 hours This means that machine S''s rate is 2 widgets/hour So, their combined rate ...” June 3, 2019 Ian Stewart posted a reply to Last year Isabella took 7 math tests and received 7 differen in the GMAT Math forum “Notice a few things here: - If her average after n tests is always an integer, then after n tests, the sum of her scores will always be divisible by n. - So after six tests, the sum of her score is a multiple of 6. Let''s call that sum, after six tests, "S" - If her scores are between ...” June 3, 2019 Ian Stewart posted a reply to GMAC Official Practice Test #5 in the GMAT Math forum “You should never assume that a sequence has any particular ''structure'' unless the question explicitly tells you it does. A sequence is just a list of numbers in order, and can have any structure at all. We can''t assume we have, say, consecutive integers here. We want to know what n is, or in ...” June 3, 2019 Ian Stewart posted a reply to Help with a problem about transformations in the GMAT Math forum “This is definitely not a GMAT question (so if you have future questions, direct them to a more relevant forum), but in general, geometric transformations cannot always be done in any order, so you should perform them in the order in which they''re listed: D then T.” June 3, 2019 Ian Stewart posted a reply to Practice Quant problem in the GMAT Math forum “2^a / 2^b is equal to 2^(a-b). So 2^(x+y)^2 / 2^(x-y)^2 is equal to 2^[ (x+y)^2 - (x-y)^2 ] We could expand both (x+y)^2 and (x-y)^2 and subtract, but it''s faster just to use the difference of squares factorization immediately, since we''re subtracting one square from another in the exponent. ...” June 3, 2019 Brent@GMATPrepNow posted a reply to If k^2 = m^2, which of the following must be true? in the Problem Solving forum “The question asks us what MUST be true. So, if we can find a case where a statement is not true, we can eliminate that answer choice. So, for example, one solution to the equation (k² = m²) is k = 1 and m = 1 Now let''s check the answer choices. A. k = m. Test: 1 = 1. Works. Keep A. B. ...” June 3, 2019 Brent@GMATPrepNow posted a reply to A company that ships boxes to a total of 12 distribution in the Problem Solving forum “We need to be able to create AT LEAST 12 codes (to represent the 12 countries). Let''s test the options. Can we get 12 or more color codes with 4 colors? Let''s see . . . 1-color codes = 4 (since there are 4 colors) 2-color codes = We need to choose 2 colors from 4. This can be ...” June 2, 2019 Ian Stewart posted a reply to Rectangle $$ABCD$$ is inscribed in circle $$P$$. What is the in the Data Sufficiency forum “That''s a very confusing diagram, because the letter ''P'', which the stem suggests is the name of the circle, appears to be used in the diagram to label the center of the circle. The same letter cannot be used for both of those things, and if I read the question alone before reading the first half ...” June 2, 2019 Ian Stewart posted a reply to What is the positive integer n? in the Data Sufficiency forum “Numbers that satisfy Statement 1 are known as "perfect numbers" in math. You certainly don''t need to know anything about "perfect numbers" for the GMAT, but I''d imagine if you weren''t familiar with them, this question could be time consuming, since using both Statements, there ...” June 2, 2019 Ian Stewart posted a reply to If j and k are positive integers, is 6 a factor of j? in the Data Sufficiency forum “Using both Statements, 6 clearly could be a factor of j, but it might be true that j = 2 and k = 3, say, or j = 3 and k =2, and that 6 is not a factor of j. So the answer is E.” June 2, 2019 Ian Stewart posted a reply to If $$a, b$$, and $$c$$ are integers, what is the value of in the Data Sufficiency forum “Just because this is so important in so many questions: if ac = 5, and a and c are integers, there are four possibilities, not two: a and c can be 5 and 1, in either order, or they can be -5 and -1, in either order. Of course, when we combine the two statements, we can discard the negative ...” June 1, 2019 Ian Stewart posted a reply to In the finite sequence of positive integers $$k_1, k_2,$$ in the Data Sufficiency forum “Since we add two consecutive terms to find the next term, once we know two consecutive terms, it is easy to work out every subsequent term in the sequence (and every earlier term, though we don''t need to do that here). Using Statement 1, we know the 4th and 5th terms are 11 and 18, so the next is ...” June 1, 2019 Ian Stewart posted a reply to Is the slope of Line 1 positive? in the Data Sufficiency forum “Each Statement is clearly insufficient alone. Using both, if line two has a slope of 1, then line two would form a 45 degree angle where it meets any horizontal line. If lines one and two meet at a 40 degree angle, then line one either creates a 5 degree or an 85 degree angle with any horizontal ...” June 1, 2019 Ian Stewart posted a reply to Of all houses on Kermit Lane, 20 have front porches, 20 have in the Data Sufficiency forum “If every house has a back yard, and, as Statement 1 tells us, 40 houses have a back yard, there are 40 houses in total, so Statement 1 is sufficient. From Statement 2, if a house has a front porch, it does not have a front yard. So if a house has a front yard, it cannot have a front porch. So we ...” June 1, 2019 Ian Stewart posted a reply to Robin drove from Townville to Villageton. Upon arriving in in the Data Sufficiency forum “The distance each way is the same. If we call it ''d'', then since time = distance/speed, Robin''s time for the first part of the trip was d/40 and for the return trip was d/60. So her total time was d/40 + d/60 = 5d/120 = d/24. Her total distance was 2d, so her average speed was (total ...” June 1, 2019 Brent@GMATPrepNow posted a reply to What is the total cost to make 7 long distance telephone in the Data Sufficiency forum “When we SCAN the statements, we see the key phrase: at least This allows us to jump straight to... Statements 1 and 2 combined There are infinitely many scenarios that satisfy BOTH statements. Here are two: Case a: Each call was 2 minutes long, for a total of 14 minutes. At$0.32 per ...”
June 1, 2019
Ian Stewart posted a reply to Peter went to the store to buy paint. Small cans cost $30 in the Data Sufficiency forum “Using Statement 1 alone, he can''t have bought zero large cans, because 220 is not divisible by 30. He can''t have bought one large can, because 140 is not divisible by 30. And he can''t have bought 3+ large cans, because then he would have spent more than$220. So he must have bought two large ...”
May 31, 2019
Ian Stewart posted a reply to A list contains twenty integers, not necessarily distinct. in the Data Sufficiency forum
“Using Statement 1 alone, we might have some scattered list of 20 distinct integers, say 10, 20, 30, 40, ...., 200. If we add one to any individual value in this list, we still have 20 distinct integers. So we can have a list with no consecutive integers. But our list could also be: 2, 2, 2, 2, ...”
May 31, 2019
Ian Stewart posted a reply to Rose grows two kinds of orchid plants, Phalaenopsises and in the Data Sufficiency forum
“Statement 1 only guarantees we have at least 14 of the P flowers, and Statement 2 only guarantees we have an even number of the G flowers (since we must be able to multiply that number by 1.5 = 3/2 and get a whole number answer). But there remain many possible numbers of P flowers using either ...”
May 31, 2019
Ian Stewart posted a reply to If N different positive integers are added and the sum is in the Data Sufficiency forum
“In the notation used in the question, S/N = sum/number of terms = the average of the list. So the question is just asking "is the average of the N numbers an integer?" Statement 1 tells us we have an odd number of integers, which is not sufficient, since we could have the list 1, 2, 3, ...”
May 31, 2019
Brent@GMATPrepNow posted a reply to Of the 60 animals on a certain farm, $$\frac{2}{3}$$ are in the Data Sufficiency forum
“Target question: How many of the animals are cows? Given: Of the 60 animals in a certain farm, 2/3 are either pigs or cows Let P = # of pigs Let C = # of cows 2/3 of 60 = 40, so we can say that P + C = 40 Statement 1: The farm has MORE THAN twice as many cows as it has pigs. In other ...”
May 31, 2019
Ian Stewart posted a reply to A certain diet program calls for eating daily calories from in the Data Sufficiency forum
“It''s a potentially confusing question, because the 40:30:30 ratio in the stem is the ratio of the "daily calories" from each source, while the numbers in Statement 1 are measured in grams, not in calories. So at first glance, looking at Statement 1, it might seem Bill followed the diet ...”
May 30, 2019
Ian Stewart posted a reply to If n is a positive integer and r is the remainder when 4 + 7 in the Data Sufficiency forum
“If, from Statement 1, n+1 is divisible by 3, then for some integer q, we know n+1 = 3q, and n = 3q - 1. Substituting "3q-1" for "n" in the expression 4 + 7n, we have 4 + 7n = 4 + 7(3q - 1) = 4 + 21q - 7 = 21q - 3 = 3(7q - 1) and since we can factor out a 3, this ...”
May 30, 2019
Ian Stewart posted a reply to A certain packing box contains books between 50 to 60. How in the Data Sufficiency forum
“There are at least three grammatical errors in the stem itself, so this might be a good SC question. I assume the question is saying we have between 50 and 60 books. Statement 1 says when we divide that number by 3, the remainder is 1. So we could have 52, 55 or 58 books (any number between 50 and ...”
May 30, 2019
Brent@GMATPrepNow posted a reply to A computer programmer needs to print 148 documents. The in the Problem Solving forum
“We can also answer this question using a step-by-step approach based on number sense. IMPORTANT: The word approximately typically suggests that we can be somewhat aggressive with our estimation There are 148 documents and the documents have an average length of 10 pages So, the TOTAL number ...”
May 29, 2019
Ian Stewart posted a reply to How many of the 60 balls in the basket are green? in the Data Sufficiency forum
“From Statement 1, 1/12 of the 60 balls are green, so 5 balls are green. So Statement 1 is sufficient. Statement 2 only tells us about 12 of the balls, so is not sufficient.”
May 28, 2019
Brent@GMATPrepNow posted a reply to x + 2y + 3z = 4 and 5x + 4y + 3z = 8. What is the value of x in the Problem Solving forum
“GIVEN: x + 2y + 3z = 4 5x + 4y + 3z = 8 ADD the two equations to get: 6x + 6y + 6z = 12 Factor: 6(x + y + z) = 12 Divide both sides by 6 to get: x + y + z = 2 Answer: B Cheers, Brent”
May 28, 2019
Brent@GMATPrepNow posted a reply to Two different primes may be said to"rhyme" around in the Problem Solving forum
“If two numbers are rhyming primes, then the integer the rhyme around will be the AVERAGE of the two primes. For example, 3 and 7 rhyme around 5. Notice that the AVERAGE of 3 and 7 is 5. Likewise, 5 and 23 rhyme around 14, and the AVERAGE of 5 and 23 is 14. Now onto the solution... List ...”
May 28, 2019
Brent@GMATPrepNow posted a reply to A certain fruit stand sold apples for $0.70 each and bananas in the Problem Solving forum “Here''s an approach where we test the POSSIBLE SCENARIOS. FACT #1: (total cost of apples) + (total cost of bananas) = 630 CENTS FACT #2: total cost of bananas is DIVISIBLE by 50, since each banana costs 50 cents. Now let''s start testing POSSIBLE scenarios. Customer buys 1 apple. 1 ...” May 28, 2019 Brent@GMATPrepNow posted a reply to From a group of 5 managers (Joo, Kendra, Lee, Marnie, and in the Problem Solving forum “Our goal is to find P(M and N both selected) There are two ways to approach this. Method #1: P(M and N both selected) = P(one of them is selected 1st AND the other selected 2nd) = P(one of them is selected 1st) x P(the other selected 2nd) = (2/5)(1/4) = 1/10 = 0.1 Aside: P(one of them ...” May 28, 2019 Ian Stewart posted a reply to In an endurance race, a car drove the whole race at a in the Data Sufficiency forum “The car is driving 180 miles per hour. If it drove more than 2 hours, all we know is that it drove more than 360 miles, so Statement 1 is not sufficient. If it drove less than 2.75 = 11/4 hours, then it drove less than (11/4)(180) = (11/2)(90) = 11*45 = 495 miles, so the total distance was certainly ...” May 27, 2019 Brent@GMATPrepNow posted a reply to Car X is 40 miles west of Car Y. Both cars are traveling in the Problem Solving forum “Let''s let Car X''s original position be the initial starting point. So, when Car X is at the initial starting point, Car Y has already traveled 40 miles. My word equation involves the conditions when Car X catches up to Car Y. At that point, we can say: Car X''s TOTAL distance traveled = ...” May 27, 2019 Brent@GMATPrepNow posted a reply to Gita is 12 years older than Harvey. In 4 years, Gita will be in the Problem Solving forum “Gita is 12 years older than Harvey. Let x = Harvey''s PRESENT age Let x + 12 = Gita''s PRESENT age In 4 years, . . . . x + 4 = Harvey''s age IN FOUR YEARS (x + 12) + 4 = Gita''s age IN FOUR YEARS . . . Gita will be twice as old as Harvey. So: (Gita''s age IN 4 YEARS) = 2(Harvey''s ...” May 26, 2019 Ian Stewart posted a reply to What is the units digit of positive integer $$p$$? in the Data Sufficiency forum “When we divide an integer by 10, its units digit is the remainder. So Statement 1 is immediately sufficient - the units digit is 8. The units digit of a number has nothing to do with the remainder you get when you divide by 11, so Statement 2 is useless (e.g. our number can be 19 or 30, which ...” May 25, 2019 Ian Stewart posted a reply to A school has $$a$$ students and $$b$$ teachers. if $$a<15 in the Data Sufficiency forum “From Statement 1, the number of students, a, is divisible by every number in that list, so it is divisible by the LCM of those numbers. If we just identify the prime divisors in that list, and their relevant exponents, we have a 2, a 5, and 3^2, so the LCM is 90. So the number of students is a ...” May 25, 2019 Ian Stewart posted a reply to In a certain alphabet, 12 letters contain a dot and a in the Problem Solving forum “Strange question - the question tells us about 36 of the letters, and there are 40 letters in total. So there are 4 letters left, and they must be in the "dot and no line" category.” May 24, 2019 Ian Stewart posted a reply to Gordon buys 5 dolls for his 5 nieces. The gifts include two in the Problem Solving forum “Any 5-letter word we make using the letters S, S, E, G, T corresponds to one way to distribute the dolls. So the word SEGTS for example corresponds to giving the S doll to the oldest child, the E to the next oldest, and so on. If the letters were different, there would be 5! words we could make ...” May 24, 2019 Ian Stewart posted a reply to A husband and wife can complete a certain task in 1 and 2 in the Data Sufficiency forum “Using whatever rates method one prefers, you can just find how long the husband and wife take, how long the children take, and take the ratio of those two times. I''d get the same time for the husband and wife: h does 2 tasks in 2 hours w does 1 task in 2 hours h+w do 3 tasks in 2 hours so 1 ...” May 24, 2019 Ian Stewart posted a reply to When the positive integer \(n$$ is divided by $$25$$, the in the Data Sufficiency forum “Using Statement 1, n can be 13, 38, 63, and 88. Using Statement 2 alone, we''ll have an infinite number of values of n, separated by 100, the LCM of 25 and 20. Using both Statements, n must be 63, and the answer is C.” May 24, 2019 Brent@GMATPrepNow posted a reply to Al and Ben are drivers for SD Trucking Company. One snowy da in the Problem Solving forum “Let''s start with a "word equation" (Ben''s travel distance) + (Al''s travel distance) = 240 miles Let t = Al''s travel time (in hours) So, t + 3= Ben''s travel time (since Ben spent 3 more hours driving) Distance = (rate)(time) So, our word equation becomes... (20)(t + 3) = ...” May 24, 2019 Brent@GMATPrepNow posted a reply to What is x in the diagram below? in the Problem Solving forum “The important thing to recognize here is that there are two SIMILAR TRIANGLES hiding in this diagram. http://s24.postimg.cc/50bvp89dt/sim_tri.jpg Notice that these two triangles share both a 90-degree angle AND the angle I''ve denoted with a purple dot. Since the 3 angles in each triangle must ...” May 24, 2019 Brent@GMATPrepNow posted a reply to j, k, m, x, y and z are positive integers. When j is divided in the Problem Solving forum “Useful remainder property: When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0 When j is divided by k, the remainder is m The above property ...” May 23, 2019 Ian Stewart posted a reply to What is the remainder when $$a$$ is divided by 4? in the Data Sufficiency forum “You could just see what happens with 1 and 3 here (the only two different odd remainders when you divide by 4), to see that Statement 1 is sufficient. Or you could prove it algebraically: we can write an odd number as 2m + 1, so if a is the square of an odd integer, a = (2m + 1)^2 = 4m^2 + 4m + 1, ...” May 23, 2019 Ian Stewart posted a reply to Nancy, a car dealer, put 4 cars on sale. All cars on sale in the Data Sufficiency forum “Is there a typo in the question? If Nancy only put 4 cars on sale, then it''s impossible for "30% of the cars with automatic gear are hybrids" to be true, because then there''s no way for the number of automatic hybrids to be an integer (unless there are zero of them, but then it makes no ...” May 23, 2019 Brent@GMATPrepNow posted a reply to Challenge question: Is positive integer p even? in the Data Sufficiency forum “------ASIDE--------------------- Here''s a useful rule: If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors. Example: 14000 = (2^4)(5^3)(7^1) So, the number of positive divisors ...” May 22, 2019 Brent@GMATPrepNow posted a new topic called j, k, m, x, y and z are positive integers. When j is divided in the Problem Solving forum “j, k, m, x, y and z are positive integers. When j is divided by k, the remainder is m. When x is divided by y, the remainder is z. If ky = 75, which of the following CANNOT be the value of mz? i) 49 ii) 50 iii) 56 A) iii only B) i and ii C) i and iii D) ii and iii E) i, ii and iii ...” May 22, 2019 Ian Stewart posted a reply to If n is an integer greater than 6, which of the following in the Problem Solving forum “Among any three consecutive integers, you always have exactly one multiple of 3. So if one of our answers here was something like (n-1)(n)(n+1), the product of three consecutive integers, it would certainly be divisible by 3. We don''t have something quite that easy, but if you look at answer A: ...” May 22, 2019 Ian Stewart posted a reply to A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in the Problem Solving forum “The diagrams are confusing, because they aren''t to scale -- in the second diagram, AF is suddenly much longer than in the first, even though the length AF hasn''t changed. Regardless, after folding the paper, the angle at E remains a 90 degree angle, the length of DE is still 12, and the lengths ...” May 22, 2019 Ian Stewart posted a reply to Mr. Smith purchases books from the bargain bin. He buys only in the Data Sufficiency forum “Using both Statements, he might have bought one$7 book, eight $2 books, and one$1 book, or he might have bought two $7 books, two$2 books and six $1 books, so the answer is E.” May 22, 2019 Brent@GMATPrepNow posted a reply to If n is an integer greater than 6, which of the following in the Problem Solving forum “One approach is to test values If n = 7, we get: (A) 7(7 + 1)(7 – 4) = (7)(8)(3). Definitely divisible by 3. KEEP (B) 7(7 + 2)(7 – 1) = (7)(9)(6). Definitely divisible by 3. KEEP (C) 7(7 + 3)(7 – 5) = (7)(10)(4). NOT divisible by 3. ELIMINATE. (D) 7(7 + 4)(7 – 2) = (7)(11)(5). NOT ...” May 22, 2019 Ian Stewart posted a reply to Each of three students is given fifteen tokens to spend at a in the Data Sufficiency forum “This is not a good question, because what you would naturally and correctly assume in any other GMAT question turns out not to be true here. If you saw a question like this, for example: Amir goes to a store with$11 and buys at least one chair. How many chairs did he buy? 1. Chairs cost $10 ...” May 21, 2019 Ian Stewart posted a reply to In the morning, Chris drives from Toronto to Oakville and in in the Data Sufficiency forum “Statement 1 is obviously not sufficient. For Statement 2, it takes just as long to drive d miles at 50 miles per hour as it does to drive 2d miles at 100 miles per hour. So if he drove half the distance at exactly 50 mph, he''d need to travel the other half instantaneously, in 0 seconds, to have ...” May 21, 2019 Brent@GMATPrepNow posted a reply to Question from mba.com mock test in the Problem Solving forum “The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. So, 120 = 120 * 2^10)] + 60 Divide both sides by 60: 2 = 2 * 2^ f = 120 * 2^ The temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit? f = 120 * 2^30)] + ...” May 21, 2019 Brent@GMATPrepNow posted a reply to OG #132 in the Problem Solving forum “We need to be able to create AT LEAST 12 codes (to represent the 12 countries). Let''s test the options. Can we get 12 or more color codes with 4 colors? Let''s see . . . 1-color codes = 4 (since there are 4 colors) 2-color codes = We need to choose 2 colors from 4. This can be ...” May 21, 2019 Brent@GMATPrepNow posted a reply to ps 500 test27 #16 in the Problem Solving forum “One approach: Salary Mary''s NET salary was x - y dollars (because Mary gave John y dollars) John''s NET salary was x + y dollars Hours worked Mary worked 8 hours John worked 10 hours In the end, John and Mary received the SAME hourly wage. So, John''s hourly wage = Mary''s ...” May 21, 2019 Brent@GMATPrepNow posted a reply to problem to solve in the Problem Solving forum “What we really have here is an algebra question requiring us to combine like terms. First, notice that K + K = 2K Using the same logic, 2^5 + 2^5 = 2(2^5) = (2^1)(2^5) = 2^6 Similarly, notice that M + M + M = 3M Using the same logic, 3^5 + 3^5 + 3^5 = 3(3^5) = (3^1)(3^5) = 3^6 So, 2^5 + ...” May 21, 2019 Brent@GMATPrepNow posted a reply to test 39 #13 in the Problem Solving forum “Here''s a related question to practice with: https://www.beatthegmat.com/intensity-scale-readings-t273997.html Cheers, Brent” May 21, 2019 Brent@GMATPrepNow posted a reply to test 38 #15 in the Problem Solving forum “red = 7 yellow = 5 green = 3 blue = 2 147,000 = (2)(2)(2)(3)(5)(5)(5)(7)(7) So, there are 3 blue beads, 1 green bead, 3 yellow beads and 2 red beads. Cheers, Brent” May 21, 2019 Brent@GMATPrepNow posted a reply to test35 # 15 in the Problem Solving forum “We want to determine how many integers end in 13 For example, 324713, 324813, 324913, 325013, . . . etc. Recognize that, for every 100 consecutive integers, only 1 will end in 13. There are 133,900 integers between 324,700 and 458,600 (since 458,600 - 324,700 = 133,900) Of those 133,900 ...” May 21, 2019 Brent@GMATPrepNow posted a reply to Help on PS problem- GMATprep in the Problem Solving forum “Let''s test the values using x = 0 So, we can reword the question as, For which of the following functions is f(0)=f(1-0) In other words, we''re looking for a function such that f(0) = f(1) A) f(x)=1-x f(0)=1-0 = 1 f(1)=1-1 = 0 Since f(0) doesn''t equal f(1), eliminate A B) f(x) = 1 - ...” May 21, 2019 Brent@GMATPrepNow posted a reply to Probability in the Problem Solving forum “We want: a) # of teams that include both John and Peter b) total # of 5-person teams possible a) # of teams that include both John and Peter Put John and Peter on the team (this can be accomplished in 1 way) Select the remaining 3 team-members from the remaining 7 players (this can be ...” May 21, 2019 Brent@GMATPrepNow posted a reply to Mr. Jones spends$ 25 on movie tickets for a party of adults in the Data Sufficiency forum
“ Given: Mr. Jones spends $25 on movie tickets for a party of adults and children. Target question: How many children''s tickets did he buy? Statement 1: Adult movie tickets cost$3 each and children''s tickets cost $2 each. There are several scenarios that satisfy statement 1. Here are ...” May 21, 2019 Brent@GMATPrepNow posted a reply to A collection of 16 coins, each with a face value of either in the Problem Solving forum “Let D = the NUMBER of 10-cent coins Let Q = the NUMBER of 25-cent coins Notice that the VALUE of Q 25-cent coins = ($0.25)Q For example, the VALUE of six 25-cent coins = ($0.25)6 =$1.50 And the VALUE of ten 25-cent coins = ($0.25)10 =$2.50 etc Likewise, the VALUE of D 10-cent coins = ...”
May 21, 2019
Brent@GMATPrepNow posted a new topic called Challenge question: Is positive integer p even? in the Data Sufficiency forum
“Is positive integer p even? (1) 4p has twice as many positive divisors as p has (2) 8p has 3 positive divisors more than p has Answer: A Source: www.gmatprepnow.com Difficulty level: 700+”
May 20, 2019
Ian Stewart posted a reply to Store S sold a total of 90 copies of a certain book during in the Data Sufficiency forum
“Using Statement 1 alone, Friday''s sales might have been greater than 11 (from Sunday through Saturday the sales might have been 1,2,3,4,8,22,50, say) or might not have been (the sales might have been 1,2,3,4,8,10,62, say). Using Statement 2 alone, we know that in the six days besides Saturday, ...”
May 20, 2019
Ian Stewart posted a reply to n is a positive integer, and k is the product of all integer in the Problem Solving forum
“This is essentially a direct copy of an official question, with one number changed: https://gmatclub.com/forum/if-n-is-a-positive-integer-and-the-product-of-all-integers-90855.html though you might notice how much more elegant the wording of the official problem is (there''s no need to ...”
May 19, 2019
Ian Stewart posted a reply to The value of the variable E is determined by adding the reci in the Problem Solving forum
“This question makes no sense - as defined, E represents a single numerical value, so E is not a "variable". And if E has a single numerical value, so does its reciprocal, so it makes no sense to ask what "can be a possible value of the reciprocal of E". An answer is either equal ...”
May 19, 2019
Ian Stewart posted a reply to In the figure above, equilateral triangle ABC is inscribed in the Problem Solving forum
“By symmetry, since the triangle is equilateral, the length of each circular arc between two adjacent corners of the triangle must make up 1/3 of the entire circumference of the circle. Since the arc ABC is two of those arcs put together, 24 is 2/3 of the circumference, and 36 is the entire ...”
May 19, 2019
Ian Stewart posted a reply to A number of individuals volunteer to walk dogs at a certain in the Data Sufficiency forum
“If we have d dogs, and v volunteers, we just want to know if d is divisible by v. Statement 1 is not sufficient, because we could have 45 dogs, and 7 volunteers, and the answer is ''no'', or 45 dogs and 9 volunteers, and the answer is ''yes''. Statement 2 is not sufficient because we could ...”
May 19, 2019
Ian Stewart posted a reply to Do at least 60 percent of the students in Pat’s class walk in the Data Sufficiency forum
“Statement 1 is not sufficient - we''d need to know something about male students. Statement 2 tells us the ratio of walkers to not-walkers is 2 to 1, so 2/3 of students walk, and since we now know exactly what percentage walk to school, we can answer the question and the answer is B.”
May 19, 2019
Ian Stewart posted a reply to What is the value of y? in the Data Sufficiency forum
“Each statement is clearly insufficient alone. Using both, from Statement 1 we can factor since we have a difference of squares: (x + y)(x - y) = 5 From Statement 2, x+y and x-y are both integers, and if x and y are each positive integers, x+y is greater than 1. Since x+y is also clearly a ...”
May 18, 2019
Ian Stewart posted a reply to In the rectangular coordinate system shown above, does the in the Data Sufficiency forum
“If a line has a negative slope, that line is falling as it moves to the right. So it is rising as it moves to the left, and eventually it will rise high enough to be in quadrant II. So Statement 1 is sufficient. Statement 2 tells us one point on the line but nothing about how the line rises or ...”
May 18, 2019
Ian Stewart posted a reply to An art gallery has only paintings and sculptures. Currently, in the Problem Solving forum
“If 1/3 of the non-displayed things are paintings, 2/3 of them are sculptures. So if 200 are sculptures, we have 300 non-displayed things in total. Since 1/3 of things are on display, the ratio of displayed to not is 1 to 2, so we have 150 things on display, and 150+300 = 450 things in total.”
May 18, 2019
Brent@GMATPrepNow posted a reply to In the figure above, if A, B, and C are the areas, respectiv in the Data Sufficiency forum
“Key concept: We''re told that the area of the BLUE circle = the area of the RED circle https://i.imgur.com/AZaIFeU.png This means we can say: A + B = B + C Now onto the question..... Target question: What is the value of B + C ? Statement 1: A + 2B + C = 24 Rewrite this as: (A + B) ...”
May 17, 2019
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Data Sufficiency lesson #7: - The Table Method Video : https://www.youtube.com/watch?v=lYfTiRIG_k4 Cheers, Brent”
May 16, 2019
Ian Stewart posted a reply to The age of a group of people follows a distribution, which in the Problem Solving forum
“95% of the distribution is within two standard deviations of the mean, so 95% of the distribution lies between A - 2SD and A + 2SD. So all of those values are less than A+2SD. The other 5% of the distribution is more than two standard deviations from the mean. Since the distribution is symmetric, ...”
May 15, 2019
Brent@GMATPrepNow posted a reply to If Mary always takes the same route to work, how long did it in the Data Sufficiency forum
“Target question: How long did it take Mary to get to work on Friday? Statement 1: It took Mary 20 minutes to get to work on Thursday. Clearly, we cannot use this information to answer the target question with certainty. Statement 1 is NOT SUFFICIENT Statement 2: Mary''s average speed ...”
May 15, 2019
Ian Stewart posted a reply to The median of n consecutive odd integers is 30. If the fifth in the Problem Solving forum
“This question makes no sense - they are misusing terminology. If you talk about a list of "consecutive" odd integers, say, then the second thing in the list follows the first thing, in sequence - the second term must be larger than the first term. But here they intend the sequence of ...”
May 14, 2019
Ian Stewart posted a reply to In the xy-coordinate system, rectangle ABCD is inscribed in the Problem Solving forum
“If a circle has the equation x^2 + y^2 = r^2, then it is a circle centered at the origin, with radius r. So our circle here is a circle of radius 5, centered at (0, 0). So, if a diagonal of the inscribed rectangle lies on the x-axis, the coordinates of its endpoints must be (-5, 0) and (5, 0). We ...”
May 14, 2019
Brent@GMATPrepNow posted a reply to x-4=z y-x=8 8-z=t For the system of equations given, what in the Data Sufficiency forum
“Target question: What is the value of z? Statement 1: x = 7 Scanning the three given equations, we see that equation i is all we need to determine the value of z i) x - 4 = z Replace x with 7 to get: 7 - 4 = z So, z = 3 Since we can answer the target question with certainty, statement 1 ...”
May 14, 2019
Brent@GMATPrepNow posted a reply to In triangle JKL shown above, what is the length of segment in the Data Sufficiency forum
“KEY CONCEPT: 30-60-90 triangles are known as special right triangles, and we know quite a bit about this kind of triangle Target question: What is the length of segment JL ? Statement 1: JK = 10 https://i.imgur.com/sKEFT1R.png Compare ΔJKL with the BASE 30-60-90 triangle. Their ...”
May 13, 2019
Ian Stewart posted a reply to 50 students of a certain class took a test. How many of them in the Data Sufficiency forum
“Using both Statements, it''s possible all 50 students got a score of ''82'', or it''s possible that 25 of them got ''81'' and 25 of them got ''83'', among other possibilities. So the answer is E.”
May 13, 2019
Ian Stewart posted a reply to A jar contains exactly 100 marbles; each marble contains in the Data Sufficiency forum
“If we have 100 marbles, and each marble is made up of 2 colours, we have 200 colours in total. Using either Statement alone, we haven''t accounted for very many of the colours, so we could have quite a few half-blue marbles or we could have none, and our probability of picking half-blue marbles ...”
May 13, 2019
Ian Stewart posted a reply to Cotto Toy Store sells Product X and Product Y at two in the Data Sufficiency forum
“Neither Statement is sufficient alone, because if the initial price of X is enormously larger than the initial price of Y, using either Statement alone, the discounted price of X will remain larger, and similarly if the initial price of Y is vastly larger than that of X, so will be Y''s discounted ...”
May 13, 2019
Ian Stewart posted a reply to Maria can either buy a basket that contains P pounds of in the Data Sufficiency forum
“The basket costs $16.50, and the p pounds of apples cost$0.95p. We want to know which of those figures is larger. Statement 1 is irrelevant, since we don''t care how many apples are in the basket -- we already know the basket costs $16.50. What we need is information about the p pounds of ...” May 13, 2019 Brent@GMATPrepNow posted a reply to A line that passes through (–1, –4) and (3, k) has a slo in the Problem Solving forum “Slope of line between the points (x1, y1) and (x2, y2) = (y2 - y1)/(x2 - x1) So, we can write: k = [k - (-4)]/[3 - (-1)] Simplify: (k + 4)/4 = k Multiply both sides by 4 to get: k + 4 = 4k Subtract k from both sides to get: 4 = 3k Divide both sides by 3 to get: 4/3 = k Answer: C Cheers, ...” May 13, 2019 Ian Stewart posted a reply to What percent of the children in the class are holding a in the Data Sufficiency forum “The answer is instantly C or E, since we''ll need to know about both boys and girls. Using both statements, we have a standard weighted average situation. If k% of boys and m% of girls are holding a popsicle, then somewhere between k% and m% of the group as a whole is holding a popsicle, where the ...” May 13, 2019 Ian Stewart posted a reply to S is a set of points in the plane. How many distinct in the Data Sufficiency forum “We clearly need to know how many points we have, since if we have, say, only 2 points, we can''t draw any triangles, but if we have many points that aren''t all in a line, we can draw at least one triangle. So Statement 1 is indispensable. But knowing we have exactly 5 points is not sufficient, ...” May 13, 2019 Ian Stewart posted a reply to In triangle JKL shown above, what is the length of segment in the Data Sufficiency forum “In general, if you know all three angles in a triangle (which we do here, since from two angles we can find the third using the fact that a triangle''s angles sum to 180), and you know one of the triangle''s sides, the other two sides are completely determined, so it must somehow be possible to work ...” May 13, 2019 Ian Stewart posted a reply to Automobile A is traveling at two-thirds the speed that Autom in the Data Sufficiency forum “Each Statement gives the same type of relationship between the two speeds, so the answer will be C, D or E. If we let a and b be the two speeds of the cars, we know that a = 2b/3. Using Statement 1 alone, you might be able to see by inspection that the speeds are 20 and 30. Or we can use ...” May 13, 2019 Brent@GMATPrepNow posted a reply to If the two digit integers M and N are positive and have the in the Problem Solving forum “This question relies on our ability to determine the VALUE of any 2-digit number. For example, what is the VALUE of 83? For many of us, it has been a very long time since we examined this (we learned this when we were 5 or 6). Most of us just say that 83 has a value of 83, but 83 is really just ...” May 13, 2019 Brent@GMATPrepNow posted a reply to If n is an integer greater than 10, then the expression (n^2 in the Problem Solving forum “-----ASIDE--------------------- There''s a nice rule says: The product of k consecutive integers is divisible by k, k-1, k-2,...,2, and 1 So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1 Likewise, the product of any 11 consecutive integers will be ...” May 12, 2019 Brent@GMATPrepNow posted a reply to If x and y are the lengths of the legs of a right triangle, in the Data Sufficiency forum “ Given: x and y are the lengths of the legs of a right triangle We have something like this: https://i.imgur.com/VxCexHO.png Target question: What is the value of xy? Statement 1: The hypotenuse of the triangle is There are infinitely-many different right triangles that meet this ...” May 11, 2019 Brent@GMATPrepNow posted a reply to In how many different ways can a soccer team finish the in the Problem Solving forum “Question rephrased: In how many different ways can we arrange the letters WWWLLD -------------ASIDE-------------------------------------- When we want to arrange a group of items in which some of the items are identical, we can use something called the If there are n objects where A of them are ...” May 11, 2019 Brent@GMATPrepNow posted a reply to Jones has worked at Firm X twice as many years as Green in the Data Sufficiency forum “We can also solve the question using one variable Given: Jones has worked at Firm X twice as many years as Green, and Green has worked at Firm X four years longer than Smith. Let G = the number of years Green worked at Firm X So, G - 4 = the number of years Smith worked at Firm X (since ...” May 10, 2019 Brent@GMATPrepNow posted a reply to In the below addition A, B, C, D, E, F, and G represent the in the Problem Solving forum “If we add two 2-digit numbers and the sum is a 3-digit number, then the 3-digit number must start with a 1. So, E = 1 In order for the sum to be a 3-digit number, A+C must be greater than 9 So, we have two options: EITHER A and C are 5 and 6, OR A and C are 4 and 6 If A and C are 5 and 6, ...” May 10, 2019 Brent@GMATPrepNow posted a reply to If xyz ≠ 0, what is the value of in the Data Sufficiency forum “Target question: What is the value of (x⁴z²)/(z²y²)? This is a good candidate for rephrasing the target question. Since z ≠ 0, we know that z² ≠ 0 So, we can safely take (x⁴z²)/(z²y²) and divide top and bottom by z² to get: x⁴/y² REPHRASED target question: What is the value ...” May 9, 2019 Brent@GMATPrepNow posted a reply to Is quadrilateral PQRS a parallelogram? in the Data Sufficiency forum “Target question: Is quadrilateral PQRS a parallelogram? If you recognize that each statement on its own is not sufficient, we can jump straight to . . . Statements 1 and 2 combined There are infinitely-many quadrilaterals that satisfy BOTH statements. Here are two: Case a: PQRS could ...” May 9, 2019 Brent@GMATPrepNow posted a reply to A lecture course consists of 595 students. The students are in the Problem Solving forum “In order to have an EQUAL number of students in each section, the number of students per section MUST BE A FACTOR of 595 Let''s do some prime factorization 595 = (5)(7)(17) From the prime factorization, we can see that answer choice A, B, D and E are all factors of 595 Answer: C Cheers, ...” May 9, 2019 Brent@GMATPrepNow posted a reply to If a and b are constants, is the expression in the Data Sufficiency forum “Target question: Is the expression defined for x = –2? This is a great candidate for rephrasing the target question. If x = -2, then the expression becomes (-2)+b/√(-2+a) There are two ways in which the expression(-2)+b/√(-2+a) is NOT defined: case i) If a = 2, then the fraction''s ...” May 9, 2019 Brent@GMATPrepNow posted a reply to Is x = y? in the Data Sufficiency forum “Target question: Is x = y? Statement 1: 2x/3 - y/3 = 1/3 Multiply both sides by 3 to get: 2x - y = 1 There are several values of x and y that satisfy this equation. Here are two: Case a: x = 1 and y = 1. In this case, the answer to the target question is YES, it is the case that x = y ...” May 9, 2019 Brent@GMATPrepNow posted a reply to The figure above represents a box that has the shape of a in the Data Sufficiency forum “Target question: What is the volume of the box? IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater ...” May 9, 2019 Brent@GMATPrepNow posted a reply to In the figure above, PQRT is a rectangle. What is the length in the Data Sufficiency forum “Let''s assign some variables to some of the lengths... https://i.imgur.com/BpaiRKm.png Target question: What is the value of x? Statement 1: The area of region PQRS is 39 and TS = 6. Region PQRS is a TRAPEZOID Area of trapezoid = (height)(base1 + base2)/2 So, we get: (x)(y + z)/2 = 39 ...” May 9, 2019 Brent@GMATPrepNow posted a reply to Charlie takes 2.5 hours to fly from Los Angeles to Mexico Ci in the Problem Solving forum “Here''s how I would answer this in my head Average speed = total distance/total time = 1200/2.5 = 2400/5 = 4800/10 = 480 Answer: D Cheers, Brent” May 9, 2019 Ian Stewart posted a reply to In an integer division operation, the divisor is x, the quot in the Data Sufficiency forum “You don''t need to know what a "dividend" is on the GMAT, and if this were a real GMAT question it would declare that all of the numbers are positive. In this question, we''re dividing z by x, and getting a quotient of y and a remainder of r. So z = xy + r Using either Statement ...” May 8, 2019 Brent@GMATPrepNow posted a reply to What amount did Jean earn from the commission on her sales in the Data Sufficiency forum “Target question: What amount did Jean earn from the commission on her sales in the FIRST HALF of 1988 ? Statement 1: In 1988 Jean''s commission was 5 percent of the total amount of her sales. We don''t know her total sales amount in 1988, AND we don''t know what happened in the FIRST HALF of ...” May 8, 2019 Brent@GMATPrepNow posted a reply to Six shipments of machine parts were shipped from a factory o in the Data Sufficiency forum “We might be able to solve this one faster by first converting the fractions to decimals. S1=0.25 S2=0.2 S3=0.17 (approx) S4=0.15 S5=0.13 (approx) S6=0.1 Statement 1: S2 and S4 were shipped on the first truck. First truck has 0.2 + 0.15 = 0.35 Since the first truck holds more than 0.5, ...” May 7, 2019 Brent@GMATPrepNow posted a reply to If a and b are integers, is a^5 < 4^b ? in the Data Sufficiency forum “\ Target question: Is a^5 > 4^b Statement 1: a³ = -27 Solve to get: a = -3 So, a^5 = (-3)^5 = -243 Since 4^b will be POSITIVE for all values of b, the answer to the target question is NO, a^5 is definitely NOT greater than 4^b Since we can answer the target question with certainty, ...” May 7, 2019 Brent@GMATPrepNow posted a reply to Anthony and Michael sit on the six-member board of directors in the Problem Solving forum “Let''s assume that we''re creating subcommittees. We want to place 6 people in the following spaces: _ _ _ | _ _ _ First, we place Michael in one subcommittee; it makes no difference which one: M _ _ | _ _ _ Now place Anthony. We can see that there are 5 spaces remaining. 2 spaces ...” May 7, 2019 Ian Stewart posted a reply to For any sequence of $$n$$ consecutive positive integers, in the Problem Solving forum “If you take the sequence 1, 2, the sum of the even integers is 2 and the sum of the odd integers is 1, so $$S_e > S_o$$ and item 1 can be true. If you take the sequence 2, 3, the sum of the even integers is 2 and the sum of the odd integers is 3, so $$S_e < S_o$$, and item 3 can be true. ...” May 7, 2019 Ian Stewart posted a reply to $$A$$ and $$B$$ are the endpoints of the longest line that in the Problem Solving forum “The longest line you can draw in a circle is a diameter, so AB is a diameter of the circle. If X is the center of the circle, then AX is a radius. The question tells us AX is 3, so the radius of the circle is 3. If you draw a diagram, and look at triangle ACX, two of the sides of that triangle, ...” May 7, 2019 Ian Stewart posted a reply to If $$x$$ is a positive integer, is $$x$$ a prime integer? in the Data Sufficiency forum “Statement 1 tells us x is one less than some prime number. If that prime is 3, then x=2, and x is prime, but if that prime is 5, x=4, and x is not prime, so Statement 1 is not sufficient. Statement 2 tells us x is 5 greater than some prime number. If that prime is 2, then x=7, and x is prime, but ...” May 7, 2019 Ian Stewart posted a reply to If a and b are integers, is a^5 < 4^b ? in the Data Sufficiency forum “4^b is always positive, no matter what b is. If a^3 = -27, then a is negative and so is a^5. So it''s certainly true that a^5 < 4^b, because negative numbers are smaller than positive numbers. So Statement 1 is sufficient. Statement 2 is not sufficient; while we know b is either 4 or -4, we ...” May 7, 2019 Brent@GMATPrepNow posted a reply to If x is 8/3 percent of y, y is what percent of x? in the Problem Solving forum “x percent = x/100 So, 8/3 percent = (8/3)/100 = (8/3)/(100/1) = (8/3)(1/100) = 8/300 GIVEN: x is 8/3 percent of y, We can write: x = 8/300 of y In other words: x = (8/300)(y) or......: x = 8y/300 y is what percent of x? Take: x = 8y/300 Multiply both sides by 300 to get: 300x = 8y ...” May 7, 2019 Ian Stewart posted a reply to A six-sided mosaic contains 24 triangular pieces of tile in the Data Sufficiency forum “If we know each triangle is equilateral with sides of length 9, and we know how many triangles we have, of course we can find the area of all of them, so Statement 1 is sufficient. That we can fit the mosaic in some rectangle limits how large the mosaic might be, but we have no idea how much ...” May 6, 2019 Ian Stewart posted a reply to Mr. Wayne bungee jumps from the top of a building straight in the Problem Solving forum “In 15-3 = 12 seconds, he passes 20 - 5 = 15 floors. If each floor is 3 meters, he covers a distance of 45 meters. So his speed is 45/12 = 15/4 = 3.75 m/s. Of course if each floor is 3 meters high, it''s not clear what it means to ''pass a floor'' (when during the 3 meters do we consider the ...” May 5, 2019 Ian Stewart posted a reply to If the two digit integers M and N are positive and have the in the Problem Solving forum “If we have a two digit number AB, where A is the tens digit and B the units digit, then the number is equal to 10A + B. So here, if A and B represent digits, our numbers are AB and BA. These are equal to 10A + B and 10B + A, and their sum is equal to 11A + 11B. This sum is clearly divisible by ...” May 5, 2019 Ian Stewart posted a reply to In 1994, Company X recorded profits that were 10% greater in the Data Sufficiency forum “We already know the ratio of the company''s profits in 1994 to profits in 1992, since we''re told the percent changes from year to year in the stem, so Statement 2 just restates information we already know, and is useless. If in 1994 the company profits were$100,000 greater than in 1993, and ...”
May 5, 2019
Ian Stewart posted a reply to The 9 squares above are to be filled with x's and o's in the Data Sufficiency forum
“From Statement 1, we know we have at least 5 O''s, and therefore at most 4 X''s. From Statement 2, we know we have at least 4 X''s, in the four corners. Neither statement is sufficient, but using both, if we have at least 4 X''s and at most 4 X''s, we must have exactly 4 X''s, and the two ...”
May 5, 2019
Ian Stewart posted a reply to In the figure above, triangle PQR has angle measures as in the Data Sufficiency forum
“If PQ = QR, the triangle is isosceles, and we have two equal angles opposite PQ and QR. So we have two 58 degree angles (x = 58), and since the sum of the three angles in a triangle is 180, we can find the third angle y and answer the question. In a triangle, the longest side is opposite the ...”
May 5, 2019
Ian Stewart posted a reply to When Tom works alone he chops 2 lbs salad in 3 minutes, and in the Problem Solving forum
“Getting the same time, 6 minutes, for both: Tom chops 4 lbs in 6 minutes Tammy chops 9 lbs in 6 minutes So when they work for the same amount of time, the ratio of the amount Tammy chops to the amount Tom chops is 9 to 4, and since 9 is 125% greater than 4, the answer is 125%. The 65 lbs in ...”
May 4, 2019
Ian Stewart posted a reply to What is the sum of all values of that satisfy the equation in the Problem Solving forum
“We can divide by 4 and get zero on both sides: 4x^2 + 16 = 32x x^2 + 4 = 8x x^2 - 8x + 4 = 0 When we factor the left side above, the factorization will look like (x - a)(x - b), where a and b are the two solutions to the quadratic. The numbers a and b will multiply to 4 (since 4 = (-a)(-b) = ...”
May 4, 2019
Ian Stewart posted a reply to Teachers in United States high schools teach an average in the Problem Solving forum
“Standard deviation is the square root of variance (a fact you almost certainly will not need to know on the GMAT), so the standard deviation here is 10, two standard deviations is thus 20, and 60 and 100 are the two values that are two standard deviations away from the mean of 80. Only 60 is an ...”
May 4, 2019
Brent@GMATPrepNow posted a reply to Last year the range of the annual salaries of the 100 employ in the Problem Solving forum
“A quick solution is to assign some values to the highest paid and lowest paid workers Let $10,000 = the lowest salary LAST YEAR Let$40,000 = the highest salary LAST YEAR This satisfies the condition that the range LAST YEAR = $30,000 If the annual salary of each of the 100 employees this ...” May 4, 2019 Brent@GMATPrepNow posted a reply to Last year the range of the annual salaries of the 100 employ in the Problem Solving forum “Hey BTGmoderatorDC, You posted this question 2 months ago: https://www.beatthegmat.com/last-year-the-range-of-the-annual-salaries-of-the-100-t306593.html Cheers, Brent” May 4, 2019 Brent@GMATPrepNow posted a reply to A certain rectangular window is twice as long as it is wide. in the Problem Solving forum “Approach #2: Algebra Let x = the width of the rectangle So, 2x = the length of the rectangle If the perimeter is 10, we can write: x + x + 2x + 2x = 10 Simplify: 6x = 10 Solve: x = 10/6 = 5/3 So, the width (x) is 5/3 And the length (2x) is 10/3 Answer: B Cheers, Brent” May 4, 2019 Brent@GMATPrepNow posted a reply to A certain rectangular window is twice as long as it is wide. in the Problem Solving forum “We COULD use algebra to solve this question. However, it''s probably faster to just test the answer choices The answer choices give us the length and width of the rectangle. So, the sum of two values will equal HALF the perimeter of the rectangle. Since we want a perimeter of 10, the ...” May 4, 2019 Brent@GMATPrepNow posted a reply to Three-fourths of the area of a rectangular lawn 30 feet wide in the Problem Solving forum “Here''s a diagram of the 30 x 40 lawn https://i.imgur.com/6dQyyQ5.png If we keep the full width (of 30 feet), then the length of the enclosure = 3/4 of 40 = 30 feet https://i.imgur.com/nRkAVRU.png So, the enclosure is a 30 by 30 square. The PERIMETER = 30 + 30 + 30 + 30 = 120 feet If ...” May 4, 2019 Brent@GMATPrepNow posted a reply to If rectangle ABCD is inscribed in the circle above, what is in the Problem Solving forum “Draw a line connecting points A and C. https://i.imgur.com/fQaxM5q.png An important circle property (see video below for more info) tells us that, if we have a 90-degree inscribed angle, then that angle must be containing ("holding") the DIAMETER of the circle. So, we know that AC = ...” May 4, 2019 Brent@GMATPrepNow posted a reply to In quadrilateral ABCD above, what is the length of AB ? in the Problem Solving forum “https://i.imgur.com/srEvM6A.png If we focus on the blue right triangle, we can EITHER recognize that legs of length 3 and 4 are part of the 3-4-5 Pythagorean triplet, OR we can apply the Pythagorean Theorem. https://i.imgur.com/L50lEKr.png Either way, we''ll see that the triangle''s ...” May 4, 2019 Ian Stewart posted a reply to If x represents the number of positive factors of integer y in the Data Sufficiency forum “A number has an odd number of divisors only if that number is a perfect square. It''s easy to see why: for a number that is not a perfect square, say 6, then all of the divisors can be ''paired up'' into pairs that produce 6 as a product: 1 and 6 2 and 3 so we have an even number of divisors. ...” May 4, 2019 Ian Stewart posted a reply to If the positive integer $$x$$ is rounded to the nearest ten, in the Data Sufficiency forum “The question is just asking "is the units digit of x greater than 5?" When we divide a positive number by 10, the remainder we get is that number''s units digit, so Statement 1 tells us "the units digit of x is even". It could be 0, 2, 4, 6 or 8, so we can''t answer the ...” May 4, 2019 Ian Stewart posted a reply to Operation F means “take the square root,” operation G me in the Problem Solving forum “If we multiply our positive number x by a negative constant c, then take the square root, we get something undefined. And if we multiply x by 0, then take a reciprocal, we get something undefined. So if we''re supposed to be able to apply these functions in any order, just to get something that ...” May 3, 2019 Ian Stewart posted a reply to In the $$xy-$$plane above, is angle $$BAC$$ greater than in the Data Sufficiency forum “They should be clear in Statement 2 what angles they''re describing - around a point, there are two different angles you can make, the small angle within the triangle, and the large angle around the outside of the triangle (the one that would sum to 360 with the angle inside the triangle). But as ...” May 3, 2019 Ian Stewart posted a reply to At a restaurant, five friends each purchased a sandwich. in the Data Sufficiency forum “Presumably they mean to ask about the sum of the prices of the sandwiches, and not about the sum of the sandwiches themselves. If Statement 1 is true, all we can say is that the sum of the prices exceeded 5*13 =$65, so that''s not sufficient. If Statement 2 is true, all we can say is that the ...”
May 3, 2019
Brent@GMATPrepNow posted a reply to A paint mixture was formed by mixing exactly 3 colors of in the Data Sufficiency forum
“Target question: How many gallons of green paint were used? Given: A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y% green paint, and z% red paint. 1 gallon of blue paint and 3 gallons of red paint were used. In other words, we ...”
May 2, 2019
Brent@GMATPrepNow posted a reply to If 2.00X and 3.00Y are 2 numbers in decimal form with thousa in the Data Sufficiency forum
“ Given: 2.00X and 3.00Y are 2 numbers in decimal form with thousandths digits X and Y Target question: Is 3(2.00X) > 2(3.00Y)? This is a good candidate for rephrasing the target question. Since X is the thousandths digit, we can write: 2.00X = 2 + X/1000 Since Y is the thousandths ...”
May 2, 2019
Ian Stewart posted a reply to Tony owns six unique matched pairs of socks. All twelve sock in the Problem Solving forum
“We can work out the probability he continues to get unmatched socks, and once that probability falls below 1/2, we''ll know he has a greater than 1/2 chance of getting at least one pair of matched socks. The first sock he picks doesn''t matter. The next sock has a 10/11 chance of not matching the ...”
May 2, 2019
Ian Stewart posted a reply to After the first two terms in a sequence of numbers, each in the Data Sufficiency forum
“If the sum of the first 3 terms is 6, then according to the definition of the sequence, the 4th term is 6. But then the fifth term is just the sum of the first 3 terms plus the 4th term, so is 6+6 = 12. Statement 1 is sufficient. If the 4th term is 6, then by the definition of the sequence, the ...”
May 2, 2019
Ian Stewart posted a reply to Jones has worked at Firm X twice as many years as Green in the Data Sufficiency forum
“If Jones has worked twice as many years as Green, and has also worked 5 years longer than Green, then Green has worked 5 years and Jones has worked 10. So Statement 2 is sufficient. We can deduce from Statement 1 that Jones has worked 5 years longer than Green, so Statement 1 is also sufficient, and ...”
May 2, 2019
Brent@GMATPrepNow posted a reply to If n^m leaves a remainder of 1 after division by 7 for all in the Problem Solving forum
“The most important piece of information is here: "for all positive integers n that are not multiples of 7" Since 2 is not a multiple of 7, then it must be the case that, for a particular value of m, 2^m leaves a remainder of 1 after division by 7 Let''s check the answer choices.... ...”
May 1, 2019
Ian Stewart posted a reply to At a community center, three separate pumps- A, B, and C in the Data Sufficiency forum
“If C alone fills 3/10 of the pool in 126 minutes, it fills the whole pool in (10/3)(126) = 1260/3 = 420 minutes, or 7 hours. So C alone would fill the pool at 3pm, even with no help from A or B, and Statement 1 is sufficient. If A+B together fill 1/8 of the pool in 55 minutes, they fill the whole ...”
May 1, 2019
Ian Stewart posted a reply to The total price of 5 pounds of regular coffee in the Data Sufficiency forum
“Since we''re never given any information about price per pound, the numbers in "5 pounds" and "3 pounds" are just a distraction. All we''re doing here is mixing some regular coffee and some decaf coffee. Say all the regular coffee costs $R and all the decaf costs$D. The stem ...”
May 1, 2019
Ian Stewart posted a reply to Is the average (arithmetic mean) of 5 different positive in the Data Sufficiency forum
“If the five numbers are, as Statement 1 and the stem tell us, five different positive multiples of 10, the smallest values we could possibly have are: 10, 20, 30, 40, 50 That''s an equally spaced list, so its average is equal to its median, so the average of the list above is 30. But that''s ...”
May 1, 2019
Ian Stewart posted a reply to A certain painting job requires a mixture of yellow, green, in the Data Sufficiency forum
“From Statement 1, 1/4 of the mixture is green paint, and since we know we have 12 quarts of paint in total, we must have 3 quarts of green paint. So Statement 1 is sufficient. Statement 2 is not sufficient because we have no information about what fraction of the mixture is white paint.”
May 1, 2019
Brent@GMATPrepNow posted a reply to If x is an integer greater than 0, what is the remainder in the Data Sufficiency forum
“Target question: What is the remainder when x is divided by 4 ? Statement 1: The remainder is 3 when x + 1 is divided by 4. ------ASIDE---------------------- There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 ...”
May 1, 2019
Brent@GMATPrepNow posted a reply to What number is 6 more than x + y ? in the Data Sufficiency forum
“Target question: What is the value of x + y + 6? Statement 1: y is 3 less than x. We can write: y = x - 3 There are several values of x and y that satisfy this equation. Here are two: Case a: x = 3 and y = 0. In this case, the answer to the target question is x + y + 6 = 3 + 0 + 6 = 9 ...”
May 1, 2019
Brent@GMATPrepNow posted a reply to Is the average (arithmetic mean) of the numbers x, y, and z in the Data Sufficiency forum
“Target question: Is the average (arithmetic mean) of the numbers x, y, and z greater than z? This is a good candidate for rephrasing the target question. Rewrite the question as "Is (x + y + z)/3 > z?" Multiply both sides by 3 to get: "Is x + y + z > 3z?" Subtract z ...”
May 1, 2019
Brent@GMATPrepNow posted a reply to Every object in a box is either a sphere or a cube, and ever in the Data Sufficiency forum
“Target question: How many objects are in the box? Given: Every object in a box is either a sphere or a cube, and every object in the box is either red or green. We can solve this using the Double Matrix Method. This technique can be used for most questions featuring a population in which ...”
May 1, 2019
Brent@GMATPrepNow posted a reply to What is the remainder when the positive integer n is divided in the Data Sufficiency forum
“Target question: What is the remainder when the positive integer n is divided by 5 ? Statement 1: When n is divided by 3, the quotient is 4 and the remainder is 1. There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 ...”
April 30, 2019
Brent@GMATPrepNow posted a reply to Is n equal to zero? in the Data Sufficiency forum
“Target question: Is n equal to zero? Statement 1: The product of n and some nonzero number is 0 (n)(non-zero number) = 0 This means n must be 0 Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: The sum of n and 0 is 0 If n + 0 = 0, we can ...”
April 30, 2019
Brent@GMATPrepNow posted a reply to If r and s are positive numbers and θ is one in the Data Sufficiency forum
“ Given: r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷ Target question: Which operation is θ ? Statement 1: If r = s, then r θ s = 0 Keep in mind that r and s are POSITIVE So, we have POSITIVE θ POSITIVE = 0 POSITIVE + POSITIVE ≠ 0 So, θ cannot ...”
April 30, 2019
Brent@GMATPrepNow posted a reply to How many hours does it take Jennifer to run y miles if she r in the Problem Solving forum
“time = distance/rate So, time = y/x Answer: B Cheers, Brent”
April 30, 2019
Brent@GMATPrepNow posted a reply to If x = 5 – 4k and y = 5k – 3, then for what value of k d in the Problem Solving forum
“We want: x = y Replace values with their equivalents: 5 - 4k = 5k - 3 Add 4k to both sides: 5 = 9k - 3 Add 3 to both sides: 8 = 9k Divide both sides by 9 to get: 8/9 = k Answer: B Cheers, Brent”
April 30, 2019
Ian Stewart posted a reply to If $$\frac{4^7+4^8+4^9+4^{10}}{5}$$ is $$x$$ times 4^7, what in the Problem Solving forum
“Just factor out 4^7 from the sum in the numerator: (4^7 + 4^8 + 4^9 + 4^10)/5 = x*4^7 4^7(1 + 4 + 4^2 + 4^3)/5 = x*4^7 and now if we divide by 4^7 on both sides, we have 1 + 4 + 4^2 + 4^3 = 5x 85 = 5x 17 = x”
April 30, 2019
Ian Stewart posted a reply to If r and s are positive numbers and θ is one in the Data Sufficiency forum
“We can just check each of the four arithmetic operations to see when each Statement will be true. If r = s, we can replace ''s'' with ''r'', so for Statement 1: r+r = 2r r-r = 0 r*r = r^2 r/r = 1 and it''s only when the operation is subtraction that we get 0 as a result, and the operation ...”
April 30, 2019
Ian Stewart posted a reply to What is the remainder when the positive integer n is divided in the Data Sufficiency forum
“Statement 1 tells us that n is equal to 13, so of course we can answer any question about n, and Statement 1 is sufficient. The remainder you get when you divide by 4 has no relationship to the remainder you get when you divide by 5, so Statement 2 is useless. For example, n could be 5, and then ...”
April 30, 2019
Ian Stewart posted a reply to In a certain first grade classroom, the average height is in the Data Sufficiency forum
“The sum of the 5 girls'' heights is 5x, and the sum of the 8 boys'' heights is 8y, so the average height is (5x + 8y)/13. So if we can find the value of 5x + 8y, we can answer the question. From Statement 1, dividing by 3 on both sides, we find 15x + 24y = 1755 5x + 8y = 1755/3 so we can ...”
April 30, 2019
Ian Stewart posted a reply to Last year, the average price of eight different products in the Data Sufficiency forum
“The answer is instantly C or E, because using either statement alone, we don''t know anything about some of the products. Using both Statements, it''s possible, say, that five of the products cost $0.10 each, and the other three cost more than$600 each. If the five cheap products increased in ...”
April 30, 2019
Ian Stewart posted a reply to A drawer contains 12 socks, of which 8 are black and 4 are in the Data Sufficiency forum
“We have 9 socks left. If, as Statement 1 tells us, the ratio of black to white socks is 2 to 1, then 2/3 of the remaining socks are black, and thus 6 are black, so Statement 1 is sufficient. Statement 2 is not sufficient because we have no information about the third sock that was removed, so the ...”
April 30, 2019
Brent@GMATPrepNow posted a reply to If a school district paid a total of $35 per desk for x desk in the Data Sufficiency forum “ Given: School district paid a total of$35 per desk for x desks and a total of $30 per table for y tables So, the TOTAL amount paid = 35x + 30y. Target question: What was the total amount that the district paid for these desks and tables?? Statement 1: The total amount the district ...” April 29, 2019 Brent@GMATPrepNow posted a reply to In a sequence of numbers in which each term is 2 more than in the Data Sufficiency forum “ Given: Sequence of numbers is such that each term is 2 more than the preceding term Target question: What is the value of term_4? Statement 1: The last term is 90. We have no idea how many terms there are in the sequence. So, the last term could be term_5 or term_9 or term_12 or . . . ...” April 29, 2019 Brent@GMATPrepNow posted a reply to Is the integer p divisible by 5 ? in the Data Sufficiency forum “Target question: Is the integer p divisible by 5? Statement 1: p is divisible by 10. If p is divisible by 10, we can write: p = 10k, for some integer k. Rewrite this as: p = (5)(2)(k) This tells us that p is a multiple of 5, which means p must be divisible by 5 Since we can answer the ...” April 29, 2019 Brent@GMATPrepNow posted a reply to If R, S, and T are points on a line in the Data Sufficiency forum “ Given: R, S, and T are points on a line, and if R is 5 meters from T and 2 meters from S There are 4 possible scenarios that meet the above conditions: https://i.imgur.com/kOeqUfZ.png Target question: How far is S from T? Statement 1: R is between S and T. When we check the 4 ...” April 29, 2019 Brent@GMATPrepNow posted a reply to If m and n are integers, what is the value of m + n ? in the Data Sufficiency forum “ Given: m and n are integers Target question: What is the value of m + n ? Statement 1: (x + m)(x + n) = x² + 5x + mn and x ≠ 0. Use FOIL to expand the left side: x² + nx + mx + mn = x² + 5x + mn Factor the two middle terms: x² + x(n + m) + mn = x² + 5x + mn At this point, we ...” April 29, 2019 Brent@GMATPrepNow posted a reply to If a and b are integers, and b > 0, does (a−1)/(b+1) = in the Data Sufficiency forum “ Given: a and b are integers, and b > 0 Target question: Does (a - 1)/(b + 1) = a/b? This is a good candidate for rephrasing the target question. Take the equation: (a - 1)/(b + 1) = a/b Cross multiply to get: (b)(a - 1) = (a)(b + 1) Expand both sides to get: ab - b = ab + a ...” April 29, 2019 Brent@GMATPrepNow posted a reply to Is the sum of two integers divisible by 10 ? in the Data Sufficiency forum “Target question: Is the sum of two integers divisible by 10 ? Statement 1: One of the integers is even. We only have information about ONE number. Statement 1 is NOT SUFFICIENT Statement 2: One of the integers is a multiple of 5. We only have information about ONE number. Statement 2 ...” April 29, 2019 Brent@GMATPrepNow posted a reply to If p, r, and s are consecutive integers in ascending in the Data Sufficiency forum “ Given: p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers Since p, r and s are EQUALLY spaced, the mean of the 3 numbers = the median of the 3 numbers. Since p < r < s, we know that r = the mean = the median. In other ...” April 29, 2019 Brent@GMATPrepNow posted a reply to Three children inherited a total of X dollars. If the oldest in the Data Sufficiency forum “ Given: Three children inherited a total of X dollars. The oldest child inherited$7,000 more than the youngest child, and the youngest child inherited $9,000 less than the middle child Let y = the amount the YOUNGEST child received So, y + 7000 = the amount the OLDEST child received And y + ...” April 29, 2019 Ian Stewart posted a reply to If a and b are integers and a is even, what is the value in the Data Sufficiency forum “Using both Statements, we might have a=2 and b=7, or we might have a = -2000 and b = -7000, among other possibilities, and we can easily get different values for a-b, so the answer is E.” April 29, 2019 Ian Stewart posted a reply to The inflation index for the year 1989 relative to the year in the Data Sufficiency forum “We know that the ratio of the price of the mixer in 1989 to the price in 1970 was 3.56 to 1. Notice then that for every dollar the mixer cost in 1970, the price increased by$2.56. So if the actual increase was $102.40, the cost in 1970 must have been 102.40/2.56, and Statement 1 is sufficient. ...” April 29, 2019 Ian Stewart posted a reply to K is a set of integers such that if the integer r is in K in the Data Sufficiency forum “If we know r is in K, then we know r+1 is in K. So if 50 is in K, we know that 51 is in K, but then we know 52 is in K, and 53 is in K, and so on, so 100 will be in K. So Statement 1 is sufficient. From Statement 2, we know 150 is in K, so we know 151, 152, 153 etc are also in K. But we don''t ...” April 29, 2019 Ian Stewart posted a reply to A total of 20 amounts are entered on a spreadsheet that has in the Data Sufficiency forum “If you have 4 values, and R is their average, then 4R is their sum, from the definition of an average (just rewrite average = sum/n so you have ''sum'' on one side). So here, 4R(1) is the sum of the four values in row 1, 4R(2) is the sum of the four values in row two, and so on, and thus 4[ R(1) ...” April 29, 2019 Ian Stewart posted a reply to If m is an integer, is m/102 an integer? in the Data Sufficiency forum “Prime factorize: 102 = 2*51 = 2*3*17 So we can be certain m/102 is an integer if we can be certain m is divisible by 2, 3 and 17. Statement 1 tells us 165m is divisible by 99, or that 165m/99 is an integer. So (33)(5m)/(33)(3) is an integer, and 5m/3 is an integer. That means the ''3'' in the ...” April 29, 2019 Ian Stewart posted a reply to If a and b are integers, and b > 0, does (a−1)/(b+1) = in the Data Sufficiency forum “We can rewrite the question: Is (a-1)/(b+1) = a/b ? Is ab - b = ab + a ? Is -b = a? from which we can see that Statement 2 tells us exactly what we want, while Statement 1 does not (if Statement 1 is true, the answer may be ''yes'', if b = 2 and a = -2, but can also be no for any other ...” April 29, 2019 Ian Stewart posted a reply to If p, r, and s are consecutive integers in ascending in the Data Sufficiency forum “The average of an equally spaced set is equal to the median of that set, so here, if p, r, s are consecutive integers in increasing order, their average is simply r, so r = x and the question is just asking if we can find r. Notice also that the sum of the three integers is therefore 3r (because by ...” April 29, 2019 Ian Stewart posted a reply to If m and n are integers, what is the value of m + n ? in the Data Sufficiency forum “If you expand the left side of Statement 1, we have (x + m)(x + n) = x^2 + 5x + mn x^2 + (m+n)x + mn = x^2 + 5x + mn and now most of the terms can be subtracted from both sides, leaving us with (m + n)x = 5x and dividing by the nonzero x, we find m+n = 5, so Statement 1 is sufficient. ...” April 29, 2019 Brent@GMATPrepNow posted a reply to Is x<y? in the Data Sufficiency forum “Target question: Is x < y? Statement 1: z< y No information about x Statement 1 is NOT SUFFICIENT Statement 2: z < x No information about y Statement 2 is NOT SUFFICIENT Statements 1 and 2 combined The combined statements tell us that x and y are both greater than z ...” April 28, 2019 Brent@GMATPrepNow posted a reply to What is the value of a^4 - b^4? in the Data Sufficiency forum “Target question: What is the value of a⁴ - b⁴? NOTE: a⁴ - b⁴ is a difference of square, which we can factor. a⁴ - b⁴ = (a² - b²)(a² + b²) So, we can REPHRASE the target question as... REPHRASED target question: What is the value of (a² - b²)(a² + b²)? Statement 1: ...” April 28, 2019 Brent@GMATPrepNow posted a reply to Which of the following could be the equation of line m? in the Problem Solving forum “First off, we can eliminate answer choice D, since y = 2 is the equation of a HORIZONTAL line, and the given line is NOT horizontal. Next, we can eliminate answer choice E, since x = -2 is the equation of a VERTICAL line, and the given line is NOT vertical. Now notice that line m has a ...” April 28, 2019 Brent@GMATPrepNow posted a reply to If S is a set of odd integers and 3 and -1... in the Data Sufficiency forum “ Given: S is a set of odd integers and 3 and –1 are in S Target question: Is –15 in S ? Statement 1: 5 is in S So far, set S looks like this: {-1, 3, 5, . . . .} So, -15 may or may not be in set S Since we cannot answer the target question with certainty, statement 1 is NOT ...” April 28, 2019 Brent@GMATPrepNow posted a reply to If r and s are positive integers... in the Data Sufficiency forum “ Given: r and s are positive integers Target question: Is r + s even? Statement 1: r is even. Since we have no information about s, we cannot determine whether r + s is even Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: s is ...” April 28, 2019 Brent@GMATPrepNow posted a reply to When positive integer k is divided by 5, the remainder is 2. in the Problem Solving forum “When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), ...” April 28, 2019 Brent@GMATPrepNow posted a reply to Is the integer x a 3-digit integer? in the Data Sufficiency forum “Target question: Is the integer x a 3-digit integer? Statement 1: x is the square of an integer. Let''s TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = 10² = 100. In this case, the answer to the target question is YES, x IS a 3-digit ...” April 28, 2019 Brent@GMATPrepNow posted a reply to If the 1st term of a sequence is 0 and the 2nd term is 1... in the Data Sufficiency forum “ Given: term1 = 0 and term2 = 1 Target question: Does term5 equal 2? Once we scan the two statements, we can probably jump straight to . . . Statements 1 and 2 combined There are several possible sequences that satisfy BOTH statements. Here are two: Case a: {0, 1, 2, 0, 2,...}. In ...” April 28, 2019 Brent@GMATPrepNow posted a reply to Is the sum of four particular integers even? in the Data Sufficiency forum “Some important rules: #1. ODD +/- ODD = EVEN #2. ODD +/- EVEN = ODD #3. EVEN +/- EVEN = EVEN #4. (ODD)(ODD) = ODD #5. (ODD)(EVEN) = EVEN #6. (EVEN)(EVEN) = EVEN Target question: Is the sum of four particular integers even? Statement 1: Two of the integers are odd and two are even. ...” April 28, 2019 Ian Stewart posted a reply to S is a set of integers such that i) if a is in S, then in the Data Sufficiency forum “Using Statement 1 alone, if ''1'' is in the set, then from rule i), we can deduce that -1 is in the set. But then using rule ii), we can''t generate any new values besides 1 and -1. So there are only two values, 1 and -1, that we can be certain are in the set, and we have no way to know if -4 is in ...” April 28, 2019 Ian Stewart posted a reply to If S is a set of odd integers and 3 and -1... in the Data Sufficiency forum “Statement 1 isn''t sufficient, since it just tells us one other value in the set. Statement 2 also isn''t sufficient alone -- while using it we can determine many other values in the set (all the positive and negative powers of 3 are in the set), we have no way to know if -15 is in the set, since ...” April 28, 2019 Ian Stewart posted a reply to Is the sum of four particular integers even? in the Data Sufficiency forum “Statement 1 tells us exactly what kind of integers we have, so using the familiar even/odd rules, we can work out if the sum will be even or odd (since odd+odd is even, and even+even is even, the sum will turn out to be even, though since it''s a DS question, we don''t actually care what the answer ...” April 28, 2019 Ian Stewart posted a reply to If the 1st term of a sequence is 0 and the 2nd term is 1... in the Data Sufficiency forum “Statement 1 tells us that the fifth term is either 0 or 2. There''s no other information anywhere in the question that tells us anything about the fifth term in the sequence, so using both statements, we have two possibilities, and the answer is E.” April 28, 2019 Brent@GMATPrepNow posted a reply to If 90/k is an integer, is k an integer? in the Data Sufficiency forum “ Given: 90/k is an integer Target question: Is k an integer? Statement 1: k > 1 Let''s TEST some values. There are several values of k that satisfy statement 1. Here are two: Case a: k = 10. Notice that 90/k = 90/10 = 9, which is an integer. In this case, the answer to the target ...” April 27, 2019 Brent@GMATPrepNow posted a reply to For a recent play performance, the ticket prices were$25 in the Data Sufficiency forum
“Target question: How many of the tickets sold were for adults? Given: A total of 500 tickets were sold for the performance Let C = # of child tickets sold Let A = # of adult tickets sold So, C + A = 500 Statement 1: Revenue from ticket sales for this performance totaled $10,500 In other ...” April 27, 2019 Brent@GMATPrepNow posted a reply to The arithmetic mean of a data set is 46 and the standard in the Problem Solving forum “-----------ASIDE----------------- A little extra background on standard deviations above and below the mean If, for example, a set has a standard deviation of 4, then: 1 standard deviation = 4 2 standard deviations = 8 3 standard deviations = 12 1.5 standard deviations = 6 0.25 ...” April 27, 2019 Brent@GMATPrepNow posted a reply to In the town of Z, the town lion roars on some days and not in the Data Sufficiency forum “Target question: What is the probability that on that day, either the town lion roared or it rained? This is a good candidate for rephrasing the target question. This is an OR probability. The OR probability rule says, P(A or B) = P(A) + P(B) - P(A and B) So, P(rained or roared) = P(rained) + ...” April 27, 2019 Brent@GMATPrepNow posted a reply to If 20 percent of x is 5y, and y = 7, what is 60 percent in the Problem Solving forum “GIVEN: 20 percent of x = 5y This means: 40 percent of x = 10y And: 60 percent of x = 15y Since y = 7, we can write: 60 percent of x = 15(7) = 105 Answer: A” April 27, 2019 Brent@GMATPrepNow posted a reply to Is x^2 > 15? in the Data Sufficiency forum “Target question: Is x² > 15? Statement 1: x > -4 Let''s TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = -1. In this case, x² = (-1)² = 1. So, the answer to the target question is NO, x² is NOT greater than 15 Case b: x = ...” April 27, 2019 Ian Stewart posted a reply to If $$n$$ and $$m$$ are positive integers, what is the in the Data Sufficiency forum “If you divide a number by 10, the remainder you get is just the number''s units digit. So the question is just asking "what is the units digit of $$3^{(4n+2)}+m$$ ?" There are other units digit/exponent methods that are more flexible, but I''ve explained those in other posts, so I''ll ...” April 26, 2019 Brent@GMATPrepNow posted a reply to If digit $$h$$ is the hudredths' digit in the decimal in the Data Sufficiency forum “ Given: Digit h is the hundredths digit in the decimal d=0.2h6 Target question: What is the value of d, rounded to the nearest TENTH? Statement 1: d < 1/4 In other words, 0.2h6 < 0.25 This means h = 0, 1, 2, 3 or 4 If h = 0, 1, 2, 3 or 4, then 0.2h6 (aka d) rounded to the nearest ...” April 26, 2019 Brent@GMATPrepNow posted a reply to In the rectangular coordinate system, line $$k$$ is defined in the Data Sufficiency forum “KEY CONCEPT: If a point lies ON a line, then the coordinates (x and y) of that point must SATISFY the equation of the line. Given: Line k is defined by the equation x - 2y + n = 0 Target question: What is the value of n? Statement 1: The x-intercept of line k is 8 In other words, ...” April 26, 2019 Brent@GMATPrepNow posted a reply to If z is a three-digit positive integer, what is the value in the Data Sufficiency forum “ Given: z is a three-digit positive integer Target question: What is the value of the tens digit of z ? Statement 1: The tens digit of z - 91 is 3 Let''s examine two EXTREME cases z - 91 = 30 z - 91 = 39 NOTE: These are extreme cases, because 30 is the smallest 2-digit number ...” April 25, 2019 Brent@GMATPrepNow posted a reply to Of the 60 animals on a certain farm, 2/3 are either pigs or in the Data Sufficiency forum “Target question: How many of the animals are cows? Given: Of the 60 animals in a certain farm, 2/3 are either pigs or cows Let P = # of pigs Let C = # of cows 2/3 of 60 = 40, so we can say that P + C = 40 Statement 1: The farm has MORE THAN twice as many cows as it has pigs. In other ...” April 25, 2019 Brent@GMATPrepNow posted a reply to Bill rides his bike to work in the morning on a route that in the Data Sufficiency forum “Here''s a similar question to practice with: https://www.beatthegmat.com/distance-t273181.html Cheers, Brent” April 24, 2019 Brent@GMATPrepNow posted a reply to What is the value of x? in the Data Sufficiency forum “Target question: What is the value of x? Statement 1: 4x = 2y − 6 Divide both sides by 2 to get: 2x = y - 3 Divide both sides by 2 (again) to get: x = (y - 3)/2 As you might guess, there are infinitely many solutions to the equation x = (y - 3)/2. Here are two: Case a: y = 3, and x = 0. ...” April 24, 2019 Brent@GMATPrepNow posted a reply to Phone plan A charges$1.25 for the first minute and $0.15 in the Problem Solving forum “Phone plan A charges$1.25 for the first minute and $0.15 for every minute thereafter. Let x = total duration of phone call (in minutes) So, the cost of an x-minute call =$1.25 + ($0.15)(x - 1) ASIDE: I created the expression ($0.15)(x - 1) because we pay $1.25 for the FIRST minute. So, if x = ...” April 24, 2019 Ian Stewart posted a reply to If the positive integer x divisible by 200? in the Data Sufficiency forum “If we prime factorize everything: The question asks if x is divisible by 2^3 * 5^2 From S1: x^2 is divisible by 2^3 * 5^4. For x^2 to be divisible by 2^3, it will need to be true that x itself is divisible by at least 2^2, since if x were only divisible by 2^1, then x^2 would only be divisible ...” April 23, 2019 Ian Stewart posted a reply to A number when divided successively by 4 and 5 leaves in the Problem Solving forum “The question means something different from what it actually says, but I can guess what it''s trying to say. When we take our number, "n", and divide it by 4, we get a remainder of 1. So n is exactly 1 greater than some multiple of 4, and we have: n = 4q + 1 It''s here where the ...” April 22, 2019 Ian Stewart posted a reply to What is the area of the shaded region in the figure shown? in the Data Sufficiency forum “Draw a vertical line starting from point E, up to the line BC. That line will divide the large rectangle (ABCD) into two smaller rectangles. Line BE cuts one of those smaller rectangles in half along the diagonal, while line EC cuts the other one in half along the diagonal. So half of each smaller ...” April 22, 2019 Ian Stewart posted a reply to What is the value of x? in the Data Sufficiency forum “From Statement 1, x must be 5. From Statement 2, either x-3 = 2, or x-3 = -2, which gives us two different values for x (5 and 1). So the answer is A.” April 22, 2019 Brent@GMATPrepNow posted a reply to A piece of twine of length t is cut into two pieces. in the Problem Solving forum “A piece of twine of length t is cut into two pieces. Let x = the length of the LONGER piece in yards So, t - x = the length of the SHORTER piece in yards The length of the longer piece is 2 yards greater than 3 times the length of the shorter piece. In other words: (longer piece) = ...” April 22, 2019 Brent@GMATPrepNow posted a reply to √(16∗20+8∗32)= in the Problem Solving forum “One option here is to evaluate (16)(20)+(8)(32), and then find the square root of the result. That''s a bit of work. We can also apply a technique called "Multiplying by Doubling and Halving" (here''s the video: I factored out the 16 = √sqrt(xy) = (√x)(√y)] √[(16)(36)] = ...” April 22, 2019 Ian Stewart posted a reply to At a community event, the total number of men, women, and in the Data Sufficiency forum “If the ratio of men to women to children is 15 to 32 to 17, then (since that ratio is reduced) the total number of people must be a multiple of 15+32+17 = 64. If the total is also less than 120, it can only be exactly 64, so we have exactly 15 men, and Statement 1 is sufficient. Statement 2 is ...” April 22, 2019 Brent@GMATPrepNow posted a reply to Sequence $$X$$ consists of $$825$$ terms, and each term in the Data Sufficiency forum “Target question: What is the value of term 500? Given: Each term after the first term is 5 more than the preceding term. Statement 1: Term 515 of sequence X is -98. Since each term is 5 more than the preceding term, we know that term 514 = -103 term 513 = -108 term 512 = -113 term ...” April 21, 2019 Brent@GMATPrepNow posted a reply to From a group of 5 managers (Joon, Kendra, Lee, Marnie and in the Problem Solving forum “Our goal is to find P(M and N both selected) Method #1: P(M and N both selected) = P(one of them is selected 1st AND the other selected 2nd) = P(one of them is selected 1st) x P(the other selected 2nd) = (2/5)(1/4) = 1/10 = 0.1 Aside: P(one of them is selected 1st) = 2/5 because I''m ...” April 21, 2019 Brent@GMATPrepNow posted a reply to What is the perimeter of quadrilateral Q? in the Data Sufficiency forum “Target question: What is the perimeter of quadrilateral Q? If we recognize that each statement alone is not sufficient, we can jump straight to...... Statements 1 and 2 combined There are several quadrilaterals satisfy BOTH statements. Here are two: Case a: Q is a rectangle with width 1 ...” April 20, 2019 Brent@GMATPrepNow posted a reply to Mary's income is 60 percent more than Tim's income, and in the Problem Solving forum “I suggest that we choose some nice values that meet the given conditions. Tim''s income is 40 percent less than Juan''s income. Let Juan''s income =$100 40% of $100 =$40 This means Tim''s income = $100 -$40 = $60 Mary''s income is 60 percent more than Tim''s income 60% of$60 = $36 So ...” April 20, 2019 Brent@GMATPrepNow posted a reply to For integers x and y, when x is divided by y, the remainder in the Problem Solving forum “Since, the question asks "Which of the following must be true?", we can eliminate any answer choice that is not necessarily true. So let''s test some values that satisfy the given conditions For integers x and y, when x is divided by y, the remainder is odd. One possible case is that ...” April 20, 2019 Brent@GMATPrepNow posted a reply to A certain library assesses fines for overdue books as follow in the Problem Solving forum “1st day -$0.10 2nd day - $0.20 or$0.40 (double or add $0.30)$0.20 is the lesser amount 3rd day - $0.40 or$0.50 (double or add $0.30)$0.40 is the lesser amount 4th day - $0.80 or$0.70 (double or add $0.30)$0.70 is the lesser amount The correct answer is B Cheers, Brent”
April 20, 2019
Brent@GMATPrepNow posted a reply to For the 5 days shown in the graph, how many kilowatt-hours in the Problem Solving forum
“List the numbers in ASCENDING ORDER to get: 19, 24, 27, 29, 31. So 27 is the median. Average = (19 + 24 + 27 + 29 + 31)/5 = 130/5 = 26. The median (27) is 1 greater than the average (26). Answer: A Cheers, Brent”
April 20, 2019
Brent@GMATPrepNow posted a reply to What are the coordinates of point B in the figure above? in the Data Sufficiency forum
“IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in the video below. Target question: What ...”
April 19, 2019
Brent@GMATPrepNow posted a reply to If (x # y) represents the remainder that results when the in the Problem Solving forum
“If y > 16, (16 # y) = 16, so we need only check the values from 1 to 15 Also, we need not check the FACTORS of 16, since they will all yield a remainder of 0 We''re left with: (16 # 3) = 1 KEEP! (16 # 5) = 1 KEEP (16 # 7) = 2 (16 # 9) = 7 (16 # 10) = 6 (16 # 11) = 5 (16 # 12) = 4 (16 # ...”
April 19, 2019
Brent@GMATPrepNow posted a reply to If x and y are positive integers, is x^2*y^2 even ? in the Data Sufficiency forum
“Target question: Is x²y² even ? Statement 1: x + 5 is a prime number So, x+5 is a prime number greater than 5, which means x+5 must be ODD (since 2 is only even prime) If x+5 is ODD, then x must be EVEN If x is EVEN, then x²y² must be even The answer to the target question is YES, ...”
April 19, 2019
Brent@GMATPrepNow posted a reply to The areas of three faces of a rectangular solid are 12, 15 a in the Problem Solving forum
“Let x = the width Let y = the length Let z = the height So, the volume = xyz Area of one face = 12 We can write: xy = 12 Area of one face = 15 We can write: xz = 15 Area of one face = 20 We can write: yz = 20 Combine to get: (xy)(xz)(yz) = (12)(15)(20) Simplify: x²y²z² = 3600 ...”
April 19, 2019
Ian Stewart posted a reply to A certain money market account that had a balance of $48,000 in the Problem Solving forum “If it earns$360 in a month, it earns $360 *12 in a year, if there''s no compounding. Dividing by the amount invested, we''ll get the interest rate for the year: (12)(360)/48000 = 1*360/4000 = 36/400 = 9/100 = 9%” April 19, 2019 Ian Stewart posted a reply to If x is an integer, then which of the following statements in the Problem Solving forum “Lots of ways to do this, for example: x^2 - x - 1 = x(x-1) - 1 Notice x(x-1) is the product of two consecutive integers, so it is the product of one odd and one even integer, and must therefore be even. When we subtract 1 from this product, we get an odd number, so x(x-1) - 1 is odd.” April 19, 2019 Ian Stewart posted a reply to A number of oranges are to be distributed evenly among a in the Data Sufficiency forum “Statement 1 is automatically true, so it really only tells us that it is possible to divide the number of baskets by 2. But we might have 2 baskets with 10 oranges each, or 20 baskets with 1 orange each, for example, so that information is not sufficient. If Statement 2 is true, then when we ...” April 19, 2019 Ian Stewart posted a reply to From a group of $$J$$ employees, $$K$$ will be selected, at in the Data Sufficiency forum “Using only Statement 1, we might be picking only from 15 employees in total, in which case it''s not likely, but also not nearly impossible, that Lisa and Philip sit together. But we might be picking from 15,000,000 employees in total, and the probability might be almost zero that we even pick Lisa ...” April 19, 2019 Brent@GMATPrepNow posted a reply to OG 2019 related questions for daily emails in the The 60-Day GMAT Study Guide forum “The OGs vary by very little with each edition. So, you can just use an earlier edition (see https://www.beatthegmat.com/official-guide-question-library-t296759.html) Cheers, Brent” April 18, 2019 Brent@GMATPrepNow posted a reply to OG 2019 related questions for daily emails in the The 60-Day GMAT Study Guide forum “Sorry, but there are no plans to update BTG''s 60-Day Study Guide to include OG2019 questions.” April 18, 2019 Brent@GMATPrepNow posted a reply to If f(2x - 1) = 4x² - 4x - 8, then f(5) = in the Problem Solving forum “Here''s one more approach: First notice that 4x² - 4x - 8 looks a lot like (2x - 1)² (2x - 1)² = (2x - 1)(2x - 1) = 4x² - 4x + 1 Now take: f(2x - 1) = 4x² - 4x - 8 Rewrite as: f(2x - 1) = 4x² - 4x + 1 - 9 = (2x - 1)² - 9 In other words, f(something) =something² - 9 In general, ...” April 18, 2019 Brent@GMATPrepNow posted a reply to y = 248 - 398x. Which of the following values of x gives in the Problem Solving forum “We can also test the answer choices.... (A) x = 200 means y = 248 - 398(200) = some number LESS THAN 248 (B) x = 100 means y = 248 - 398(100) = some number LESS THAN 248 (C) x = 0.5 means y = 248 - 398(0.5) = some number LESS THAN 248 (D) x = 0 means y = 248 - 398(0) = some number EQUAL TO ...” April 18, 2019 Brent@GMATPrepNow posted a reply to If sequence S has 120 terms, what is the 105th term of S? in the Data Sufficiency forum “Target question: What is the 105th term of S? Given: Sequence S has 120 terms Statement 1: The first term of S is −8. We have no information about the nature of the sequence. So, knowing the value of term 1 won''t help is determine the value of term 105 Since we cannot answer the ...” April 18, 2019 Brent@GMATPrepNow posted a reply to Does x + c = y + c ? in the Data Sufficiency forum “Target question: Does x + c = y + c ? This is a good candidate for rephrasing the target question. Take the equation x + c = y + c, and subtract c from both sides to get: x = y REPHRASED target question: Does x = y ? Aside: Here’s a video with tips on rephrasing the target question: ...” April 17, 2019 Brent@GMATPrepNow posted a reply to If n is a prime number greater than 3, what is the remainder in the Problem Solving forum “Choose ANY prime number greater than 3, and test it. If n = 5, then n² = 5² = 25 When 25 is divided by 12, the quotient is 2 and the remainder is 1 Answer: B Cheers, Brent” April 17, 2019 Brent@GMATPrepNow posted a reply to Is integer x odd? in the Data Sufficiency forum “Target question: Is integer x odd? Statement 1: 2x + 1 is odd There are several values of x that satisfy statement 1. Here are two: Case a: x = 1. Notice that 2x + 1 = 2(1) + 1 = 3, which is odd. In this case, the answer to the target question is YES, x IS odd Case b: x = 2. Notice that 2x ...” April 17, 2019 Brent@GMATPrepNow posted a reply to When 1,000 children were inoculated with a certain vaccine, in the Data Sufficiency forum “Target question: How many of the children developed inflammation but not fever? One approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). ...” April 16, 2019 Brent@GMATPrepNow posted a reply to Is xy > 0? in the Data Sufficiency forum “Target question: Is xy > 0? Statement 1: x - y > -2 Let''s TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 5 and y = 1. In this case, xy = (5)(1) = 5. So, the answer to the target question is YES, xy IS greater than 0 Case b: ...” April 16, 2019 Brent@GMATPrepNow posted a reply to If x and y are positive integers and x = 10y + 5, what is in the Problem Solving forum “GIVEN: x = 10y + 5 Factor out 5 to get: x = 5(2y + 1) We can see that x is a multiple of 5, which also means x is divisible by 5, which means the remainder will by ZERO when x is divided by 5 Answer: A Cheers, Brent” April 16, 2019 Brent@GMATPrepNow posted a reply to Last Problem in OG12 Diagnostic in the Problem Solving forum “As with all VIACs (Variables In the Answer Choices questions), we can solve this via the INPUT-OUTPUT approach (as Mitch has done) or via an ALGEBRAIC approach. Typically, when the answer choices look complex (as they do here), I find the INPUT-OUTPUT approach easier. However, the algebraic ...” April 16, 2019 Brent@GMATPrepNow posted a reply to Which of the following is equivalent to in the Problem Solving forum “Here''s another approach.... Take: $$\frac{x+y}{3}-\frac{x-y}{4}$$ Find common denominator: $$\frac{4(x+y)}{12}-\frac{3(x-y)}{12}$$ Expand numerators: $$\frac{4x+4y}{12}-\frac{3x-3y)}{12}$$ Combine fractions: $$\frac{(4x+4y)-(3x-3y)}{12}$$ Simplify numerator: $$\frac{x+7y}{12}$$ ...” April 15, 2019 Brent@GMATPrepNow posted a reply to A man spends$48 to buy 6 hamburgers and 8 colas for his in the Problem Solving forum
“Let H = price of one hamburger Let C = price of one cola A man spends $48 to buy 6 hamburgers and 8 colas for his office workers. 6H + 8C = 48 The next day, he buys 5 hamburgers and 4 colas and spends$32. 5H + 4C = 32 Assuming the prices of hamburgers and colas remain constant, what ...”
April 15, 2019
Brent@GMATPrepNow posted a reply to Alice, Benjamin, and Carol each try independently to win a in the Problem Solving forum
“P(exactly 2 win) = P(A wins and B wins and C loses OR B wins and C wins and A loses OR A wins and C wins and B loses) = P(A wins and B wins and C loses) + P(B wins and C wins and A loses) + P(A wins and C wins and B loses) Let''s calculate each probability P(A wins and B wins and C loses) = ...”
April 15, 2019
Brent@GMATPrepNow posted a reply to If n is an integer, is (100−n)n an integer? in the Data Sufficiency forum
“Target question: Is (100 - n)/n an integer? Statement 1: n > 4 Let''s TEST some values There are infinitely many values of n that satisfy statement 1. Here are two: Case a: n = 5. In this case, (100 - n)/n = (100 - 5)/5 = 95/5 = 19. So, the answer to the target question is YES, (100 - ...”
April 14, 2019
Brent@GMATPrepNow posted a reply to f(x) = x^2 - x. For which of the following values of a is in the Problem Solving forum
“GIVEN: f(x) = x² - x So, f(8) = 8² - 8 = 56 I. a = -7 So, f(-7) = (-7)² - (-7) = 56 This means f(a) ≥ f(8) Check the answer choices. . . ELIMINATE B and C II. a = -8 So, f(-8) = (-8)² - (-8) = 72 This means f(a) ≥ f(8) Check the answer choices. . . ELIMINATE A II. a = -9 ...”
April 14, 2019
Brent@GMATPrepNow posted a reply to What is the largest value of integer n such that in the Problem Solving forum
“98 = (2)(7)(7) = (2^1)(7^2) So, 98^98 = (2^1)(7^2)]^98 = (2^98)(7^196) What is the largest value of integer n such that 98^98 is divisible by 7^n? Since 98^98 = (2^98)(7^196), the largest value of n is 196 Answer: E Cheers, Brent”
April 14, 2019
Brent@GMATPrepNow posted a reply to A certain series is defined by the following recursive rule: in the Problem Solving forum
“I''m not crazy about this question. Typically, when we talk about series, Sn represents the SUM of the first n terms of that series. However, based on the official answer, Sn seems to represent the value of TERM n. Cheers, Brent”
April 12, 2019
Brent@GMATPrepNow posted a reply to Mary and Kate are running clockwise around a circular track in the Problem Solving forum
“To get a better idea of what''s happening, let''s sketch the set-up: https://i.imgur.com/SwHzFJD.png Mary is faster than Kate, we can say that Kate has a 250 meter head start. In other words, when Mary closes that 250-meter gap, she will pass Kate for the FIRST time. ...”
April 11, 2019
Brent@GMATPrepNow posted a reply to What is the sum of the cubes of the first ten positive? in the Problem Solving forum
“Let''s look for a pattern 1³ = 1 = 1² 1³ + 2³ = 9 = 3² 1³ + 2³ + 3³ = 36 = 6² 1³ + 2³ + 3³ + 4³ = 100 = 10² 1³ + 2³ + 3³ + 4³ + 5³ = 225 = 15² See the pattern yet? 1 + 2 = 3 3 + 3 = 6 6 + 4 = 10 10 + 5 = 15 First we add 2, then we add 3, then 4, then 5, etc ...”
April 11, 2019
Brent@GMATPrepNow posted a reply to If 0.00012345 is between 1/10^n and 1/10^{n-1}, what is the in the Problem Solving forum
“We need to examine powers of 10 that are smaller than AND greater than 0.00012345 We know that: 0.0001 < 0.00012345 < 0.001 Rewrite as FRACTIONS to get: 1/10,000 < 0.00012345 < 1/1,000 Rewrite as POWERS OF 10 to get: 1/10⁴ < 0.00012345 < 1/10³ We''re told that 0.00012345 ...”
April 10, 2019
Brent@GMATPrepNow posted a reply to GMAT Prep Practice Test Quant Questions #4 in the GMAT Math forum
“ Given: wx = y Target question: What is the value of xy ? Statement 1: wx²= 16 We can rewrite this as: (wx)(x) = 16 Since wx = y, we can replace wx with y to get: (y)(x) = 16 So, the answer to the target question is xy = 16 Since we can answer the target question with certainty, ...”
April 9, 2019
Brent@GMATPrepNow posted a reply to A camera lens filter kit containing 5 filters sells for $in the Problem Solving forum “2 of them are priced at$10.45 each, 2 at $12.05 each, 1 at$17.50 TOTAL cost when purchased individually = (2 x $10.45) + (2 x$12.05) + (1 x $17.50) =$20.90 + $24.10 +$17.50 = $62.50 The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased ...” April 9, 2019 Brent@GMATPrepNow posted a reply to Machine A produces pencils at a constant rate of 9000 in the Problem Solving forum “To MINIMIZE machine B''s operating time, we must MAXIMIZE the time machine A''s operating time. So, let machine A operate for the full 8 hours. In 8 hours, machine A produces 72,000 pencils So, the number of pencils machine B must make = 100,000 - 72,000 = 28,000 Time = output/rate So, ...” April 9, 2019 Brent@GMATPrepNow posted a reply to Any decimal that has only a finite number of nonzero digits in the Data Sufficiency forum “Target question: Is r/s a terminating decimal? Statement 1: 90 < r < 100 There are several pairs of values that meet this condition. Here are two: Case a: r = 91 and s = 2, in which case r/s = 91/2 = 45.5 = a terminating decimal Case b: r = 91 and s = 3, in which case r/s = 91/3 = ...” April 8, 2019 Brent@GMATPrepNow posted a reply to A sewing store buys fabric X by the bolt at the wholesale in the Data Sufficiency forum “Target question: What is the wholesale price of a bolt of fabric X? Given: Each bolt contains 50 meters of fabric X Statement 1: The store sells fabric X for$6.25 per meter. No information about the relationship between the WHOLESALE price and the RETAIL price Statement 1 is NOT ...”
April 8, 2019
Brent@GMATPrepNow posted a reply to There are 10 books on a shelf: 5 English books, 3 Spanish in the Problem Solving forum
“Let''s use the complement. That is, P(Event A happening) = 1 - P(Event A not happening) So, here we get: P( 2 different languages) = 1 - P(NOT 2 different languages) So, we can write: P(2 different languages) = 1 - P(the 2 languages are the SAME) P(the 2 languages are the SAME) P(the 2 ...”
April 8, 2019
Brent@GMATPrepNow posted a reply to Any feedback on the Orion GMAT prep? in the Helpful Resources forum
“Sorry - I know almost nothing about that company. Cheers, Brent”
April 7, 2019
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Data Sufficiency lesson #6: - Rephrasing the Target Question Video : https://www.youtube.com/watch?v=MyG1K3ee69w Cheers, Brent”
April 7, 2019
Brent@GMATPrepNow posted a reply to In a certain game only one player can win and only one in the Data Sufficiency forum
“Target question: What is the probability that Katelyn wins at least one of the 3 games? This is a good candidate for rephrasing the target question. In order to determine P(Katelyn wins at least one of the 3 games), we need to know the probability that Katelyn wins if they play ONE game. We ...”
April 7, 2019
Brent@GMATPrepNow posted a reply to Question of the Week - 3 (The value of the variable E is...) in the Problem Solving forum
“A fast approach is to use some estimation. E = 1/2 + 1/4 + 1/6 + 1/8 + 1/10 + 1/12 + 1/14 + 1/16 + 1/18 + 1/20 ≈ 0.5 + 0.25 + 0.15 + 0.1 + 0.1 + 0.1 + 0.05 + 0.05 + 0.05 + 0.05 ≈1.4 Which of the following can be a possible value of the reciprocal of E? The reciprocal of E ...”
April 7, 2019
Ian Stewart posted a reply to Harry and Ron work for the same company but earn different in the Data Sufficiency forum
“Say Harry earns $H, and has$E in expenses, while Ron earns $R, and spends$S. Then Harry saves H-E dollars, and Ron saves R-S dollars. Statement 1 tells us: H + S > R + E H - E > R - S or in other words, Harry''s savings exceed Ron''s savings. Now, it''s not clear what is meant ...”
April 6, 2019
Ian Stewart posted a reply to n is a positive integer greater than 2. If y = 9^0 + 9^1+ in the Data Sufficiency forum
“If you look at the units digits of various powers of 9, you''ll see they alternate between 1 and 9: 9^0 ends in 1 9^1 ends in 9 9^2 ends in 1 9^3 ends in 9 and so on. So if we add 9^0 + 9^1 + 9^2 + ... + 9^n, we''ll get something ending in 0 when n is even, and something ending in 1 when n ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to Is the positive integer x an even number? in the Data Sufficiency forum
“OA=E Target question: Is x an even number? Jump straight to..... Statements 1 and 2 combined There are infinitely many values of x that satisfy BOTH statements. Here are two: Case a: x = 32. In this case, the answer to the target question is YES, x IS an even number Case b: x = 17. ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to During a trip that they took together, Carmen, Juan, Maria, in the Problem Solving forum
“Let x = the number of miles Rafael drove Average = 80 So, (72 + 78 + 83 + x)/4 = 80 Multiply both sides by 4 to get: 72 + 78 + 83 + x = 320 Simplify: 233 + x = 320 Solve: x = 87 Answer: D”
April 6, 2019
Brent@GMATPrepNow posted a reply to If a certain animated cartoon consists of a total of 17,280 in the Data Sufficiency forum
“Target question: How many minutes will it take to run the cartoon? Given: cartoon consists of a total of 17,280 frames Statement 1: The cartoon runs without interruption at the rate of 24 frames per second. Time = (output)/(rate) So, time = (17,280 frames)/(24 frames per second) NOTE: ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to While a family was away on vacation, they paid in the Problem Solving forum
“..... paid a neighborhood boy $11 per week to mow their lawn... So, in 3 weeks, the amount the family paid for lawn-moving = (3 weeks)($11/week) = $33 ...the family paid$4 per DAY to feed and walk their dog... 3 weeks = 21 DAYS So, the amount the family paid for dog care = (21 days)($4/day) = ...” April 6, 2019 Brent@GMATPrepNow posted a reply to Last year$48,000 of a certain store's profit was shared in the Problem Solving forum
“Each owner received 3 times as much as each employee Let E = the amount (in dollars) that ONE employee received So, 3E = the amount (in dollars) that ONE owner received Last year \$48,000 of a certain store''s profit was shared by its 2 owners and their 10 employees. In other words: 3E + 3E + ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to Alice is twice as old as Brian and Cathy is 6 years in the Problem Solving forum
“GIVEN: Alice is a years old Alice is twice as old as Brian This also means Brian is HALF as old as Alice So, Brian''s age = a/2 Cathy is 6 years younger than Brian So, Cathy''s age = (Brian''s age) - 6 So, Cathy''s age = (a/2) - 6 How old is Cathy in terms of a ? Cathy''s age = (a/2) - ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to For all numbers m and n... in the Problem Solving forum
“GOAL: Find the value of 4?3 GIVEN: m?n = (2m - n)(m+ n) So, 4?3 = (2(4) - 3)(4+ 3) = (5)(7) = 35 Answer: A Cheers, Brent”
April 6, 2019
Brent@GMATPrepNow posted a reply to If x and y are two points on the number line what is the in the Data Sufficiency forum
“Target question: What is the value of x + y? Statement 1: 6 is halfway between x and y. KEY CONCEPT: The average (arithmetic mean) of 2 numbers is HALFWAY between those 2 numbers. For example, the average of 1 and 9 is 5. Notice that 5 is HALFWAY between 1 and 9. So, statement is ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to The residents of Town X participated in a survey to in the Problem Solving forum
“---------ASIDE-------------------- A little extra background on standard deviations above and below the mean If, for example, a set has a standard deviation of 4, then: 1 standard deviation = 4 2 standard deviations = 8 3 standard deviations = 12 1.5 standard deviations = 6 0.25 ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to In the xy-coordinate system, line k has slope 1/2 and passes in the Problem Solving forum
“Let''s first determine the equation of line k A quick approach is the write the equation of line k in slope y-intercept form: y = mx + b, where m = slope and b = y-intercept. We''re told that the slope = 0.5 and the point (0,5) tells us that the y-intercept is 5 So, the equation of line k is: ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to In a certain office, the ratio of men to women is 3/4. in the Problem Solving forum
“Another approach: Let M = number of men CURRENTLY in the office Let W = number of women CURRENTLY in the office In a certain office, the ratio of men to women is CURRENTLY 3/4. We can write: M/W = 3/4 Cross multiply to get: 4M = 3W Rewrite as: 4M - 3W = 0 If 10 men were added to the ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to In a certain office, the ratio of men to women is 3/4. in the Problem Solving forum
“In a certain office, the ratio of men to women is 3/4. This tells us that, out of EVERY 7 people in the office, 3 are men and 4 are women. It also tells us that the TOTAL number of men and women currently in the office is divisible by 7 When we check the answer choices, we see that A, B and E ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to In the diagram above, points A, B, C, D, and E represent the in the Problem Solving forum
“points A, B, C, D, and E represent the five teams in a certain league in which each team must play each of the other teams exactly once. Let''s first determine the total number of games that will be played. There are 5 teams, so each team will play 4 games (since a team can''t play itself) So, ...”
April 6, 2019
Ian Stewart posted a reply to Is BG > EC? in the Data Sufficiency forum
“BG is the height of triangle ABC (when we use AC as our base), and EC is the height of triangle DEF (when we use DF as our base). It''s confusing to use all those capital letters, so let''s use ''h'' for the height BG, and ''j'' for the height EC. We also have three important lengths along the ...”
April 6, 2019
Ian Stewart posted a reply to If a certain positive integer is divided by 9, the ..... in the Data Sufficiency forum
“Statement 1 tells us our number is 30 greater than some multiple of 45, so our number is equal to 45q + 30, for some integer q. But 45q + 30 = 5(9q + 6), which is clearly divisible by 5, so the remainder is 0 when we divide our number by 5, and Statement 1 is sufficient, even without using any ...”
April 6, 2019
Ian Stewart posted a reply to In the figure above, if the length of MO is 10 in the Data Sufficiency forum
“If you knew that the seemingly-vertical line of length ''h'' was at right angles to the line MO, then it would be easy, with both statements, to use Pythagoras to find the lengths of all of the sides. But without knowing if we have a right angle there, we can''t do much, and the answer is E. ...”
April 5, 2019
Brent@GMATPrepNow posted a reply to John and Mary were each paid x dollars in advance to do a in the Problem Solving forum
“One approach: Salary Mary''s NET salary was x - y dollars (because Mary gave John y dollars) John''s NET salary was x + y dollars Hours worked Mary worked 8 hours John worked 10 hours In the end, John and Mary received the SAME hourly wage. So, John''s hourly wage = Mary''s ...”
April 5, 2019
Brent@GMATPrepNow posted a reply to On a certain sightseeing tour, the ratio of the number in the Data Sufficiency forum
“Let W = # of women Let M = # of men Let C = # of children Target question: What is the value of M? Given: The ratio of the number of women to the number of children was 5 to 2 In other words, W : C = 5 : 2 Statement 1: On the sight-seeing tour, the ratio of the number of children to ...”
April 5, 2019
Brent@GMATPrepNow posted a reply to Five friends - Ross, Phoebe, Chandler, Joey, and Monica in the Problem Solving forum
“Take the task of feeding the 5 friends and break it into stages. We’ll begin with the most restrictive stage(s). Stage 1: Select a pizza for Phoebe Since Phoebe will only eat Margherita pizza, there''s only 1 pizza we can serve her. So, we can complete stage 1 in 1 way Stage 2: ...”
April 5, 2019
Brent@GMATPrepNow posted a reply to The y intercept of a line L is 4. If the slope of L is in the Problem Solving forum
“Let''s draw a bunch of lines with a negative slope AND have a y-intercept of 4 (ie, passes through the point (0,4)) We get: http://i1168.photobucket.com/albums/r500/GMATPrepNow/x-int_zpsswbinqns.png As we can see, the x-intercept can have ANY POSITIVE value. So, the x-intercept COULD be 6, ...”
April 5, 2019
Brent@GMATPrepNow posted a reply to In the rectangular solid above, if each dimession of the in the Data Sufficiency forum
“Here''s a very similar (official) practice question: https://www.beatthegmat.com/volume-of-rectangular-solid-t273956.html Cheers, Brent”
April 5, 2019
Brent@GMATPrepNow posted a reply to Is x < 0? in the Data Sufficiency forum
“Target question: Is x < 0? Two important rules: ODD exponents preserve the sign of the base. So, (NEGATIVE)^(ODD integer) = NEGATIVE and (POSITIVE)^(ODD integer) = POSITIVE An EVEN exponent always yields a positive result (unless the base = 0) So, (NEGATIVE)^(EVEN integer) = ...”
April 5, 2019
Brent@GMATPrepNow posted a reply to In the sequence S, each term after the first is twice the in the Problem Solving forum
“term1 = 3 term2 = (3)(2) = (3)(2¹) term3 = (3)(2)(2) = (3)(2²) term4 = (3)(2)(2)(2) = (3)(2³) term5 = (3)(2)(2)(2)(2) = (3)(2⁴) . . term14 = (3)(2^13) term15 = (3)(2^14) term16 = (3)(2^15) What is the sum of the 14th, 15th, and 16th terms in sequence S? Sum = (3)(2^13) + ...”
April 5, 2019
Brent@GMATPrepNow posted a reply to If x, y, and d are integers and d is odd, are both x and y in the Data Sufficiency forum
“ Given: x, y, and d are integers and d is odd Target question: Are both x and y divisible by d? Statement 1: x+y is divisible by d. Let''s TEST some values. There are several values of x, y and d that satisfy statement 1. Here are two: Case a: x = 6, y = 9 and d = 3. Notice that 6+9 = ...”
April 4, 2019
Brent@GMATPrepNow posted a reply to m and n are positive integers. Are m and n consecutive integ in the Data Sufficiency forum
“ Given: m and n are positive integers. Target question: Are m and n consecutive integers? Statement 1: m² + n² = 5 Since m and n are positive integers, there are only two possible solutions: Solution #1: m = 1 and n = 2 Solution #2: m = 2 and n = 1 In BOTH possible cases, the ...”
April 3, 2019
Brent@GMATPrepNow posted a reply to If Norbert can cut up one plastic six pack container in 30 in the Problem Solving forum
“We can solve this question by applying equivalent ratios For every 30 seconds that elapse, Norbert can cut up 1 plastic six-pack container In other words, for every 0.5 MINUTES that elapse, Norbert can cut up 1 plastic six-pack container Let t = the time (in MINUTES) to cut up 512 plastic ...”
April 2, 2019
Brent@GMATPrepNow posted a reply to For what percent of those tested for a certain infection was in the Data Sufficiency forum
“I just want to point out that Jay has done a perfect job employing a technique known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it. Here, we have a population of patients, and the ...”
April 2, 2019
Ian Stewart posted a reply to What is the value of 10^x · 10^y? in the Data Sufficiency forum
“I imagine there''s a typo in the question somewhere, because as written, the statements aren''t consistent, and the answer is not D (it would be A). It seems more likely the question is meant to say something like: What is $$10^x 10^y$$ ? 1. 2^(x+y) = 16 2. 5^(x+y) = 625 Since 10^x * 10^y ...”
April 1, 2019
Ian Stewart posted a reply to Barry walks from one end to the other of a 30-meter long in the Problem Solving forum
“If s is his speed, and w the speed of the walkway, then when he walks with the walkway, his net speed is s+w, and when he walks against the walkway, his net speed is s-w. Using the familiar S = D/T equation for both cases, we have: s+w = 30/30 = 1 s-w = 30/120 = 1/4 and adding these two ...”
April 1, 2019
Ian Stewart posted a reply to For any given x and any positive integer n in the Problem Solving forum
“For any sequence question, it is usually a good idea to work out the first few terms until you understand the structure of the sequence. Here, if s_n = x^(2n - 1) then plugging in n =1, 2 and 3 we find: s_1 = x^1 s_2 = x^3 s_3 = x^5 and so on. We want to multiply these terms together, ...”
April 1, 2019
Ian Stewart posted a reply to For positive integers n, the integer part of the nth term in the Problem Solving forum
“The digits long after the decimal point are not going to matter here, since they only make a minuscule contribution to the sum, and we only need a rough estimate. If we work out the first seven terms, truncating each to one decimal place, we have: 1.2 2.4 3.6 4.8 5.1 6.1 7.1 When we ...”
April 1, 2019
Ian Stewart posted a reply to Is xy > 0? in the Data Sufficiency forum
“xy > 0 will be true if x and y have the same sign, so if both are positive, or if both are negative. x^2 is always positive or zero, so Statement 1 tells us almost nothing (it only tells us x is not zero). In Statement 2, we can divide by y^2 on both sides, because we know y^2 is positive (so ...”
April 1, 2019
Ian Stewart posted a reply to Is the slope of line z positive? in the Data Sufficiency forum
“If two lines are perpendicular, their slopes are negative reciprocals, so if one line has a slope of m, the other has a slope of -1/m. So from Statement 1, if line m has a slope of -1/4, the perpendicular line z must have a slope of 4, and Statement 1 is sufficient. Knowing about one point on a ...”
April 1, 2019
Brent@GMATPrepNow posted a reply to What is the number of cans that can be packed in a certain in the Data Sufficiency forum
“Target question: What is the number of cans that can be packed in a certain carton? Let''s head straight to..... Statements 1 and 2 combined Consider these two conflicting cases (that satisfy BOTH statements): Case a: the dimensions of the box are numbers are 1 x 1 x 2304 (inches), in ...”
April 1, 2019
Brent@GMATPrepNow posted a reply to 2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8=? in the Problem Solving forum
“Let''s look for a pattern... We want: 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = ? 2 + 2 + 2^2 = 4 + 4 = 8 = 2^3 So, 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 2^3 + 2^3 = 2(2^3) = 2^4 So, 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 2^4 + ...”
April 1, 2019
Brent@GMATPrepNow posted a reply to If n is the smallest of three consecutive positive integers in the Problem Solving forum
“There''s a nice rule says: The product of k consecutive integers is divisible by k, k-1, k-2,...,2, and 1 So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1 Likewise, the product of any 11 consecutive integers will be divisible by 11, 10, 9, . . . 3, ...”
April 1, 2019
Brent@GMATPrepNow posted a reply to A collection of 36 cards consists of 4 sets of 9 cards in the Data Sufficiency forum
“Target question: What is the number on the card? Given: A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9. Statement 1: The units digit of the sum of the numbers on the remaining 35 cards is 6. 1+2+3+4+5+6+7+8+9=45 Since there are 4 sets of ...”
April 1, 2019
Brent@GMATPrepNow posted a reply to If x = 1 – 2y, what is z? in the Data Sufficiency forum
“Target question: What is the value of z? Given: x = 1 – 2y Statement 1: 5x + 10y + z = 5 Replace x with 1 – 2y to get: 5(1 – 2y) + 10y + z = 5 Expand: 5 - 10y + 10y + z = 5 Simplify: 5 + z = 5 Solve: z = 0 Since we can answer the target question with certainty, statement 1 is ...”
April 1, 2019
Brent@GMATPrepNow posted a reply to Is x > 0? in the Data Sufficiency forum
“Target question: Is x > 0? Statement 1: x² > 0 This statement doesn''t feel sufficient, so I''ll TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = 1. In this case, the answer to the target question is YES, it is the case that x > ...”
April 1, 2019
Brent@GMATPrepNow posted a reply to If y is the smallest positive integer such that 3,150 in the Problem Solving forum
“Key concept: The prime factorization of a perfect square (the square of an integer) will have an EVEN number of each prime. For example, 36 = (2)(2)(3)(3) And 400 = (2)(2)(2)(2)(5)(5) Likewise, 3150y must have an EVEN number of each prime in its prime factorization. So, 3150y = ...”
April 1, 2019
Ian Stewart posted a reply to Points (a, b) and (c, d) lie on line L in the coordinate in the Data Sufficiency forum
“When you subtract y-coordinates of two points, you''re just finding the distance between them purely in the vertical direction. That''s sometimes called the "rise". Similarly when you subtract x-coordinates of two points, you''re finding the purely horizontal distance between them, ...”
March 31, 2019
Ian Stewart posted a reply to If √k is not an integer, then is k a prime number? in the Data Sufficiency forum
“Using both statements, k can be 2, and thus prime, or -1, and not prime, so the answer is E.”
March 31, 2019
Ian Stewart posted a reply to Alice bought a certain number of 30 cent stamps, 35 cent in the Data Sufficiency forum
“Using Statement 2 alone, if she bought x stamps at 30 cents, and x stamps at 40 cents, she spent 70x cents in total just on those stamps. If she only spent 420 cents overall, then x clearly is no greater than 6. But if she also bought some 35 cent stamps, x must be strictly less than 6. And ...”
March 31, 2019
Ian Stewart posted a reply to If $$n$$ is a positive integer and $$r$$ is the remainder in the Data Sufficiency forum
“n-1, n and n+1 are three consecutive integers. If, as Statement 1 tells us, n is odd, then n-1 and n+1 are both even -- in fact, they are consecutive even numbers. If you take any two consecutive even integers, one of them will always be a multiple of 4, so Statement 1 guarantees that (n-1)(n+1) is ...”
March 31, 2019
Ian Stewart posted a reply to How many hours did it take Helen to drive from her house to in the Data Sufficiency forum
“Statement 1 is clearly insufficient. Using Statement 2, maybe her speed was 8 km/hr, and the total distance was 16 km, so took 2 hours. Then if her speed was 8 km/hr greater, so was 16 km/hr, she would have saved an hour. But we know there must also be a solution where her speed was 72 km/hr, ...”
March 31, 2019
Ian Stewart posted a reply to In the diagram above, O is the center of the circle and ACDE in the Data Sufficiency forum
“If you connect a diameter of a circle to a point C on the circle, you always form a right angle at C, so Statement 2 tells us nothing new, and is useless. Using only Statement 1, since we know we have a right triangle, and we know two of its sides (the hypotenuse is twice the radius, so is 4), we ...”
March 31, 2019
Ian Stewart posted a reply to In the figure above, all angles are right angles. If the len in the Data Sufficiency forum
“The perimeter of the figure is identical to the perimeter of a rectangle with sides a and b (if you just draw the two lines in the top right corner that you''d need to draw to make that rectangle, you''ll see that you''re adding a line of length v to the top side, and a line of length u to the ...”
March 31, 2019
Brent@GMATPrepNow posted a reply to If 3 less than twice a certain number is equal to 2 more in the Problem Solving forum
“Let x be the number 3 less than twice a certain number is equal to 2 more than 3 times the number We can write: 2x - 3 = 3x + 2 So: -3 = x + 2 Solve: -5 = x 5 less than 5 times the number is 5 times the number = 5(-5) = -25 So, 5 less than 5 times the number = -25 - 5 = -30 Answer: A ...”
March 31, 2019
Brent@GMATPrepNow posted a reply to Which of the following inequalities is an algebraic in the Problem Solving forum
“When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know: Rule #1: If |something| < k, then –k < something < k Rule #2: If |something| > k, then EITHER something > k OR something < -k Note: these rules assume that k is positive (A) |x| ≤ 3 ...”
March 31, 2019
Brent@GMATPrepNow posted a reply to In how many ways a criket team consisting of 5 batsmen, 4 in the Problem Solving forum
“Take the task of creating a cricket team and break it into stages. Stage 1: Select 5 batsmen Since the order in which we select the batsmen does not matter, we can use combinations. We can select 5 batsmen from 7 batsmen in 7C5 ways (21 ways) So, we can complete stage 1 in 21 ways ...”
March 29, 2019
Brent@GMATPrepNow posted a reply to What percentage of his bills did Stanley pay before their in the Data Sufficiency forum
“Target question: What percentage of his bills did Stanley pay before their due dates last month? This is a great candidate for rephrasing the target question. Aside: We have a free video with tips on rephrasing the target question: Let P = # of bills PAID before due date Let T = TOTAL # of ...”
March 29, 2019
Brent@GMATPrepNow posted a reply to If $$n$$ is a positive integer and $$r$$ is the remainder in the Data Sufficiency forum
“ Given: r is the remainder when (n² - 1) is divided by 8 Target question: What is the value of r? Statement 1: n is odd Let''s test some ODD values of n If n = 1, then n² - 1 = 1² - 1 = 0, and 0 divided by 8 leaves remainder 0. So, the answer to the target question is r = 0 If n = 3, ...”
March 29, 2019
Brent@GMATPrepNow posted a reply to If √k is not an integer, then is k a prime number? in the Data Sufficiency forum
“ Given: √k is not an integer Target question: Is k a prime number? Statement 1: k < 10 Let''s TEST some values. There are several values of k that satisfy statement 1. Here are two: Case a: k = 1.3 (√1.3 is not an integer). In this case, the answer to the target question is NO, ...”
March 29, 2019
Brent@GMATPrepNow posted a reply to The ratio of boys to girls in Class A is 3 to 4. The ratio in the Problem Solving forum
“The ratio of boys to girls in Class A is 3 to 4. Let B = number of boys in class A Let G = number of girls in class A We get: B/G = 3/4 Cross multiply to get: 4B = 3G Class A has one more boy and two more girls than class B So B - 1 = number of boys in class B So G - 2 = number of girls in ...”
March 29, 2019
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Data Sufficiency lesson #5: - Summarizing Information Video : https://www.youtube.com/watch?v=cK9PR3SLsSA Cheers, Brent”
March 27, 2019
Brent@GMATPrepNow posted a reply to The water from one outlet, flowing at a constant rate, can in the Problem Solving forum
“So, let''s say that the volume of the pool is 45 gallons. The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours So, this outlet pumps at a rate of 5 gallons per hour The water from a second outlet, flowing at a constant rate, can fill the same pool in 5 ...”
March 27, 2019
Brent@GMATPrepNow posted a reply to If a positive integer t is not divisible by 5, how many poss in the Problem Solving forum
“Since t is NOT divisible by 5, we need only test t = 1, 2, 3 and 4 If t = 1, then t⁴ = 1, and 1 divided by 5 leaves remainder 1 If t = 2, then t⁴ = 16, and 16 divided by 5 leaves remainder 1 If t = 3, then t⁴ = 81, and 81 divided by 5 leaves remainder 1 If t = 4, then t⁴ = 256, and ...”
March 27, 2019
Brent@GMATPrepNow posted a reply to At a certain school, the student to teacher ratio is 52 to 9 in the Problem Solving forum
“There''s a nice integer properties rule that says: If j is a multiple of d, and k is NOT a multiple of d, then j-k (and j+k) is NOT a multiple of d For example, since 56 is a multiple of 7, and 11 is NOT a multiple of 7, then 56-11 is NOT a multiple of 7 At a certain school, the student to ...”
March 27, 2019
Brent@GMATPrepNow posted a new topic called At a certain school, the student to teacher ratio is 52 to 9 in the Problem Solving forum
“At a certain school, the student to teacher ratio is 52 to 9. If 38 students and 11 teachers leave, which of the following COULD represent the number of students and teachers remaining at the school? A) 532 students and 88 teachers B) 794 students and 162 teachers C) 1106 students and 225 ...”
March 26, 2019