GMATGuruNY posted a reply to If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? in the Problem Solving forum
“(r + 1/r)² = 5 r + 1/r = √5 (r + 1/r)² = 5 r² + 1/r² + 2(r)(1/r) = 5 r² + 1/r² + 2 = 5 r² + 1/r² = 3 Multiplying the blue equation and the red equation, we get: (r² + 1/r²)(r + 1/r) = 3√5 r³ + (r²)(1/r) + (1/r²)(r) + 1/r³ = 3√5 r³ + (r + 1/r) + 1/r³ = 3√5 ...”
2 minutes ago
GMATGuruNY posted a reply to A dessert recipe calls for 50% melted chocolate and 50% in the Problem Solving forum
“Chocolate percentage in the incorrect sauce: 40%. Chocolate percentage in the pure chocolate: 100%. Chocolate percentage in the mixture: 50%. Let I = the incorrect sauce and C = the pure chocolate. The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS. ...”
27 minutes ago
GMATGuruNY posted a reply to Skier Lindsey Vonn completes a straight 300-meter downhill in the Problem Solving forum
“Downhill speed - uphill speed = (x+10) - (x-8) = 18. Implication: The downhill speed is 18 mps greater than the uphill speed. We can PLUG IN THE ANSWERS, which represent the downhill speed. Since the downhill speed is 18 mps greater than the uphill speed, the correct answer must be GREATER ...”
Today
GMATGuruNY posted a reply to Jeremiah invests his savings of $120,000 by dividing it in the Problem Solving forum
“On the GMAT, compounded interest is typically just a bit more than simple interest. Since the answer choices are all greater than 2% -- the percentage given in the prompt -- they must represent the HIGHER interest rate, with 2% representing the LOWER interest rate. Lower rate: Since 3/4 of ...”
Today
GMATGuruNY posted a reply to If m and n are positive integers, is m+n divisible by 15? in the Data Sufficiency forum
“Rule: MULTIPLE OF X + MULTIPLE OF X = MULTIPLE OF X MULTIPLE OF X + NON-MULTIPLE OF X = NON-MULTIPLE OF X 225 = 9*25 Statements combined: Case 1: m=9 and n=25*15, with the result that m is a multiple of 9, n is a multiple of 15, and mn = 9*25*15 = 225*15 = multiple of 225 In this case, m+n ...”
Today
GMATGuruNY posted a reply to What is the smallest positive integer n such that n / 420 ca in the Problem Solving forum
“A fraction will yield a terminating decimal if the prime-factorization of its denominator contains only 2''s and/or 5''s. n/420 = n/(2*2*3*5*7). For a terminating decimal to be yielded, the prime factors in red must CANCEL OUT with n, leaving only 2''s and 5''s in the denominator. Thus, the ...”
Today
GMATGuruNY posted a reply to The consultant explained that companies in the Sentence Correction forum
“Generally, a one-word adverb such as tirelessly will not be positioned between a verb and its direct object. Incorrect: Companies lobby tirelessly government officials. Here, tirelessly (adverb) is awkwardly positioned between lobby (verb) and government officials (direct object). Correct: ...”
Yesterday
GMATGuruNY posted a reply to one another vs. others? in the Sentence Correction forum
“Some grammarians -- including me -- reserve each other for two elements and one another for more than two. Other grammarians consider the two modifiers interchangeable. A club has exactly three members: Ann, Beth, and Carol. The sentence above implies the following: Ann, Beth and Carol ...”
Yesterday
GMATGuruNY posted a reply to If arc PQR above is a semicircle, what is the length of diam in the Data Sufficiency forum
“An INSCRIBED ANGLE is formed by two chords. Thus, angle PQR is an inscribed angle. An inscribed angle that intercepts the diameter is a RIGHT ANGLE. Thus, angle PQR is a right angle, implying that triangle PQR is a RIGHT TRIANGLE. http://s15.postimage.org/xozmfjdh3/PQR.jpg In the figure ...”
Yesterday
GMATGuruNY posted a reply to Reiko drove from point A to point B at a constant speed, and in the Data Sufficiency forum
“Test the THRESHOLD. Since we want to know whether the speed from A to B is greater than 40mph, the threshold here is 40mph. Statement 1: Reiko''s average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour. Let the distance in each direction = 40 ...”
March 19, 2019
GMATGuruNY posted a reply to Danny spends $360 buying his favorite dolls. If he buy only in the Problem Solving forum
“Since a small doll costs $1 less than a large doll, the answer choices imply the following options for the price of a small doll: 4 5 6.2 7 8 Given that all of the values in the prompt are INTEGERS, the price of a small doll is almost certain to be a factor of 360. Only the values in blue ...”
March 18, 2019
GMATGuruNY posted a reply to Of the 25 cars sold at a car dealership, some had auto trans in the Data Sufficiency forum
“The following cases satisfy both statements: Case 1: 2 cars have neither 1 car has both antilock breaks and automatic transmission 22 cars have only automatic transmission. Case 2: 2 cars have neither 22 cars have both antilock breaks and automatic transmission 1 car has only automatic ...”
March 18, 2019
GMATGuruNY posted a reply to A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 in the Problem Solving forum
“Determine the WORST-CASE-SCENARIO -- for each color of ball, the MAXIMUM number that can be removed WITHOUT removing 5 of the same color: 3 red 4 green 4 yellow 4 blue 4 white Sum = 3+4+4+4+4 = 19 Implication: It is possible to remove 19 balls without selecting 5 of the same color. ...”
March 18, 2019
GMATGuruNY posted a reply to To fill an order, a manufacturer had to produce 1000 tools in the Data Sufficiency forum
“Prompt: Total production = 1000n Statement 1: Total production for the first 5 days = 5*600 = 3000 Statement 2: Total production for the last 4 days = 4*1500 = 6000 Case 1: n=9, with no days between the first 5 days and the last 4 days Total production = 1000n = 1000*9 = 9000 Total ...”
March 17, 2019
GMATGuruNY posted a reply to What is the sum of all values of that satisfy the equation 4 in the Problem Solving forum
“For any quadratic in the form x² + bx + c = 0: Product of the roots = c Sum of the roots = -b Given equation: 4x² + 16 = 32x 4x² - 32x + 16 = 0 x² - 8x + 4 = 0 In the resulting quadratic, b=-8. Thus: Sum of the roots = -(-8) = 8. The correct answer is E.”
March 17, 2019
GMATGuruNY posted a reply to Set P {a, b, c, d, e, f, g} Set Q {a, b, c, d, e, f} in the Problem Solving forum
“One approach: Show that four of the five answers do NOT have to be true. P--> a=1, b=2, c=3, d=5, e=6, f=7, g=4 Range = 7-1 = 6, median = 4, mean = (1+2+3+5+6+7+4)/7 = 28/7 Q --> a=1, b=2, c=3, d=5, e=6, f=7 Range = 7-1 = 6, median = (3+5)/2 = 4, mean = (1+2+3+5+6+7)/6 = 24/6 = 4 ...”
March 17, 2019
GMATGuruNY posted a reply to If n is a positive integer and r is the remainder when in the Data Sufficiency forum
“What is the remainder when (n+1)(n-1) is divided by 8? Statement 1: Since n is odd, both n-1 and n+1 are EVEN, implying that (n-1)(n+1) = the product of two consecutive even integers. Given any two consecutive even integers, one will be a multiple of 4, while the other will be an even ...”
March 16, 2019
GMATGuruNY posted a reply to The sum of the weekly salaries of 5 employees is $3,250. If in the Problem Solving forum
“Since each salary increases by 10%, the sum increases by 10%. 10% of 3250 = 325. Average increase per employee = (total increase)/(number of employees) = 325/5 = 65. The correct answer is E.”
March 16, 2019
GMATGuruNY posted a reply to A rectangle has sides x and y and diagonal z. What is the pe in the Data Sufficiency forum
“Always look for special triangles such as 3-4-5 and 5-12-13. Statement 2: Case 1: https://i.postimg.cc/V0JX8Hqv/rectangle-with-x-y-and-z-1.png Case 2: https://i.postimg.cc/DWCWwPyX/rectangle-with-x-y-and-z-2.png Since each case will yield a different perimeter, INSUFFICIENT. Statement ...”
March 15, 2019
GMATGuruNY posted a reply to combinations in the Problem Solving forum
“The portion in red is incorrect: it should be not 4C1 but 2C1. If we select two upper case letters from two sets of twins, we must then select one lower case letter from the OTHER TWO SETS OF TWINS, yielding only two options for the lower case letter. For example: If we select A and B for the two ...”
March 15, 2019
GMATGuruNY posted a reply to If N is a positive two-digit integer, is N+1 prime? in the Data Sufficiency forum
“Good catch. In my solution, the lone exception (N=29) is now noted.”
March 14, 2019
GMATGuruNY posted a reply to If N is a positive two-digit integer, is N+1 prime? in the Data Sufficiency forum
“Statement 1: Any integer whose digits sum to a multiple of 3 must itself be a multiple of 3. Since N has a digit sum of 11, N+1 must have a digit sum of 12. One exception: If N=29, then N+1 = 30, which has a digit sum of 3. Since the digit sum of N+1 must be a multiple of 3 -- either 12 or 3 -- ...”
March 14, 2019
GMATGuruNY posted a reply to If √x+√y=7 and √x-√y=5, what is the value of xy? in the Problem Solving forum
“Adding the two equations, we get: 2√x = 12 √x = 6 x = 36 Substituting √x = 6 into √x+√y=7, we get: 6 + √y = 7 √y = 1 y = 1 Thus: xy = 36*1 = 36 The correct answer is C.”
March 14, 2019
GMATGuruNY posted a reply to If f(x)=ax^2+bx+c, where a, b and c are integers, is b=0? in the Data Sufficiency forum
“Statement 1: Since (49, 0) and (-49, 0) are both solutions, the quadratic must be as follows: f(x) = (x-49)(x+49) = x² - 49² In the resulting quadratic, b=0. Thus, the answer to the question stem is YES. SUFFICIENT. Statement 2: If x-49 is a factor of the equation, then f(49) = 0. Case ...”
March 14, 2019
GMATGuruNY posted a reply to Ashley and Vinnie work on a sales staff with 8 other in the Problem Solving forum
“From the 10 people, 5 will be selected. Thus, P(Ashley is selected) = 5/10. From the 9 remaining people, 4 will be selected. Thus, P(Vinnie is selected) = 4/9. To combine these probabilities, we multiply: 5/10 * 4/9 = 2/9. The correct answer is C. Similar problem: ...”
March 14, 2019
GMATGuruNY posted a reply to A cosmetics company would like to market a six-item gift in the Problem Solving forum
“From 10 items, the number of ways to choose a bundle of 6 = 10C6 = (10*9*8*7*6*5)/(6*5*4*3*2*1) = 210. Subtracting the 49 bundles already eliminated from consideration, we get: 210-49 = 161. The correct answer is B.”
March 13, 2019
GMATGuruNY posted a reply to Set M is composed of the positive even integers up to 100. in the Problem Solving forum
“For any EVENLY SPACED SET: Count = (biggest - smallest)/(increment) + 1. Average = (biggest + smallest)/2. Sum = (count)(average). The INCREMENT is the difference between successive values. Even integers between 2 and 100, inclusive: Here, the integers are EVEN, so the increment = 2. Count ...”
March 13, 2019
GMATGuruNY posted a reply to A set of 51 different integers has a median of 30 and a in the Problem Solving forum
“Range = biggest - smallest Smallest = biggest - range Since the range = 60, we get: Smallest = biggest - 60 To minimize the smallest integer, we must minimize the biggest integer. Since the median of the 51 distinct integers = 30, there must be 25 integers above 30, with the other 25 ...”
March 13, 2019
GMATGuruNY posted a reply to What is the sum of the integers from 1 to 999, inclusive? A in the Problem Solving forum
“For any set of consecutive integers: Count = biggest - smallest + 1. Average = (biggest + smallest)/2. Sum = (count)(average). In the set above: Count = 999 - 1 + 1 = 999. Average = (999 + 1)/2 = 500. Sum = (999)(500) = (1000-1)(500) = 500000-500 = 499500. The correct answer is B.”
March 13, 2019
GMATGuruNY posted a reply to Peter and Tom shared the driving on a certain trip. If Peter in the Problem Solving forum
“Let the time for each driver = 1 hour. Let the total distance = 5 miles, implying that Peter''s distance = (2/5)(5) = 2 miles and that Tom''s distance = 5-2 = 3 miles. Since Peter drives 2 miles in 1 hour, Peter''s rate = 2 mph. Since Tom drives 3 miles in 1 hour, Tom''s rate = 3 mph. Thus: ...”
March 13, 2019
GMATGuruNY posted a reply to Which of the following could be the number of diagonals of a in the Problem Solving forum
“To form a diagonal, we must choose 2 vertices. But any pair of vertices that forms a side of the polygon cannot serve to form a diagonal. Thus: Number of diagonals = (number of ways to choose 2 vertices) - (number of sides of the polygon) When the prompt includes the phrase which of the ...”
March 12, 2019
GMATGuruNY posted a reply to Alice, Bob, Cindy, Darren, Eddie, Fabian sit on six chairs a in the Problem Solving forum
“To count circular arrangements: 1. Place someone in the circle 2. Count the number of ways to arrange the REMAINING people Once Alice has been placed in the circle: Number of options for Bob = 1. (Must be in the seat opposite Alice) Number of options for Cindy = 4. (Any of the 4 remaining ...”
March 12, 2019
GMATGuruNY posted a reply to If x and y are positive integers, x/y=? in the Data Sufficiency forum
“Statement 1: Case 1: x=2 and y=1, with the result that 2^(x+y) * 3^(xy) = 2³3² = 72 In this case, x/y = 2/1 = 2. Case 2: x=1 and y=2, with the result that 2^(x+y) * 3^(xy) = 2³3² = 72 In this case, x/y = 1/2 = 1/2. Since x/y can be different values, INSUFFICIENT. Statement 2: Here, x=2 ...”
March 12, 2019
GMATGuruNY posted a reply to Roman City in the Critical Reasoning forum
“E: mosaic designs with which artisans who lived in various parts of the Roman Empire were familiar. Here, the two blue portions constitute an adjective serving to modify designs. Question: What KIND of designs? Answer: Designs WITH WHICH ARTISANS WERE FAMILIAR. Put another way: Artisans were ...”
March 11, 2019
GMATGuruNY posted a reply to Carmen currently works 30 hours per week at her part-time jo in the Data Sufficiency forum
“Rate and time have a RECIPROCAL relationship. If the hourly rate DOUBLES, then the same income will be yielded in 1/2 the total time. Statement 1: Actual hourly rate = 225/30 = $7.50, implying that an additional $1.50 per hour will increase the hourly rate to $9. (increased hourly ...”
March 11, 2019
GMATGuruNY posted a reply to schistosomiasis and malaria. in the Critical Reasoning forum
“M --> more than 50% of all disease cases over the past 5 years S --> 40% of all disease cases 5 years ago, 30% of all disease cases now For each answer choice: Try to devise a case that aligns with the information in the passage but CONTRADICTS the answer choice, thus proving that the ...”
March 9, 2019
GMATGuruNY posted a reply to Verbal Review 18 : Kudzu, an Asian vine in the Sentence Correction forum
“Generally, COMMA + SINCE after a clause serves to express a CAUSAL relationship. An OA in GMATPrep: Prospecting for gold was a relatively easy task, since erosion put gold literally within reach of anybody with a pan. Here, the clause in blue serves to express what CAUSED prospecting to be a ...”
March 9, 2019
GMATGuruNY posted a reply to If p is a positive integer, is 2p + 1 prime? in the Data Sufficiency forum
“Statements combined: Case 1: p=11 --> p is prime, but its units digits is not prime In this case, 2p+1 = 2*11 + 1 = 23. Since 23 is prime, the answer to the question stem is YES. Case 2: p=19 --> p is prime, but its units digit is not prime In this case, 2p+1 = 2*19 + 1 = 39. Since 39 ...”
March 9, 2019
GMATGuruNY posted a reply to If a certain reel of film runs at 5/6 of a frame per second, in the Problem Solving forum
“2580 frames * (1 second)/(5/6 frame per second) * (1 minute)/(60 seconds) = 2580/50 = a little over 50 minutes. The correct answer is B.”
March 9, 2019
GMATGuruNY posted a reply to When positive integer x is divided by positive interger y, in the Problem Solving forum
“When one positive integer is divided by another, we typically represent what is left over as a REMAINDER or as a DECIMAL. There is a relationship between the two representations: Remainder/Divisor = Decimal. When 5 is divided by 2: Remainder representation: 5/2 = 2 R1 Decimal ...”
March 8, 2019
GMATGuruNY posted a reply to The R students in a class agree to contribute equally to buy in the Problem Solving forum
“Let y=$10 and R=10 students, with the result that the original share per student = ($10)/(10 students) = $1. Let x=9, implying that the number of students decreases by 9 to 1. New share per student = ($10)/(1 student) = $10. Increase in share per student = 10-1 = $9. The correct answer must ...”
March 8, 2019
GMATGuruNY posted a reply to Is the average (arithmetic mean) of x, y, and z equal to the in the Data Sufficiency forum
“Statement 1: In other words, y is HALFWAY BETWEEN x and z, implying that x, y and z are EVENLY SPACED. For any evenly spaced set, the average = the median. Thus, the answer to the question stem is YES. SUFFICIENT. Statement 2: x+z = 2y (x+z)/2 = y Implication: y is the average of x and z ...”
March 7, 2019
GMATGuruNY posted a reply to What is the remainder when -12 is divided by -5? in the Problem Solving forum
“This problem is not relevant to the GMAT. On the GMAT, problems involving remainders are constrained to POSITIVE INTEGERS. From the Math Review in the OG: If x and y are positive integers, there exist unique integers q and r, called the quotient and remainder, respectively, such that y = xq + r ...”
March 7, 2019
GMATGuruNY posted a reply to A triangle of area 30 is formed by the line x/c + y/(c+7) - in the Problem Solving forum
“Given that the area and the answer choices are all integers, the triangle is probably a Pythagorean Triple. The only Pythagorean Triple with an area of 30 is 5-12-13. In the given equation, test c=5, with the result that c+7 = 12: x/5 + y/12 - 1 = 0 If x=0, then y=12, implying a y-intercept ...”
March 5, 2019
GMATGuruNY posted a reply to Joey works at a clothing store and receives an employee in the Problem Solving forum
“Since the discount = 10% = 1/10, and the resulting discount price is an integer value, the regular price must be a dollar value that is a multiple of 10. The correct answer is E.”
March 5, 2019
GMATGuruNY posted a reply to When 32 is divided by k, the remainder is k-3. What is the in the Data Sufficiency forum
“Dividing 32 by k leaves a remainder of k-3. In other words, 32 is equal to k-3 more than a multiple of k: 32 = ak + (k-3), where a is a nonnegative integer and k is an integer such that k≥3. Simplifying 32 = ak + (k-3), we get: 35 = ak + k 35 = k(a+1) The resulting equation implies that ...”
March 5, 2019
GMATGuruNY posted a reply to If x and y are positive integers and (x-y)^2+y^2=25, which o in the Problem Solving forum
“Identify two perfect squares that sum to 25: 1, 4, 9, 16... The two values in blue sum to 25. If y=3 and x=7, then (x-y)² = (7-3)² = 16 and y² = 9, with the result that (x-y)² + y² = 25. The correct answer is B.”
March 5, 2019
GMATGuruNY posted a reply to OG Before 1988, insurance companies in California in the Sentence Correction forum
“Generally, COMMA + VERBing serves to modify the nearest preceding action and the agent of this action. Given this rule, I received a PM requesting that I justify the usage of COMMA + needing in the OA: Insurance companies in California were free to charge whatever rates the market would bear, ...”
March 3, 2019
GMATGuruNY posted a reply to In a certain school, there are 160 boys and 240 girls. If 15 in the Problem Solving forum
“Left-handed boys = 15% of 160 = 24. Left-handed girls = 25% of 240 = 60. (total left-handed)/(total students) = (24+60)/(160+240) = 84/400 = 21/100 = 21%. The correct answer is C.”
March 2, 2019
GMATGuruNY posted a reply to If \(2^{4x}=3,600\), what is the value of \((2^{(1-x)})^2\)? in the Problem Solving forum
“\((2^{(1-x)})^2\) = \(2^{2-2x}\) = \(2^2/2^{2x}\) = \(4/2^{2x}\) We need to know the value of \(2^{2x}\): \(2^{4x}=3,600\) \((2^{2x})^2=3,600\) \(2^{2x}= 60\) Substituting \(2^{2x}= 60\) into \(4/2^{2x}\), we get: 4/60 = 1/15 The correct answer is B.”
March 2, 2019
GMATGuruNY posted a reply to Car B starts at point X and moves clockwise around a circula in the Problem Solving forum
“π ≈ 3. Car B is traveling for more than 10 hours, so answer choices D and E are too small, and A is unlikely. The correct answer is either B or C. Circumference of track = 20π ≈ 60 miles. In 10 hours, distance for B = 2*10 = 20 miles. 60-20 = 40 miles between A and B. A and B now ...”
March 2, 2019
GMATGuruNY posted a reply to Which of following satisfies the inequality (2x-49)(x^2+6x+1 in the Problem Solving forum
“The two factors must have DIFFERENT SIGNS. Each of the answer choices will yield a positive value for x² + 6x + 10. Thus, the correct answer must yield a negative value for 2x-49. Only A is viable: (2*24) - 49 = -1. The correct answer is A.”
March 1, 2019
GMATGuruNY posted a reply to Andrew bought pizzas for his swim team. Pepperoni pizzas in the Problem Solving forum
“Posted and answered about a week ago: https://www.beatthegmat.com/andrew-bought-pizzas-for-his-swim-team-pepperoni-pizzas-cos-t306615.html#827261”
March 1, 2019
GMATGuruNY posted a reply to The three squares above share vertex A with AF = FE and AE = in the Problem Solving forum
“Let AF=FE=1, with the result that AE=ED=2: https://i.postimg.cc/2qmj2KbL/probability-and-three-squares.png As the figure illustrates: shaded region = 1+1+1 = 3 ABCD = 4*4 = 16 shaded/ABCD = 3/16 The correct answer is D.”
March 1, 2019
GMATGuruNY posted a reply to In a certain clothing store, the most expensive pair of in the Problem Solving forum
“Option D indicates that 12 pairs of cheap socks can be bought, not 9. Unfortunately, 9 is not among the answer choices. The OA implies that each pair of cheap socks costs not $2 but $1.50. Because $1.50 is not an integer value, the brute-force approach is a bit tricky here.”
March 1, 2019
GMATGuruNY posted a reply to In a certain clothing store, the most expensive pair of in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the number of cheap pairs that can be purchased for $18. When the correct answer is plugged in, the number of expensive pairs that can be purchased will be 3 less than the number of cheap pairs that can be purchased. B will yield an ugly price for each ...”
February 28, 2019
GMATGuruNY posted a reply to Working simultaneously and independently at an identical con in the Problem Solving forum
“Use the following equation: (machines)(time) / output = (machines)(time) / output In the equation above: Machines and time are INVERSELY PROPORTIONAL. As the number of machines increases, the amount of time required to produce the same output decreases. Machines and output are DIRECTLY ...”
February 28, 2019
GMATGuruNY posted a reply to The restorative power of sleep is graphically approximated b in the Problem Solving forum
“Multiplying the equation by -1, we get: y = x² - 16x - 36 y = (x-18)(x+2) The restorative power -- the value of y -- is equal to 0 when x=18 or x=-2. Since the time cannot be a negative value, only x = 18 hours is viable. The correct answer is E.”
February 28, 2019
GMATGuruNY posted a reply to In June 1989, what was the ratio of the number of sales tran in the Data Sufficiency forum
“What is (June X)/(June Y)? Statement 1: In June 1989, Salesperson X made 50 percent more sales transactions than Salesperson Y did in May 1989. (June X)/(May Y) = 150/100 = 3/2. INSUFFICIENT. Statement 2: In June 1989, Salesperson Y made 25 percent more sales transactions than in May ...”
February 28, 2019
GMATGuruNY posted a reply to How many whole numbers between 100 and 400, inclusive, conta in the Problem Solving forum
“(integers with the digit 2) = (all integers between 100 and 399, inclusive) - (integers without the digit 2) All integers between 100 and 399, inclusive: For any set of consecutive integers, count = biggest - smallest + 1. In this case: count = 399-100+1 = 300 Integers without the digit 2: ...”
February 27, 2019
GMATGuruNY posted a reply to A square playground has the same area as a rectangular in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent a side of the square. Since the dimension of the rectangular playground are INTEGER values, the correct answer is probably also an integer. When the correct answer is plugged in, the square and the rectangle will have the same area. D: 50, implying ...”
February 27, 2019
GMATGuruNY posted a reply to Two hoses are pouring water into an empty pool. Hose 1 alone in the Problem Solving forum
“Let the pool = 12 gallons. Since Hose 1 takes 6 hours to fill the 12-gallon pool, the rate for Hose 1 = w/t = 12/6 = 2 gallons per hour. Since Hose 2 takes 4 hours to fill the 12-gallon pool, the rate for Hose 2 = w/t = 12/4 = 3 gallons per hour. Since the combined rate for the two hoses = 2+3 = ...”
February 27, 2019
GMATGuruNY posted a reply to What is the value of a+b? in the Data Sufficiency forum
“Statements combined: Adding the two equations, we get: a² + b²+ 2ab - 2a - 2b = 63 (a+b)² - 2(a+b) = 63 (a+b)(a+b-2) = 63 Let x = a+b. Substituting x=a+b into (a+b)(a+b-2) = 63, we get: (x)(x-2) = 63 x² - 2x - 63 = 0 (x-9)(x+7) = 0 x=9 or x=-7 Since x=a+b, it is possible that ...”
February 26, 2019
GMATGuruNY posted a reply to On a Saturday night, each of the rooms at a certain motel in the Problem Solving forum
“If 10 rooms are rented for $40 instead of $60 -- a decrease of $20 per room -- the total decrease = 10*20 = $200. Since the value in blue constitutes a 25% reduction in the total rent, it must be equal to 1/4 of the total rent: 200 = (1/4)R 800 = R. The correct answer is B.”
February 26, 2019
GMATGuruNY posted a reply to A manufacturer makes umbrellas at the cost of c dollars per in the Problem Solving forum
“How many umbrellas can it afford to sell at the below-cost rate of b dollars per umbrella and still make a 100% profit? If c=1 and r=2 -- implying that the cost per umbrella = $1 and that the retail price per umbrella = $2 -- then 100% profit will be yielded only if ALL of the umbrellas are sold at ...”
February 26, 2019
GMATGuruNY posted a reply to On rainy mornings, mo drinks exactly N cups of hot chocolate in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the number of rainy days. When the correct answer is plugged in, the total number of cups = 26. B: 3 rainy days, implying 4 non-rainy days Since 5 cups of tea are consumed are on each of the 4 non-rainy days, the total number of tea cups = 5*4 = 20. ...”
February 26, 2019
GMATGuruNY posted a reply to It takes Carlos 9 minutes to drive from home to work at an in the Problem Solving forum
“(new rate)/(old rate) = (6 miles per hour)/(22 miles per hour) = 6/22 = 3/11. Rate and time have a RECIPROCAL relationship. Since the new rate is 3/11 of the old rate, the new time must be 11/3 of the old time: (11/3)(9 minutes) = 33 minutes. The correct answer is B.”
February 26, 2019
GMATGuruNY posted a reply to A is the set of 6-digit positive integers whose first three in the Problem Solving forum
“The GMAT is unlikely to test divisibility by 7. An integer of the form XYZXYZ must be divisible by 7, but this issue seems irrelevant to the GMAT. For this reason, I''ve replaced answer choice A with the value in red: To determine whether an integer is divisible by 11: 1. From the left to ...”
February 26, 2019
GMATGuruNY posted a reply to What is the difference between the areas of the squares ABCD in the Data Sufficiency forum
“Statement 1: Case 1: DC=10 and EC=6, with the result that CDE = (1/2)(10)(6) = 30 In this case, ABCD-EFGC = 10² - 6² = 100 - 36 = 64. Case 2: DE=20 and EC=3, with the result that CDE = (1/2)(20)(3) = 30 In this case, ABCD-EFGC = 20² - 3² = 400 - 9 = 391. Since ABCD-EFGC can be different ...”
February 25, 2019
GMATGuruNY posted a reply to How many positive two-digit numbers are odd, not divisible b in the Problem Solving forum
“For any set of consecutive integers: count = biggest - smallest + 1 Thus: Number of two-digit integers between 10 and 99, inclusive = 99-10+1 = 90. Of these 90 consecutive integers, 1 of every 3 will be a multiple of 3, implying that 2/3 will NOT be divisible by 3: (2/3)(90) = 60. Of these ...”
February 25, 2019
GMATGuruNY posted a reply to 2016 OG CR 30 in the Critical Reasoning forum
“Why do people who do regular volunteer work live longer? The argument concludes that ENDORPHINS are the cause. One way to weaken this conclusion is to suggest an ALTERNATE CAUSE. D: People tend not to become involved in regular volunteer work unless they are healthy and energetic to begin with. ...”
February 25, 2019
GMATGuruNY posted a reply to Vivian drives to her sister’s house and back. She takes th in the Problem Solving forum
“When the SAME DISTANCE is traveled at two different speed, the average speed for the entire trip will be just a little less than the average of the two speeds. The reason: The trip at the lower speed takes longer than the trip at the higher speed. Since more time is spent at the lower speed, the ...”
February 25, 2019
GMATGuruNY posted a reply to Before January, the price of a dress was D and the price of in the Problem Solving forum
“Let H=100 and D=500. D increased by 40% = 500 + (40/100)(500) = 500+200 = 700. H increased by 50% = 100 + (50/100)(100) = 100+50 = 150. New sum = 700+150 = 850. Amount paid = new sum discounted by 30% = 850 - (30/100)(850) = 850-255 = 595. The question stem asks for the amount paid. The ...”
February 25, 2019
GMATGuruNY posted a reply to All assets in Karina's investment portfolio are divided betw in the Problem Solving forum
“To MINIMIZE the percent for the largest balance, MAXIMIZE the percents for the 3 smallest balances. We can PLUG IN THE ANSWERS, which represent the percent in the largest balance. When the correct answer is plugged in, the 4 percents will sum to 100%. Since the question stem asks for the smallest ...”
February 25, 2019
GMATGuruNY posted a reply to In a certain class, the ratio of girls to boys is 5:4. How m in the Data Sufficiency forum
“g:b = 5:4 = 10:8 = 15:12 = 20:16 = 25:20... Statement 1: In other words, 4 boys are equal to 20% of the current number of boys, implying the blue ratio above, since 20% of 20 boys = 4 boys. In the blue ratio above, the number of girls = 25. SUFFICIENT. Statement 2: Test the smaller red ...”
February 24, 2019
GMATGuruNY posted a reply to The total of company C's assets in 1994 was 300% greater in the Problem Solving forum
“Let N dollars in 1992 = 1. Since the assets in 1993 are 300% greater than the N dollars in 1992, the assets in 1993 = 1 + (300% of 1) = 1+3 = 4. Since the assets in 1994 are 400% greater than the assets in 1993, the assets in 1994 = 4 + (400% of 4) = 4 + 16 = 20. The question stem asks for ...”
February 23, 2019
GMATGuruNY posted a reply to Andrew bought pizzas for his swim team. Pepperoni pizzas cos in the Problem Solving forum
“13x + 17y = 184. Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104... Multiple of 17: 17, 34, 51, 68, 85, 102, 119.... The values in blue sum to 184. Since 65/13 = 5 and 119/17 = 7, the number of pizzas = 5+7 = 12. The correct answer is A.”
February 23, 2019
GMATGuruNY posted a reply to Nathan took out a student loan for 1200$ at 10 percent in the Problem Solving forum
“Since the 10% rate is compounded annually, the amount of interest increases by 10% each year: First-year interest = 10% of 1200 = 120. Second-year interest = (first-year interest) + 10% = 120 + 12 = 132. Third-year interest = (second-year interest) + 10% = 132 + 13.2 = 145.2. Total interest = ...”
February 22, 2019
GMATGuruNY posted a reply to Ten theater students are to begin work on a set for a in the Problem Solving forum
“(50 days)/(60 days) = 5/6. To finish the job in 5/6 of the normal time, the crew requires 6/5 of the normal number of students -- an increase of 1/5: (1/5)(10) = 2 more students. The correct answer is A.”
February 22, 2019
GMATGuruNY posted a reply to In how many ways a cricket team consisting of 5 batsmen, 4 in the Problem Solving forum
“From 7 batsmen, the number of ways to choose 5 = 7C5 = (7*6*5*4*3)/(5*4*3*2*1) = 21. From 6 bowlers, the number of ways to choose 4 = 6C4 = (6*5*4*3)/(4*3*2*1) = 15. From 3 wicketkeepers, the number of ways to choose 1 = 3. From 3 allrounders, the number of ways to choose 1 = 3. To combine these ...”
February 22, 2019
GMATGuruNY posted a reply to How many different arrangements are possible to place seven in the Problem Solving forum
“Let the 3 math books = A, B, C and the remaining 4 books = D, E, F, G. Since the 3 math books must be next to one another, put them together in a block: E.”
February 22, 2019
GMATGuruNY posted a reply to If 1/x-1/y=1/z, what is the value of y, in terms of x and z? in the Problem Solving forum
“Let x=1 and y=3/2, with the result that 1/z = 1 - 2/3 = 1/3, so z=3. Since the question stem asks for the value of y, the correct answer must yield 3/2 when x=1 and z=3. Since B and D include x-z and thus will yield a negative result, eliminate B and D. Since E includes only multiplication and ...”
February 22, 2019
GMATGuruNY posted a reply to Is p^3 < p? in the Data Sufficiency forum
“Statements combined: Case 1: p=0, with the result that p is an integer less than 1 In this case, p³=p, so the answer to the question stem is NO. Case 2: p=-2, with the result that p is an integer less than 1 In this case, p³ < p, so the answer to the question stem is YES. Since the answer ...”
February 22, 2019
GMATGuruNY posted a reply to In the figure shown, AB = AC = 12. Which of the following is in the Problem Solving forum
“https://i.postimg.cc/06HLPxqC/circle-in-a-sector.png AOP passes through the center of the inscribed circle and thus must BISECT sector ACB. AB, AP and AC are all radii of sector ACB and thus are equal. The prompt indicates AB=AC=12. Thus: AP=12. As shown in the figure, AOM is a 30-60-90 ...”
February 22, 2019
GMATGuruNY posted a reply to The sum of two integers is 27. The larger integer is 25% in the Problem Solving forum
“25% greater = 1/4 greater. If the smaller integer = 4, then the larger integer = 4 + (1/4)4 = 5. The values in red imply that the two integers summing to 27 must be in a RATIO OF 4 TO 5: 4, 5 8, 10 12, 15 The case in blue sums to 27, with the result that larger-smaller = 15-12 = 3. The ...”
February 21, 2019
GMATGuruNY posted a reply to In the figure above, the angle marked at c has been created in the Data Sufficiency forum
“Since b and c form a straight line, b+c = 180. Thus, the calculate a+b+c, we need to know the value of a. Question stem, rephrased: What is the value of a? Statement 1: SUFFICIENT. Statement 2: No information about a. INSUFFICIENT. The correct answer is A.”
February 21, 2019
GMATGuruNY posted a reply to At a certain committee meeting only associate professors and in the Problem Solving forum
“Total number of items brought to the meeting = 21. (10 charts and 11 pencils) Number of items brought by each person = 3. (Either 2 pencils and 1 chart or 1 pencil and 2 charts) Thus: Number of people = (total number of items)/(number of items per person) = 21/3 = 7. The correct answer is B.”
February 21, 2019
GMATGuruNY posted a reply to Four cards are chosen from a standard deck: two aces (one of in the Problem Solving forum
“The following cases are possible: (-1)(1) = -1 (-1)(-2) = 2 (-1)(2) = -2 (1)(-2) = -2 (1)(2) = 2 (-2)(2) = -4 Of the 6 cases above, the 4 in blue each yield a product that is negative, odd or both: 4/6 = 2/3 ≈ 67%. The correct answer is D.”
February 20, 2019
GMATGuruNY posted a reply to A box contains 1 red ball, 3 green balls, 5 yellow balls, 7 in the Problem Solving forum
“Determine the WORST-CASE-SCENARIO -- for each color of ball, the MAXIMUM number that can be removed WITHOUT removing 7 of the same color: 1 red 3 green 5 yellow 6 blue 6 white 6 black Sum = 1+3+5+6+6+6 = 27. Implication: It is possible to remove 27 balls without selecting 7 of the same ...”
February 19, 2019
GMATGuruNY posted a reply to If M, N are integers greater than 1 such that 2M<N, which in the Problem Solving forum
“54, 52 and 50 are options for TWICE the sum. Thus, I, II, and III imply the following options for the ACTUAL SUM: I: 27 II: 26 III: 25 Case 1: M=2 Since it is required that N>2M, N≥5 M=2 and N=5 --> sum = 2+3+4+5 = 14 M=2 and N=6 --> sum increases by 6 --> 14+6 = 20 M=2 and ...”
February 19, 2019
GMATGuruNY posted a reply to If A and B are two fixed constants such that the system in the Problem Solving forum
“The system will have an infinite number of solutions for (x, y) if the two equations are THE SAME: 2(x+y) - A = 0 --> 2x + 2y - A = 0 --> 6x + 6y - 3A = 0 3x + By - 6 = 0 -----------------------> 6x +2By - 12 = 0 The equations in blue will be the same if 3A=12 and 2B=6, with the result ...”
February 18, 2019
GMATGuruNY posted a reply to Is m > n? in the Data Sufficiency forum
“Both statements are satisfied if n=1 and m=2 or if n=1 and m=-2. Since m > n in the first case but m < n in the second case, the two statements combined are INSUFFICIENT. The correct answer is E.”
February 18, 2019
GMATGuruNY posted a reply to If the original price of an item in a retail store is marked in the Data Sufficiency forum
“Let the original price = 100. Then the markup = (m/100)*100 = m. The resulting price = 100+m. The subsequent discount = d/100*(100+m) = d + md/100 Thus, the total percent change = percent increase - percent decrease = m - d - md/100. For the final price to be greater than the original price, ...”
February 17, 2019
GMATGuruNY posted a reply to In triangle ABC, point X is the midpoint of side AC and poin in the Data Sufficiency forum
“http://s7.postimage.org/6u5drpql3/triangle_RCS_1.jpg Triangles RCS and ABC: Side RC = 1/4(AC). Side SC = 1/4(BC). The two triangles share angle BCA. Triangles with a shared angle (BCA) formed by corresponding sides in the same proportion (RC:AC = 1:4, SC:BC = 1:4) are SIMILAR. Thus, ...”
February 17, 2019
GMATGuruNY posted a reply to A and B start from Opladen and Cologne respectively at the in the Problem Solving forum
“When two elements travel at different speeds, their TIME RATIO to travel the same distance will always be the same. If A takes 1/2 as long as B to travel 10 miles, then A will take 1/2 as long as B to travel 1000 miles. If A takes 3 times as long as B to travel 500 miles, then A will take three ...”
February 17, 2019
GMATGuruNY posted a reply to Flor is choosing three of five colors of paint to use for in the Problem Solving forum
“Let the 5 colors be GYABC. From the 5 colors, the number of ways to choose 3 = 5C3 = (5*4*3)/(3*2*1) = 10. Of these 10 combinations, 3 are not allowed: GYA GYB GYC Subtracting these 3 bad combinations, we get: 10-3 = 7. The correct answer is A.”
February 17, 2019
GMATGuruNY posted a reply to If a = 15! + 13, which of the following are factors of a? I in the Problem Solving forum
“MULTIPLE OF X + MULTIPLE OF X = MULTIPLE OF X. MULTIPLE OF X + NON-MULTIPLE OF X = NON-MULTIPLE OF X. Since the prime-factorization of 15! includes 13, we get: a = 15! + 13 = multiple of 13 + multiple of 13 = multiple of 13. Since a is a multiple of 13, option I is a factor of a. Eliminate ...”
February 16, 2019
GMATGuruNY posted a reply to If a coin has an equal probability of landing heads up or ta in the Problem Solving forum
“P(H) = 1/2. P(T) = 1/2. One way to get exactly 1 heads in 3 flips: P(HTT) = 1/2 * 1/2 * 1/2 = 1/8. Since H can appear in a total of 3 positions -- 1st flip, 2nd flip, or 3rd flip -- we multiply by 3: 1/8 * 3 = 3/8 = 0.375. The correct answer is C.”
February 16, 2019
GMATGuruNY posted a reply to A magician has five animals in his magic hat: 3 doves and 2 in the Problem Solving forum
“AND means MULTIPLY. OR means ADD. Case 1: 2 doves P(1st animal is a dove) = 3/5. (Of the 5 animals, 3 are doves.) P(2nd animal is a dove) = 2/4. (Of the 4 remaining animals, 2 are doves.) Since in Case 1 we need the 1st animal to be a dove AND the 2nd animal to be a dove, we MULTIPLY the ...”
February 16, 2019
GMATGuruNY posted a reply to What is the value of (2^{2020} + 2^{2018}) / (2^{2020}-2^{20 in the Problem Solving forum
“(2²⁰²⁰ + 2²⁰¹⁸)/(2²⁰²⁰ - 2²⁰¹⁸) = (2²⁰¹⁸)(2² + 1) / (2²⁰¹⁸)(2² - 1) = 5/3. The correct answer is B.”
February 15, 2019
GMATGuruNY posted a reply to If Rebeca drives to work at x mph she will be one minute lat in the Data Sufficiency forum
“In deference to your mother, the offensive second "c" has been removed from my solution.”
February 15, 2019
GMATGuruNY posted a reply to A certain military vehicle can run on pure Fuel X, pure Fuel in the Data Sufficiency forum
“Statement 1: X = 20 miles per gallon. Y = 40 miles per gallon. Since the mixture of X and Y in the tank allows 200 miles to be covered using 8 gallons, we get: X+Y = 200/8 = 25 miles per gallon. To determine how X and Y must be combined to yield a rate of 25 miles per gallon, use ALLIGATION. ...”
February 15, 2019
GMATGuruNY posted a reply to If Rebeca drives to work at x mph she will be one minute lat in the Data Sufficiency forum
“To make the math easier, we can replace the given values with rounder numbers, as follows: Since Rebeca arrives 1 hour late when traveling at the lower speed and 1 hour early when traveling at the higher speed, the time at the lower speed must be 2 hours greater than the time at the higher ...”
February 15, 2019
GMATGuruNY posted a reply to Which of the following numbers is closest to 100*(11-sqrt( in the Problem Solving forum
“100(11 - √119)(11 + √119) = 100(11² - √119²) = 100(121-119) = 100*2 = 200. When the correct answer is multiplied by 11+√119, the result must be as close as possible to 200. 11+√119 = 11 + (a bit less than 11) = a bit less than 22. Since 9*22 = 198, multiplying 9.2 by a bit less than ...”
February 14, 2019
GMATGuruNY posted a reply to What is the value of a^3+b^3 ? in the Data Sufficiency forum
“Statement 1: Case 1: a=0 and b=1, with the result that a+b = 0+1 = 1 In this case, a³+b³ = 0³ + 1³ = 1 Case 2: a=2 and b=-1, with the result that a+b = 2-1 = 1 In this case, a³+b³ = 2³ + (-1)³ = 7 Since a³+b³ can be different values, INSUFFICIENT. Statement 2: Case 3: a=1 and b=1, ...”
February 14, 2019
GMATGuruNY posted a reply to A group of x people is practicing levitation yoga. One-fourt in the Problem Solving forum
“Let x=12. Since 1/4 of the people rise up, the number who rise up = (1/4)(12) = 3. Since 3 people come back down, EVERYONE who rises up comes back down, with the result that all 12 people are practicing yoga on the ground. How many people are now practicing yoga on the ground? The correct ...”
February 14, 2019
GMATGuruNY posted a reply to How many prime factors does the number X have? 1) X is divi in the Data Sufficiency forum
“Statement combined: Case 1: X = 53*2 = 106, with the result that X is divisible by 1, 2, 53, and 106 In this case, X has TWO prime factors: 2 and 53 Case 2: X = 53³, with the result that X is divisible by 1, 53, 53², and 53³ In this case, X has only ONE prime factor: 53 Since the number of ...”
February 13, 2019
GMATGuruNY posted a reply to A terminating decimal is a number with a finite number of in the Data Sufficiency forum
“A fraction will yield a terminating decimal if -- when the fraction is fully reduced -- the prime-factorization of its denominator includes only 2''s and or 5''s. Statement 1: Let x = an odd multiple of 5. Since the next largest odd multiples of 5 will be x+10 and x+20, we get: p = x + (x+10) ...”
February 12, 2019
GMATGuruNY posted a reply to If O is the center of the circle with diameter AB and T is a in the Problem Solving forum
“A radius drawn to a tangent point yields a RIGHT ANGLE: https://i.postimg.cc/Wq6BDNH7/two-triangles-and-semicircle-1.png In the figure above: Radius OT forms a right angle at tangent point T. OA and OT are radii and thus are equal. Since OA=OT, opposite angles OAT and ATO are equal. We can ...”
February 12, 2019
GMATGuruNY posted a reply to A positive 5-digit integer is called "friendly" if in the Problem Solving forum
“Total number of friendly numbers = total number of ways to arrange the 5 digits = 5! = 120. There are 5 options for the first digit: 1, 2, 3, 4, or 5. 120/5 = 24. Thus, the 120 friendly numbers are composed of five 24-number ranges, as follows: The integers beginning with 1 constitute friendly ...”
February 12, 2019
GMATGuruNY posted a reply to How many numbers between 1 and 200, inclusive, have a 2 in in the Problem Solving forum
“An integer is divisible by 4 if its last two digits form a multiple of 4. Two-digit multiples of 4 with a units digit of 2: 12, 32, 52, 72, 92 Since the last two digits must be one of the options above, between 1 and 200 there are 10 integers that have a units digit of 2 and are divisible by 4: ...”
February 12, 2019
GMATGuruNY posted a reply to If triangles ABC and CDE are each equilateral, what is the s in the Data Sufficiency forum
“Statement 1: Case 1: AC = 10 and CE = 15, with the result that AE = 10+15 = 25 In this case, ABC + CDE = (10+10+10) + (15+15+15) = 75. Case 2: AC= 5 and CD = 20, with the result that AE = 5+20 = 25 In this case, ABC + CDE = (5+5+5) + (20+20+20) = 75. Since the sum of the perimeters is the same ...”
February 12, 2019
GMATGuruNY posted a reply to If m is a positive odd integer, what is the average (arithme in the Data Sufficiency forum
“For any EVENLY SPACED SET: average = median Statement 1: Here, the set consists of consecutive multiples of 3 and thus is evenly spaced. Case 1: 3, 6, 9 Average = median = 6. Case 2: 6, 9, 12 Average = median = 9. Since different averages are possible, INSUFFICIENT. Statement 2: Case ...”
February 12, 2019
GMATGuruNY posted a reply to If there is a 20% chance of rain every day for the next 7 in the Problem Solving forum
“Options D and E should appear as shown below: P(exactly n times) = P(one way) * all possible ways. Let R = rain and N = no rain. Since P(R) = 20% = 2/10, P(N) = 80% = 8/10 = 2³/10. P(one way): One way to get exactly 2 days of rain is to have rain on the first 2 days but not on the ...”
February 12, 2019
GMATGuruNY posted a reply to Working together, Machine A and Machine B can produce a tota in the Data Sufficiency forum
“Since A+B take 4 hours to produce 200 widgets, the combined rate for A+B = w/t = 200/4 = 50 widgets per hour. To determine A''s time to produce 200 widgets, we need to know A''s rate. Question stem, rephrased: What is A''s rate? Statement 1: Since B takes 5 hours to produce 50 widgets, ...”
February 10, 2019
GMATGuruNY posted a reply to Triangle XYZ is an isosceles right triangle. If side XY is l in the Problem Solving forum
“The sides of an isosceles right triangle are in the following ratio: x - x - x√2, where x and x constitute the base and height and x√2 is the hypotenuse. Since the triangle has a base of x, a height of x, and an area of 16, we get: (1/2)(x)(x) = 16 x² = 32 x = √32 Since XY is longer ...”
February 9, 2019
GMATGuruNY posted a reply to Machines X and Y work at their respective constant rates. Ho in the Data Sufficiency forum
“Statement 1: Time and rate are RECIPROCALS. Since X and Y together take 2/3 as long as X alone, X and Y together work 3/2 as fast as X alone. Thus, if X''s rate alone = 2 units per hour, then X and Y''s combined rate = (3/2)(2) = 3 units per hour, implying that Y''s rate alone = 3-2 = 1 unit ...”
February 9, 2019
GMATGuruNY posted a reply to Seven children — A, B, C, D, E, F, and G — are going to in the Problem Solving forum
“Since A and B must occupy adjacent positions, consider AB a single element in the arrangement. The number of ways to arrange the 6 elements AB, C, D, E, F and G = 6! = 720. In 1/2 of these arrangements, C will be to the LEFT of AB. In the remaining 1/2 of these arrangements,C will be to the ...”
February 9, 2019
GMATGuruNY posted a reply to Is abc at least 4? in the Data Sufficiency forum
“Nice problem, Fabio! Statement 1: Case 1: a=4, b=1 and c=1, with the result that b+c≥2 In this case, abc = 4, so the answer to the question stem is YES. Case 2: a=0, b=1 and c=1, with the result that b+c≥2 In this case, abc = 0, so the answer to the question stem is NO. Since the answer ...”
February 8, 2019
GMATGuruNY posted a reply to What is the remainder when the positive integer n is divided in the Data Sufficiency forum
“Statement 1: If n=5, then the remainder when n is divided by 6 = 5/6 = 0 R5. If n=10, then the remainder when n is divided by 6 = 10/6 = 1 R4. Since different remainders are possible, INSUFFICIENT. Statement 2: Since n is a multiple of 12, n must also be a multiple of 6, with the result that ...”
February 8, 2019
GMATGuruNY posted a reply to An electrical supplies store sells 140 power stabilizer in the Problem Solving forum
“Since at least $5600 in profit must be earned by 140 units, the minimum required markup per unit = 5600/140 = $40. Thus, the minimum selling price = (cost per unit) + (minimum required markup per unit) = 16+40 = 56. The correct answer is D.”
February 8, 2019
GMATGuruNY posted a reply to In the xy coordinate plane, line L and line K intersect at in the Data Sufficiency forum
“Statement 1: The product of the x-intercepts of line L and K is positive. K has a negative x-intercept, L has a negative x-intercept, the product of the slopes is positive: http://s4.postimage.org/ie5nbe78/lines_l_and_k_1.jpg K has a positive x-intercept, L has a positive x-intercept, the ...”
February 8, 2019
GMATGuruNY posted a reply to If x and y are positive integers, is x an even integer? in the Data Sufficiency forum
“Statements combined: Case 1: x=1 and y=1, with the result that x(y+5) = 6 and 6y²+41y+25 = 72 In this case, x is ODD, so the answer to the question stem is NO. Case 2: x=2 and y=1, with the result that x(y+5) = 12 and 6y²+41y+25 = 72 In this case, x is EVEN, so the answer to the question ...”
February 7, 2019
GMATGuruNY posted a reply to What is the average (arithmetic mean) of x and y? in the Data Sufficiency forum
“SUM = (COUNT)(AVERAGE). Statement 1: x+y+k = (count)(average) = 3*7 = 21. No way to determine the value of x+y. INSUFFICIENT. Statement 2: x+y+3k = (count)(average) = 3*13 = 39. No way to determine the value of x+y. INSUFFICIENT. Statements combined: Subtracting x+y+k=21 from ...”
February 7, 2019
GMATGuruNY posted a reply to If a and b are integers, is a + b + 3 an odd integer? (1) in the Data Sufficiency forum
“a+b+3 = ODD only if a and b are both odd or both even. Question stem, rephrased: Are a and b both odd or both even? Statement 1: ab = ODD implies that a and b are both odd. Thus, the answer to the question stem is YES. SUFFICIENT. Statement 2: a-b = EVEN implies that a and b are either ...”
February 7, 2019
GMATGuruNY posted a reply to In the coordinate plane, Line A has a slope of -1 and an in the Problem Solving forum
“Line A includes points (1, 0) and (a, b) and has a slope of -1. Thus: (b - 0)/(a-1) = -1 b = -a + 1 a+b = 1. The correct answer is B. The information about Line B is irrelevant.”
February 5, 2019
GMATGuruNY posted a reply to In how many ways can a 4-letter word be formed from the in the Problem Solving forum
“Alternate approach: Case 1: VVCC, where the first two letters are vowels and the last 2 letters are consonants Number of options for the first vowel = 4. (Any of the 4 vowels) Number of options for the second vowel = 3. (Any of the 3 remaining vowels) Number of options for the first consonant ...”
February 5, 2019
GMATGuruNY posted a reply to A contractor combined x tons of a gravel mixture that in the Data Sufficiency forum
“x = 10% gravel y = 2% gravel. z = the MIXTURE of x and y = 5% gravel. To determine the required ratio of x to y, use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS. Step 1: Plot the 3 percentages on a number line, with the percentages for x and y on the ends and the ...”
February 4, 2019
GMATGuruNY posted a reply to Bank Depositors (GMAT Prep) in the Critical Reasoning forum
“I received a PM requesting that I respond. Premise: Insurance removes from depositors any financial incentive to find out whether the bank that holds their money is secure against failure. Conclusion: The insurance is partly responsible for the high rate of bank failures. To determine the ...”
February 3, 2019
GMATGuruNY posted a reply to In the graduating class of a certain college, 48 percent of in the Problem Solving forum
“Every student is EITHER male OR female. Every student is EITER older OR younger. For an EITHER/OR problem, use a DOUBLE MATRIX to organize the data: _______________M______F_______Total older: younger: total: Let total students = 100: _______________M______F_______Total ...”
February 3, 2019
GMATGuruNY posted a reply to Kate and Danny each have $10. Together, they flip a fair coi in the Problem Solving forum
“For every tails, Kate gets $1; for every heads, she loses $1. 0 tails, 5 heads: Kate has 10+0-5 = $5 1 tails, 4 heads: Kate has 10+1-4 = $7 2 tails, 3 heads: Kate has 10+2-3 = $9 3 tails, 2 heads: Kate has 10+3-2 = $11 4 tails, 1 heads: Kate has 10+4-1 = $13 5 tails, 0 heads: Kate has ...”
February 3, 2019
GMATGuruNY posted a reply to A paint crew gets a rush order to paint 80 houses in a new d in the Problem Solving forum
“Let y=0, implying that NONE of the 80 houses are painted at the original rate of x houses per week, with the result that ALL 80 houses are painted at the greater rate of (5/4)x houses per week. The total time it takes them to paint all the houses under this scenario is what fraction of the time ...”
February 1, 2019
GMATGuruNY posted a reply to Three pipes P, Q, and R are attached to a tank. P and Q indi in the Problem Solving forum
“Let the tank = 60 liters. Since P takes 3 hours to fill the 60-liter tank, P''s rate = 60/3 = 20 liters per hour. Since Q takes 4 hours to fill the 60-liter tank, Q''s rate = 60/4 = 15 liters per hour. Since R takes 5 hours to empty the 60-liter tank, R''s rate = -(60/5) = −12 liters per ...”
February 1, 2019
GMATGuruNY posted a reply to If ( x – y – 2 )^2 + ( x + z + 3 )^2 = 0, then what is t in the Problem Solving forum
“Let x=0. Plugging x=0 into (x-y-2)² + (x+z+3)² = 0, we get: (-y-2)² + (z+3)² = 0 Since neither (-y-2)² nor (z+3)² can be negative, the resulting equation is valid only if -y-2=0 and z+3=0, with the result that y=-2 and z=-3. Thus, y+z = -2 + (-3) = -5 The correct answer is E.”
February 1, 2019
GMATGuruNY posted a reply to Cars J and K are making the trip from City A to City B. Car in the Problem Solving forum
“Since J catches up to K, J and K travel the same distance. Let t = J''s time. Since K leaves 15 minutes earlier than J, K''s time = t+15. Rate and time have a RECIPROCAL RELATIONSHIP. Since K''s rate is 80% of J''s rate, the ratio of K''s rate to J''s rate = 8/10 = 4/5. Thus, the ratio of ...”
January 31, 2019
GMATGuruNY posted a reply to f(2x-1) = ( x + 2 ) / ( x – 2 ). What is f(x)? in the Problem Solving forum
“Let x=1. Plugging x=1 into f(2x-1) = ( x + 2 ) / ( x – 2 ), we get: f(2*1 - 1) = (1+2)/(1-2) f(1) = -3. When x=1, the question stem becomes: What is f(1)? Since f(1) = -3, the correct answer must yield -3 when x=1. Only A works: f(1) = (1+5)/(1-3) = 6/-2 = -3. The correct answer is A.”
January 31, 2019
GMATGuruNY posted a reply to A lecture course consists of 595 students. The students are in the Problem Solving forum
“(students per section)(number of sections) = 595 students number of sections = 595/(students per section). The equation in blue indicates that 595 must be divisible by the number of students per section. An integer is divisible by 3 only if its digit sum is a multiple of 3. The digit sum of ...”
January 30, 2019
GMATGuruNY posted a reply to Question about idioms and verbs in the Sentence Correction forum
“Correct: The contractors demolished the building to keep it from falling. Here, to keep is not an adjective modifying contractors but an ADVERB modifying demolished, expressing WHY the contractors DEMOLISHED the building. Question: WHY did the contractors demolish the building? Answer: TO KEEP it ...”
January 30, 2019
GMATGuruNY posted a reply to DS work rate problem in the Data Sufficiency forum
“Statement 1: Case 1: Job = 12 units Since A and B together take 4 hours to complete the 12-unit job, the combined rate for A+B = 12/4 = 3 units per hour. Since A alone takes 6 hours to complete the 12-unit job, A''s rate alone = 12/6 = 2 units per hour. B''s rate = (combined rate for A+B) - ...”
January 30, 2019
GMATGuruNY posted a reply to PS arithmetic in the Problem Solving forum
“An alternate approach is to BALLPARK. √2 ≈ 1.4 √3 ≈ 1.7 (1+√3) * √(2 + √3) ≈ (2.7)(√3.7) = (2.7)(a bit less than 2) = a bit less than 5.4. When we evaluate the answer choices, only C is a bit less than 5.4: √2(2 + √3) ≈ (1.4)(3.7) = 5.18. The correct answer is C.”
January 30, 2019
GMATGuruNY posted a reply to DS arithmetic in the Data Sufficiency forum
“Statement 1: The inequality implies that a is POSITIVE, allowing us to cross-multiply: 1*2 > a*1 2 > a Since 2>a and a>b>0, we get: 2>a>b>0 Thus, b<2. SUFFICIENT. Statement 2: If b=2, we get: 1/a + 1/2 = 1 1/a = 1/2 a=2 Not possible, since the prompt ...”
January 30, 2019
GMATGuruNY posted a reply to The sum of 4 different odd integers is 64. in the Data Sufficiency forum
“Statement 1: Since the numbers are EVENLY SPACED, median = sum/count: 64/4 = 16. Since the median = 16, the 4 odd integers must be as follows: 13, 15, 17, 19. Thus, the greatest of the 4 odd integers = 19. SUFFICENT. Statement 2: The 4 odd integers yielded by Statement 1 -- 13, 15, ...”
January 30, 2019
GMATGuruNY posted a reply to To create a part for a certain piece of machinery, four equa in the Problem Solving forum
“The four 18-degree shaded regions = 4*18 = 72 degrees. The entire circle = 360 degrees. (shaded regions)/(entire circle) = 72/360 = 1/5. Thus: (unshaded regions)/(entire circle) = 1 - 1/5 = 4/5 = 80%. The correct answer is E.”
January 29, 2019
GMATGuruNY posted a reply to When 12 marbles are added to a rectangular aquarium, the wat in the Problem Solving forum
“The desired height increase = 11/4 inches. 12 marbles yield a height increase of 3/2 inches. Thus: (desired height increase of 11/4 inches) * (12 marbles)/(height increase of 3/2 inches) = (11/4 * 12)/(3/2) = 33/(3/2) = (33*2)/3 = 11*2 = 22 marbles. The correct answer is D.”
January 28, 2019
GMATGuruNY posted a reply to A certain company has 18 equally qualified applicants for 4 in the Problem Solving forum
“From 18 applicants, the number of ways to choose 4 = 18C4 = (18*17*16*15)/(4*3*2*1) = (3*17*4*15) = 51*60 = 3060. The correct answer is E.”
January 28, 2019
GMATGuruNY posted a reply to A new tower has just been built at the Verbico military in the Problem Solving forum
“Let the PRE-TOWER number of beds = the LCM of the denominators in the problem = 3*5 = 15. Then the CURRENT number of beds = 3*15 = 45, implying that the number of beds in the NEW tower = 45-15 = 30. Occupied beds = (1/3)15 + (1/5)30 = 11. Non-occupied beds in the new tower = 30-11 = 19. ...”
January 28, 2019
GMATGuruNY posted a reply to Machines A and B, working together, take t minutes to in the Problem Solving forum
“One more approach: Since A+B together complete the job in t minutes: Job = (A''s output in t minutes) + (B''s output in t minutes) If A works alone for t minutes, A can then complete the rest of the job in 64 minutes. In this case, the rest of the job = B''s output in t minutes. Thus, A''s ...”
January 27, 2019
GMATGuruNY posted a reply to Prompted by observations of seemingly related species in the Sentence Correction forum
“A present perfect verb (has + VERBed or have + VERBed) expresses a PAST ACTION that affects the present. Generally, the usage of a present perfect verb implies that the subject of the verb still exists. Incorrect: The dinosaurs have evolved over time. The sentence above is illogical because the ...”
January 27, 2019
GMATGuruNY posted a reply to Machines A and B, working together, take t minutes to in the Problem Solving forum
“Always keep your eye on the answer choices. Since A''s time alone (t+64) is greater than B''s time alone (t+25), the ratio of A''s time alone to B''s time alone must be GREATER THAN 1. Eliminate A, C and D. Since the ratio of A''s time to B''s time = (t+64)/(t+25), option E implies the ...”
January 27, 2019
GMATGuruNY posted a reply to A certain library assesses fines for overdue books as in the Problem Solving forum
“First day: Total fine = 10. For each additional day, the total fine either increases by 30 or doubles -- whichever results in a lesser amount. Second day: Adding 30 cents to the 1-day fine, we get 10+30 = 40. Doubling the 1-day fine, we get 2*10 = 20. Total fine = lesser amount = 20. ...”
January 27, 2019
GMATGuruNY posted a reply to If the drama club and music club are combined, what percent in the Data Sufficiency forum
“Clearly, neither statement alone is sufficient. Statements combined: Case 1: No one is a member of both clubs Total males = 15+10 = 25. Total members = 16+20 = 36. Resulting fraction: (total males)/(total members) = 25/36. Case 2: Every male in the music club is also in the drama ...”
January 26, 2019
GMATGuruNY posted a reply to Frank and Georgia started traveling from A to B at the same in the Problem Solving forum
“Let d = the number of miles between A and B. Since Georgia travels the entire d miles between A and B and then an additional 60 miles back toward A, Georgia''s distance = d+60. Since Frank travels all but 60 of the d miles between A and B, Frank''s distance = d-60. Since Georgia''s travels 3/2 ...”
January 26, 2019
GMATGuruNY posted a reply to Ratio in the Problem Solving forum
“Let S = the entire season (in other words, the mixture of M and N). Alligation can be performed only with percentages or fractions. Step 1: Convert the ratios to FRACTIONS. M: Since win:losses = 1:2, and 1+2=3, wins/total = 1/3. N: Since wins:losses = 1:3, and 1+3=4, wins/total = 1/4. ...”
January 25, 2019
GMATGuruNY posted a reply to How many factors greater than 1 do 120, 210, and 270 have in in the Problem Solving forum
“120 = 30*4 210 = 30*7 270 = 30*9 The GCF = the value in blue = 30. Factors of 30 greater than 1: 2, 3, 5, 6, 10, 15, 30 --> 7 factors Thus, 120, 210, and 270 have 7 common factors greater than 1. The correct answer is D.”
January 24, 2019
GMATGuruNY posted a reply to Stacy and Katie plan to walk the 27-mile scenic route across in the Problem Solving forum
“Since Stacy and Katie travel toward each other, they WORK TOGETHER to cover the 27 miles between them. Since Stacy is 1/4 faster than Katie, for every 4 miles that Katie travels, the distance traveled by Stacy = 4 + (1/4)(4) = 5 miles. Thus, of every 9 miles traveled when Stacy and Katie work ...”
January 24, 2019
GMATGuruNY posted a reply to If when a certain integer x is divided by 5, the remainder in the Problem Solving forum
“Since dividing x by 5 yields a remainder, x is not a multiple of 5 and thus not a multiple of 10. Since x is not a multiple of 10, x/10 cannot yield an integer value. The correct answer is B.”
January 22, 2019
GMATGuruNY posted a reply to Mary and Kate are running clockwise around a circular track in the Problem Solving forum
“Since Mary is behind Kate by 250 meters -- half the circumference of the track -- she will catch up to Mary when she has traveled 250 meters more than Kate. To catch up to Kate a second time, Mary must then travel one more lap than Kate -- in other words, 500 meters more than Kate. Implication: ...”
January 22, 2019
GMATGuruNY posted a reply to If y=|x-1|+|x+1|, then y=? in the Data Sufficiency forum
“|x-1| = the distance between x and 1. |x+1| = the distance between x and -1. -1<--|x+1|-->x<--|x-1|-->1 Here, since the total distance between the two endpoints is 2, the sum of the 2 distances in red is 2. If x is any value between the two endpoints, then the sum of the two ...”
January 22, 2019
GMATGuruNY posted a reply to A = (2-3+4)^{11}, and B = (-2+3-4)^{11}. What is the value o in the Problem Solving forum
“A = (2-3+4)¹¹ = 3¹¹ B = (-2+3-4)¹¹ = (-3)¹¹ = -3¹¹ Thus: A+B = 3¹¹ - 3¹¹ = 0 2^(A+B) = 2⁰ = 1. The correct answer is C.”
January 22, 2019
GMATGuruNY posted a reply to GMAT OG 2019 The Commerce Department reported that in the Sentence Correction forum
“were + VERBing is the plural form of the PAST PROGRESSIVE tense (also known as the past continuous tense). The past progressive tenses serve to express actions that happen CONTINUOUSLY FOR A LIMITED DURATION OF TIME. OA: While businesses were expanding their production, unsold goods were piling ...”
January 22, 2019
GMATGuruNY posted a reply to Machine A produces pencils at a constant rate of 9000 in the Problem Solving forum
“To minimize B''s time, we must maximize A''s time. Since each machine can work for at most 8 hours, let A''s time = 8 hours. Since A''s rate = 9000 pencils per hour, the number of pencils produced by A in 8 hours = rt = 9000*8 = 72,000. Remaining pencils = 100,000 - 72,000, = 28,000. Since ...”
January 21, 2019
GMATGuruNY posted a reply to A bowl contains pecans, cashews, and almonds in a ratio of 6 in the Problem Solving forum
“Original ratio values: P.................................................C...............................................A 6x<---distance of 4x--->10x<---distance of 5x--->15x Options for the new ratio: I) 1 : 2 : 3 I) 2 : 3 : 4 III) 4 : 7 : 10 The ratio values in each ...”
January 21, 2019
GMATGuruNY posted a reply to If x-2y=4, then x^2-4xy+4y^2-x+2y=? in the Problem Solving forum
“Let x=4 and y=0, with the result that x-2y = 4. Plugging x=4 and y=0 into x² - 4xy + 4y² - x + 2y, we get: 4² - 0 + 0 - 4 + 0 = 12. The correct answer is A.”
January 21, 2019
GMATGuruNY posted a reply to A company bought some desks at a price of $150 each and some in the Data Sufficiency forum
“Test the THRESHOLD. In the question stem, the threshold is 40 CHAIRS. The total cost of 40 chairs = 40*50 = 2000. Statement 1: The total price of the desks and chairs is 5,000. It is possible that 40 chairs are purchased (at a total cost of $2000) or that MORE CHAIRS are purchased. ...”
January 20, 2019
GMATGuruNY posted a reply to What is the value of x? in the Data Sufficiency forum
“Statement 1: To have exactly 3 positive factors, x must be the square of a prime number. Factors of x=2²=4: 1, 2, 4 Factors of x=3²=9: 1, 3, 9 Factors of x=5²=25: 1, 5, 25. Since x can be different values, INSUFFICIENT. Statement 2: Clearly INSUFFICIENT. Statements combined: x ...”
January 20, 2019
GMATGuruNY posted a reply to The average American spends y dollars on food per month, exc in the Problem Solving forum
“Monthly food expense except in January: Let y=$2. Discount in January: Let x=100%. Since $2 is spent each month for 8 of the first 9 months, the total spent during these 8 months = 8*2 = 16. Since food purchases are 100% lower in January -- implying that they are FREE in January -- the amount ...”
January 20, 2019
GMATGuruNY posted a reply to In a certain pet shop, 1/3 of the pets are dogs and 1/5 of in the Data Sufficiency forum
“Alternate approach: To determine the ratio of birds to dogs, plug in a TEST VALUE for the total number of pets. Let b = the number of birds and d = the number of dogs. Let the test value for the total number of pets = the LCM of 3 and 5 = 15. Since 1/5 are birds, b = 1/5 * 15 = 3. Since 1/3 ...”
January 19, 2019
GMATGuruNY posted a reply to How many hours did it take Helen to drive from her house to in the Data Sufficiency forum
“Statement 1: If d=72, then t = d/r = 72/72 = 1 hour. If d=144, then t = 144/72 = 2 hours. Since the time can be different values, INSUFFICIENT. Statement 2: Time and rate have a RECIPROCAL RELATIONSHIP: If the time is cut in HALF, then the rate DOUBLES. If the time DOUBLES, then the ...”
January 18, 2019
GMATGuruNY posted a reply to If tank X contains only gasoline, how many kiloliters of gas in the Data Sufficiency forum
“Let G = the gas in the tank and C = the capacity of the tank. Statement 1: G - (1/2)G = (1/3)C No way to solve for G. INSUFFICENT. Statement 2: G + 0.75 = C No way to solve for G. INSUFFICIENT. Statements combined: Since we have two variables (G and C) and two distinct linear ...”
January 18, 2019
GMATGuruNY posted a reply to If Jake loses 8 pounds, he will weigh twice as much as his s in the Problem Solving forum
“Here, the value in red is the sum of Jake''s weight and TWICE the sister''s weight: 187 + 2(89.5) = 366. But the prompt gives an integer value for the sum of Jake''s weight and the sister''s ACTUAL weight -- a constraint that forces Jake''s weight to be an even integer.”
January 17, 2019
GMATGuruNY posted a reply to If Jake loses 8 pounds, he will weigh twice as much as his s in the Problem Solving forum
“The sum of Jake''s weight and his sister''s weight is an INTEGER VALUE. The answer choices indicate that Jake''s weight is an INTEGER VALUE. Implication: The sister''s weight must also be an integer value. Thus, the value in red -- 89.5 -- is not a valid option for the sister''s weight. Given ...”
January 17, 2019
GMATGuruNY posted a reply to The speed of a boat is 5 times the speed at which a river fl in the Problem Solving forum
“Let the river''s rate = 1 mph and the boat''s rate = 5 mph. When the boat travels DOWNRIVER, the boat and the river WORK TOGETHER, so we ADD their rates: 5+1 = 6 mph. When the boat travels UPRIVER, the boat and the river COMPETE, so we SUBTRACT their rates: 5-1 = 4 mph. Rate and time have ...”
January 17, 2019
GMATGuruNY posted a reply to If Jake loses 8 pounds, he will weigh twice as much as his s in the Problem Solving forum
“ALWAYS KEEP YOUR EYE ON THE ANSWER CHOICES. If Jake loses 8 pounds, he will weigh twice as much as his sister. j-8 = 2s j = 2s + 8 = even + even = even. Since Jake''s weight must be an EVEN VALUE, the correct answer is E.”
January 17, 2019
GMATGuruNY posted a reply to Sarah is in a room with 6 other children. If the other child in the Data Sufficiency forum
“Let S = Sara''s age. Sum of the ages = 2+4+5+8+10+13+S = 42+S. Statement 1: Since the average age is equal to an INTEGER -- the fourth largest age -- we get: Sum of the ages = (number of ages)(average age) = (7)(INTEGER) = multiple of 7. The blue expression and the red expression each ...”
January 16, 2019
GMATGuruNY posted a reply to If the median and the range of the data set 1, 1, 2, 2, 3, 3 in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the value of m. When the correct answer is plugged in, the median will be equal to the range. Note: When the prompt includes the phrase which of the following, the correct answer is likely to be D or E. E: m=3 Resulting set: 1, 1, 2, 2, m=3, 3, 3, ...”
January 16, 2019
GMATGuruNY posted a reply to Henry eats X scones in X percent of the time it takes Rachel in the Problem Solving forum
“Let X=8 and Y=4. Henry eats X scones in X percent of the time it takes Rachel to eat Y scones. Since Henry eats X=8 scones in 8% of the time it takes Rachel to eat Y=4 scones -- 10 minutes, according to the prompt -- the time for Henry to eat 8 scones = 8% of 10 minutes = (8/100)(10) = 4/5 ...”
January 15, 2019
GMATGuruNY posted a reply to A rectangular wall has dimensions of 800 by 300. If the wall in the Problem Solving forum
“number of tiles = (wall area)/(tile area) = (800*300)/(25*12) = 32*25 = 800. The correct answer is E.”
January 15, 2019
GMATGuruNY posted a reply to In a 200 member association consisting of men and women, exa in the Problem Solving forum
“Consider the following equation: 7x + 5y = 70. If x and y are nonnegative integers, the following solutions are possible: x=10, y=0 x=5, y=7 x=0, y=14. Notice the following: The value of x changes in increments of 5 (the coefficient for y). The value of y changes in increments of ...”
January 15, 2019
GMATGuruNY posted a reply to The cost of a square slab is proportional to its thickness a in the Data Sufficiency forum
“x is directly proportional to y implies the following: x/y = k. x = ky. In each case, k is a CONSTANT. The cost of a square slab is proportional to its thickness and also proportional to the square of its length. Thus: c = k * T * L². What is the cost of a square slab that is 3 meters ...”
January 15, 2019
GMATGuruNY posted a reply to Thomasville tree planting in the Critical Reasoning forum
“species may be singular or plural. Passage: Planting trees primarily from the species that turns out to have the best record of survival will assure downtown Thomasville of an abundant tree population 20 years from now. Here, the verb attributed to species is turns. Since turns is singular, ...”
January 14, 2019
GMATGuruNY posted a reply to Three machines have equal constant work rates. It takes h + in the Problem Solving forum
“(number of machines)(number of hours) = number of toys that are produced. In the prompt above, the blue values are THE SAME. Implication: 2 machines take h+3 hours to produce the same number of toys as 3 machines in 2 hours: 2(h+3) = 3h 2h + 6 = 3h 6 = h. Since 3 machines produce 360 toys ...”
January 14, 2019
GMATGuruNY posted a reply to If Jay has 99 problems, in how many ways can he select k of in the Data Sufficiency forum
“Rule: nCr = nC(n-r) Examples: 5C2 = 5C(5-2) = 5C3. 10C3 = 10C(10-3) = 10C7. 99C5 = 99C(99-5) = 99C94. Statement 2: Jay can select k-1 of his problems in 4851 different ways. Since 4851 is relatively small, test small values for k-1. Case 1: k-1 = 2 From 99 problems, the number of ...”
January 14, 2019
GMATGuruNY posted a reply to A tank has two water pumps Alpha and Beta and one drain Gamm in the Problem Solving forum
“Let x = 2 hours, y = 3 hours and z = 4 hours. Let the tank = 12 gallons. Since Alpha takes 2 hours to fill the 12-gallon tank, Alpha''s rate = w/t = 12/2 = 6 gallons per hour. Since Beta takes 3 hours to fill the 12-gallon tank, Beta''s rate = w/t = 12/3 = 4 gallons per hour. Since Gamma takes ...”
January 13, 2019
GMATGuruNY posted a reply to To furnish a room in model home, an interior decorator is to in the Problem Solving forum
“Since 150 combinations are possible, we get: (number of ways to choose 2 chairs)(number of ways to choose 2 tables) = 150. From 5 chairs, the number of ways to choose 2 = 5C2 = (5*4)/(2*1) = 10. Thus: (10)(number of ways to choose 2 tables) = 150 number of ways to choose 2 tables = 150/10 = ...”
January 11, 2019
GMATGuruNY posted a reply to Carlos runs a lap around the track in x seconds. His second in the Problem Solving forum
“Let x = 5 seconds for the first lap, implying 10 seconds for the second lap, 3 seconds for the third lap, and a total of 18 seconds for all 3 laps. (18 seconds)/(3 laps) = (6 seconds)/(1 lap) = 1/10 minute per lap. The correct answer must yield a value of 1/10 when x=5. Only D works: (x+1)/60 ...”
January 11, 2019
GMATGuruNY posted a reply to Every day in the morning Ross cycles for 2 hours. He always in the Problem Solving forum
“The information in red is irrelevant. Only the following facts matter: Ross travels onward at a rate of 1 mile every 12 minutes. He travels home for twice the onward distance at half the onward speed. Onward speed = 1 mile per 12 minutes = 5 miles per 60 minutes = 5 mph. Let the onward ...”
January 11, 2019
GMATGuruNY posted a reply to At a certain fruit stand, the price of each apple is 40 in the Problem Solving forum
“The original total cost of the 10 pieces of fruit = 10*56 = 560. According to the answers, after 1, 2, 3, 4, or 5 oranges are removed -- so that 9, 8, 7, 6, or 5 pieces of fruit remain -- the average cost per piece decreases to 52. Since the original total cost is a multiple of 10, and the price ...”
January 11, 2019
GMATGuruNY posted a reply to This year, x people won an Olympic medal for water in the Problem Solving forum
“Let x = the product of the two denominators in the prompt = 3*4 = 12. Since 1/3 won a medal for swimming, the number who won a medal for swimming = (1/3)(12) = 4. Since 1/4 of the medal winners for swimming also won a medal for diving, the number who won both a medal for swimming and a medal for ...”
January 10, 2019
GMATGuruNY posted a reply to (7+43+7-43)^2 is equal to which of the following? in the Problem Solving forum
“√3 ≈ 1.7. 7 + 4√3 ≈ 7 + (4)(1.7) = 13.8. 7 - 4√3 ≈ 7 - (4)(1.7) = 0.2. Thus, the given expression can be approximated as follows: (√13.8 + √0.2)² = a little more than 13.8. Only D is viable. The correct answer is D.”
January 10, 2019
GMATGuruNY posted a reply to PLease help me with the concept! in the Sentence Correction forum
“Offhand, I cannot cite an official SC that violates the rule discussed above.”
January 10, 2019
GMATGuruNY posted a reply to What is the greatest possible area of a triangular region in the Problem Solving forum
“Given two sides of a triangle, the greatest possible area will be achieved if the two sides form a RIGHT ANGLE and serve as the triangle''s base and height. For the problem above, I posted an illustrated solution here: ...”
January 9, 2019
GMATGuruNY posted a reply to Stock - Number of shares V ------------------- 68 W ------- in the Problem Solving forum
“Original range = (greatest number of shares) - (smallest number of shares) = 112-45 = 67. After 24 shares of Y are purchased, new Y = 94+24 = 118. After 20 shares of X are sold, new X = 56-20 = 36. New range = (new greatest number of shares) - (new smallest number of shares) = 118-36 = 82. ...”
January 9, 2019
GMATGuruNY posted a reply to On a certain Monday, Carlos drove to work at an average in the Problem Solving forum
“When the SAME DISTANCE is traveled at two different speeds, the average speed for the entire trip will be CLOSER TO THE LOWER SPEED than to the higher speed. The reason: The portion traveled at the lower speed takes LONGER. Since more time is spent at the lower speed than at the higher speed, the ...”
January 8, 2019
GMATGuruNY posted a reply to A department manager distributed a number of pens, pencils, in the Data Sufficiency forum
“Statement 1: The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively. Since 2+3+4 = 9, the total number of pens + pencils + pads must be a multiple of 9. No way to determine the exact number of staff members. INSUFFICIENT. Statement 2: ...”
January 8, 2019
GMATGuruNY posted a reply to Because natural gas is composed mostly of methane in the Sentence Correction forum
“Both of the following are viable: Vehicles powered by natural gas emit less of certain pollutants than those burning gasoline or diesel fuel. Vehicles powered by ndatural gas emit less of certain pollutants than do those burning gasoline or diesel fuel. The inclusion of do is optional. With or ...”
January 8, 2019
GMATGuruNY posted a reply to If the graph of y = x^2 + ax + b passes through the points ( in the Data Sufficiency forum
“What is the value of n-m? (m,0) and (n,0) are the two points where y=0 and the graph intersects the x-axis. Thus, m and n are the x-intercepts of the graph. Since m < n, n-m > 0. Question rephrased: What is the positive difference between the x-intercepts? Statement 1: 4b = a²-4 Test ...”
January 8, 2019
GMATGuruNY posted a reply to If x is integer and 3 | x |+x < 4, what is the value of x in the Data Sufficiency forum
“3|x| < 4-x Case 1: Signs unchanged 3x < -x 4x < 4 x < 1 Case 2: Signs changed in the absolute value 3(-x) < 4-x -2x < 4 x > -2 Question stem, rephrased: If x is an integer such that -2 < x < 1, what is the value of x? Statement 1: x < 0 Here, x must ...”
January 8, 2019
GMATGuruNY posted a reply to In 1991, the price of a house was 80% of its original price. in the Problem Solving forum
“Let the original price = 100. 1991 price = 80% of 100 = 80. 1992 price = 60% of 100 = 60. Percent decrease from 80 to 60 = (Difference/Larger) * 100 = (20/80) * 100 = 25. The correct answer is B.”
January 7, 2019
GMATGuruNY posted a reply to The main ingredient in a certain prescription drug capsule c in the Problem Solving forum
“Each capsule contains 600 milligrams of ingredient. 10⁶ milligrams = 1 kilogram. 1 kilogram of ingredient = 500 dollars. To determine the cost per capsule, we must use the relationships above to convert 600 milligrams into dollars: (600 milligrams) * (1 kilogram)/(10⁶ milligrams) * ...”
January 7, 2019
GMATGuruNY posted a reply to The numbers of women is singular or plural? in the Sentence Correction forum
“percent may serve as a NOUN. Of the students in the class, eighty percent passed the test. Here, eighty percent is a NOUN serving as the subject of passed. twice is a MODIFIER. It cannot serve as the subject of a sentence. Of the students in the class, twice passed the test. The sentence ...”
January 7, 2019
GMATGuruNY posted a reply to If f(a*b) = f(a) + f(b), what is the value of f(1)? in the Problem Solving forum
“Let a=1 and b=2. Plugging a=1 and b=2 into f(ab) = f(a) + f(b), we get: f(1*2) = f(1) + f(2) f(2) = f(1) + f(2) 0 = f(1). The correct answer is C.”
January 7, 2019
GMATGuruNY posted a reply to A store sells erasers for 0.23$ per piece and pencil for in the Data Sufficiency forum
“Consider the following equation: 5x + 7y = 70. If x and y are nonnegative integers, the following solutions are possible: x=0, y=10 x=7, y=5 x=14, y=0. Notice the following: The value of x changes in increments of 7 (the coefficient for y). The value of y changes in increments of 5 (the ...”
January 6, 2019
GMATGuruNY posted a reply to the mixture to make the ratio of milk and water in the new m in the Problem Solving forum
“The ratio of milk and water in a mixture is 2:1, Let milk = 2 liters and water = 1 liter. Some quantity of water is added to the mixture to make the ratio of milk and water in the new mixture 1:2. Since the resulting amount of water must be double the original 2 liters of milk, the resulting ...”
January 6, 2019
GMATGuruNY posted a reply to Little Texas Drilling Company has three wells, each producin in the Problem Solving forum
“Given the answer choices, the prompt should read as follows: A''s rate = (1 barrel)/(2 minutes) * (60 minutes)/(1 hour) = 30 barrels per hour. B''s rate = (1 barrel)/(3 minutes) * (60 minutes)/(1 hour) = 20 barrels per hour. C''s rate = (1 barrel)/(15 minutes) * (60 minutes)/(1 hour) = 15 ...”
January 6, 2019
GMATGuruNY posted a reply to If y = |2 + x| - |2 – x| and |2x – 15| < 2, how many in the Problem Solving forum
“|a-b| = the distance between a and b |a+b| = |a-(-b)| = the distance between a and -b y = |2 + x| - |2 – x| y = |x+2| - |x-2| y = |x-(-2)| - |x-2| y = the subtraction of two distances: (distance between x and -2) - (distance between x and 2) On the number line: ...”
January 5, 2019
GMATGuruNY posted a reply to Seven cars of seven different models are going to park in in the Problem Solving forum
“Let the 7 cars be A, B, C, D, P, Q and S. Since P and Q must occupy adjacent positions, consider PQ a single element in the arrangement. The number of ways to arrange the 6 elements A, B, C, D, PQ and S = 6! = 720. In 1/2 of these arrangements, S will be to the LEFT of PQ. In the ...”
January 5, 2019
GMATGuruNY posted a reply to Which of the following must be non-negative? in the Problem Solving forum
“D: (a-0.9)(a-0.9) = (a-0.9)². The square of a value cannot be negative. The correct answer is D.”
January 5, 2019
GMATGuruNY posted a reply to Machine M and Machine N working alone at their constant rate in the Data Sufficiency forum
“Statement 1: Case 1: N = 4000 nails per hour, M = 2000 nails per hour Since N''s rate = 4000 nails per hour, the time for N to produce 8000 nails = 8000/4000 = 2 hours. Since M''s rate = 2000 nails per hour, the time for M to produce 6000 nails = 6000/2000 = 3 hours. In this case, M works longer ...”
January 5, 2019
GMATGuruNY posted a reply to Each of the 25 balls in a certain box is either red, blue, in the Data Sufficiency forum
“Let: W = the total number of white marbles. E = the total number of even marbles. WE = the total number of white even marbles. Statement 1: Thus, WE = 0. No way to determine the value of W or E. INSUFFICIENT. Statement 2: Implication: W-E = (0.2)(25) = 5. Case 1: W=10, E=5, WE=0 ...”
January 4, 2019
GMATGuruNY posted a reply to Allison always leaves her office at 5.00pm and reaches her in the Data Sufficiency forum
“Statement 2: Brittany always leaves the hotel at exactly 5.30pm. To see the situation more clearly, plug in a value for the distance between the hotel and the office. Let the distance = 6 miles. Since Allison takes 1 hour -- from 5 to 6pm -- to travel the entire distance, Alison''s rate = d/t = ...”
January 4, 2019
GMATGuruNY posted a reply to If y = 2 + 2K and y≠0y≠0, then 1/y + 1/y + 1/y + 1/y = ? in the Problem Solving forum
“Let k=0, implying that y = 2 + 2*0 = 2. Plugging y=2 into 1/y + 1/y + 1/y + 1/y, we get: 1/2 + 1/2 + 1/2 + 1/2 = 2. The correct answer must yield a value of 2 when k=0. Only B works: 2/(1+k) = 2/(1+0) = 2. The correct answer is B.”
January 4, 2019
GMATGuruNY posted a reply to OG Verbal 2016-SC# 63 in the Sentence Correction forum
“In my previous response, I provided links to three official examples. This construction seems viable.”
January 4, 2019
GMATGuruNY posted a reply to OG Verbal 2016-SC# 63 in the Sentence Correction forum
“It is possible for back-to-back modifiers joined solely by a comma to have the same referent. Three examples: http://www.beatthegmat.com/the-hognose-snake-puts-on-an-impressive-bluff-t93558.html http://www.beatthegmat.com/parallelism-issue-t96011.html ...”
January 4, 2019
GMATGuruNY posted a reply to In a sports club, 6 players are divided into 3 teams of 2 pl in the Problem Solving forum
“The usage of the term arrangements is misleading. The prompt seems intended to ask the following: The first player selected can be paired with any of the 5 other players. Thus, the number of options for the first player selected = 5. At this point, 4 players remain. The next player ...”
January 4, 2019
GMATGuruNY posted a reply to This morning, a certain sugar container was full. Since then in the Data Sufficiency forum
“The determine the percent decrease, we need to know the RATIO between the remaining amount of sugar after cookie-making and the original amount of sugar. Statement 1: Case 1: Remaining sugar after cookie-making = 10 pounds Since the remaimning amount of sugar would need to increase by 30% to ...”
January 3, 2019
GMATGuruNY posted a reply to Is x/y < 0? in the Data Sufficiency forum
“Question stem, rephrased: Do x and y have different signs? Statement 1: |x+y| < |x|+|y| Since an absolute value cannot be negative, both sides here are NONNEGATIVE, enabling us to safely square the inequality: (|x+y|)²< (|x|+|y|)² x² + y² + 2xy < x² + y² + 2|x||y| xy < ...”
January 3, 2019
GMATGuruNY posted a reply to If the average of four numbers is 35, how many of the in the Data Sufficiency forum
“Sum of the 4 numbers = (quantity)(average) = 4*35 = 140. Statement 1: None of the numbers are exactly 3 To save time, check whether it''s possible to get different answers to the question stem while also satisfying Statement 2. Case 1: 0, 33, 33, 74 --> sum = 0+33+33+74 = 140 In this ...”
January 3, 2019
GMATGuruNY posted a reply to If a car traveled from Townsend to Smallville at an average in the Data Sufficiency forum
“Statement 1: The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend. Case 1: Distance between Townsend and Smallville = 80 miles Time to travel from Townsend to Smallville at a speed of 40 mph = 80/40 = 2 hours. Time to travel from Smallville to Townsend = ...”
January 3, 2019
GMATGuruNY posted a reply to On each lab that René completed he received either 100 in the Data Sufficiency forum
“Let x = the number of 100-point labs and y = the number of 85-point labs. Question stem, rephrased: What is the value of x? Statement 1: 100x + 85y = 1140 20x + 17y = 228 The value in blue implies the following: Since 20x will have a units digit of 0, 17y must have a UNITS DIGIT OF 8. ...”
January 3, 2019
GMATGuruNY posted a reply to Absolute value in the Problem Solving forum
“Alternate approach: Since an absolute value cannot be negative -- implying that the right side of the equation must be NONNEGATIVE -- we know that x≥0. If x²-6=x, we get: x²-x-6=0 (x-3)(x+2) = 0 Only the factor in green implies a nonnegative option for x: x-3=0 x=3. The correct ...”
January 3, 2019
GMATGuruNY posted a reply to What is the units digit of the number z? in the Data Sufficiency forum
“The usage of number implies that we should consider NON-INTEGER values. Both statements are satisfied by z=18.1 and z=19.1 Since the units digit of z can be different values, the two statements combinecd are INSUFFICIENT. The correct answer is E.”
January 2, 2019
GMATGuruNY posted a reply to Is √(x+1)^2=x+1 ? in the Data Sufficiency forum
“√(a²) = |a|. Question stem, rephrased: Is |x+1| = x+1? The answer will be YES if x+1 is NONNEGATIVE: x+1≥0 x≥-1. Question stem, rephrased again: Is x≥-1? Statement 1: x=0 or x=2. Since x≥-1 in both cases, the answer to the question stem is YES. SUFFICIENT. Statement 2: ...”
December 31, 2018
GMATGuruNY posted a reply to If f(x)=1-(1/x), then f(f(f(x)))=? in the Problem Solving forum
“Let x=2 and apply the function three times: f(2) = 1 - 1/2 = 1/2. f(1/2) = 1 - 1/(1/2) = -1. f(-1) = 1 - (1/-1) = 2. The correct answer must yield a value of 2 when x=2. Only A works. The correct answer is A.”
December 31, 2018
GMATGuruNY posted a reply to Singular or Plural Verb with None in the Sentence Correction forum
“Any BAG taken on the subway IS subject to search by the police. Any BAGS taken on the subway ARE subject to search by the police. In each of these sentences, any is a MODIFIER describing the subject in blue. In the first sentence, the verb (is) is SINGULAR to match the singular subject in blue. ...”
December 31, 2018
GMATGuruNY posted a reply to Brady, Charlie, and Daryl play on the same baseball team. Th in the Data Sufficiency forum
“Statement 1: No information about Charlie or Daryl. INSUFFICIENT. Statement 2: For every 2 home run hits made by Charlie and Daryl combined, Brady made 4 home run hits, implying that Brady made 4 of every 6 home run hits: 4/6 = 2/3. SUFFICIENT. The correct answer is B.”
December 31, 2018
GMATGuruNY posted a reply to Skier Lindsey Vonn completes a straight 300-meter downhill r in the Problem Solving forum
“Downhill speed - uphill speed = (x+10) - (x-8) = 18. Implication: The downhill speed is 18 mps greater than the uphill speed. We can PLUG IN THE ANSWERS, which represent the downhill speed. Since the downhill speed is 18 mps greater than the uphill speed, the correct answer must be GREATER ...”
December 31, 2018
GMATGuruNY posted a reply to Two dogsled teams raced across a 300 mile course in Wyoming. in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent B''s speed. When the correct answer is plugged in, B''s time - A''s time = 3 hours. For each team: Time = distance/speed = 300/speed. B: B''s speed = 15 mph, implying that A''s speed = 15+5 = 20 mph In this case, B''s time - A''s time = 300/15 - ...”
December 30, 2018
GMATGuruNY posted a reply to In a stack of boards at a lumber yard, the 20th board counti in the Problem Solving forum
“1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 = 16 20 = 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 In the rendering above: The red values represent the number of boards when counting from the TOP. The blue values represent the number of boards when counting from the ...”
December 30, 2018
GMATGuruNY posted a reply to If the original price of an item in a retail store is marked in the Data Sufficiency forum
“Let the original price = 100. Then the markup = (m/100)*100 = m. The resulting price = 100+m. The subsequent discount = d/100*(100+m) = d + md/100 Thus, the total percent change = percent increase - percent decrease = m - d - md/100. For the final price to be greater than the original price, ...”
December 30, 2018
GMATGuruNY posted a reply to Mark has fewer than 9 coins. Each coin is either a quarter in the Data Sufficiency forum
“Statement 1: To MINIMIZE the number of coins so that a sum of 170 cents is yielded by at most 8 coins, we must MAXIMIZE the number of quarters. Since 7*25 = 175 cents, the number of quarters must be less than 7. 170 cents will be yielded by 6 quarters (totaling 150 cents) and 2 dimes (totaling 20 ...”
December 28, 2018
GMATGuruNY posted a reply to Pumping alone at their respective constant rates, one inlet in the Problem Solving forum
“Let the tank = 36 gallons. Since the first pipe takes 3 hours to fill 1/2 the tank -- and (1/2)(36) = 18 gallons -- the rate for the first pipe = w/t =18/3 = 6 gallons per hour. Since the second pipe takes 6 hours to fill 2/3 of the tank -- and (2/3)(36) = 24 gallons -- the rate for the second ...”
December 27, 2018
GMATGuruNY posted a reply to Solution A is 20% salt and Solution B is 80% salt. If you in the Problem Solving forum
“Since the desired salt percentage -- 50% -- is HALFWAY between the salt percentages for A and B (20% and 80%), the resulting solution must contain equal amounts of A and B. The correct answer is C.”
December 27, 2018
GMATGuruNY posted a reply to If the ratio of the price of 1 kilogram Camembert cheese to in the Data Sufficiency forum
“What is the value of T-C? Statement 1: T:B = 4:5. To combine T:B = 4:5 and C:B = 5:8, the element common to both ratios -- B -- must be represented by the SAME VALUE in each: T:B = 4:5 = 32:40. C:B = 5:8 = 25:40. Combining the two ratios, we get: C:T:B = 25:32:40. Case 1: T=32 and C=25, ...”
December 26, 2018
GMATGuruNY posted a reply to In a village of 100 households, 75 least one DVD player, 80 in the Problem Solving forum
“Let D = DVD owners, C = cellphone owners, and M = MP3 owners. T = D + C + M - (DC + DM + CM) - 2(DCM). The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS. When we add together everyone in D, everyone in C, and everyone in M: Those in exactly 2 of the groups (DC + DM + ...”
December 26, 2018
GMATGuruNY posted a reply to A certain punch contains grape juice, orange juice, and in the Problem Solving forum
“The sum of the parts of the ratio = 2+3+7 = 12. Thus -- of every 12 ounces -- 2 ounces are grape juice, 3 ounces are orange juice, and 7 ounces are pineapple juice. Since grape juice constitutes 2 of every 12 ounces, the amount of grape juice is equal to 2/12 of the total: (2/12)(156) = 2*13 = ...”
December 26, 2018
GMATGuruNY posted a reply to If x is a factor of positive integer y, then which of the fo in the Problem Solving forum
“Strategy: Try to show that four of the answer choices do NOT have to be positive. Case 1: x=1 and y=1 In this case, A, B and D are not positive. Eliminate A, B and D. Case 2: x=1 and y=2 In this case, C is not positive. Eliminate C. The correct answer is E.”
December 26, 2018
GMATGuruNY posted a reply to The sum of 4 different odd integers is 64. What is the value in the Data Sufficiency forum
“Statement 1: Since the numbers are EVENLY SPACED, median = sum/count: 64/4 = 16. Since the median = 16, the 4 odd integers must be as follows: 13, 15, 17, 19. Thus, the greatest of the 4 odd integers = 19. SUFFICENT. Statement 2: The 4 odd integers yielded by Statement 1 -- 13, 15, 17, 19 ...”
December 26, 2018
GMATGuruNY posted a reply to If x^2+y^2=28 and xy=11, what is the value of (x+y)^2? in the Problem Solving forum
“Every test-taker should know the following quadratic identities: (x+y)² = x² + y² + 2xy (x-y)² = x² + y² - 2xy (x+y)(x-y)² = x² - y² Substituting x²+y²=28 and xy=11 into (x+y)² = x² + y² + 2xy, we get: (x+y)² = 28 + 2*11 = 50. The correct answer is C. An alternate ...”
December 25, 2018
GMATGuruNY posted a reply to There are 10 books on a shelf: 5 English books, 3 Spanish bo in the Problem Solving forum
“P(2 different languages) = 1 - P(2 of the same language). Case 1: P(2 English books are selected) P(1st book is English) = 5/10. (Of the 10 books, 5 are English.) P(2nd book is English) = 4/9. (Of the 9 remaining books, 4 are English.) To combine these probabilities, we multiply: 5/10 * 4/9 = ...”
December 25, 2018
GMATGuruNY posted a reply to If the farmer sells 75 of his chickens, his stock of feed wi in the Problem Solving forum
“Total amount of feed = (number of chickens)(number of days). The number of chickens is INVERSELY PROPORTIONAL to the number of days. If the number of chickens DOUBLES, then the feed will last for 1/2 the number of days. If the number of chickens TRIPLES, then the feed will last for 1/3 the ...”
December 24, 2018
GMATGuruNY posted a reply to While driving on a highway, Harry and Ron crossed checkpoint in the Problem Solving forum
“9am-10am: Since Harry reaches checkpoint P at 9am -- and travels at rate of 30 mph -- from 9am to 10am Harry travels 30 miles beyond checkpoint P. Thus, when Ron reaches checkpoint P at 10am, he is 30 miles behind Harry. Checkpoint Q: When people compete, SUBTRACT THEIR RATES. Every hour Ron ...”
December 23, 2018
GMATGuruNY posted a reply to Work/Rate in the Data Sufficiency forum
“Let J = the number of hours that John works. Since John assembles 3 chairs per hour, the number of chairs assembled by John = 3J. Let L = the number of hours that Larry works. Since Larry assembles 4 chairs per hour, the number of chairs assembled by Larry = 4L. Since John and Larry work a total ...”
December 21, 2018
GMATGuruNY posted a reply to Five friends - Ross, Phoebe, Chandler, Joey and Monica - in the Problem Solving forum
“Number of options for Phoebe = 1. (Must be Margherita.) Number of options for Ross = 3. (Of the 4 remaining pizzas, any but Hawaiian.) Number of options for Chandler = 3. (Any of the 3 remaining pizzas.) Number of options for Joey = 2. (Either of the 2 remaining pizzas.) Number of options for ...”
December 21, 2018
GMATGuruNY posted a reply to At the Trenchard Oaks apartment complex, a two-bedroom apart in the Problem Solving forum
“Let the monthly rent for a one-bedroom apartment = $2, implying that the monthly rent for a two-bedroom apartment = 2 + (50% of 2) = 2 + 1 = $3. Since the monthly rent for a one-bedroom apartment = $2, the total amount required to rent a one-bedroom apartment for 12 months = 2*12 = 24. If Alex ...”
December 20, 2018
GMATGuruNY posted a reply to absolute value in the Problem Solving forum
“The CRITICAL POINTS are where the expressions inside the absolute values are equal to 0. x+5 = 0 when x=-5. Substituting x=-5 into y = |x+5|-|x-5|, we get: y = |-5+5| - |-5-5| = 0-10 = -10. x-5 = 0 when x=5. Substituting x=5 into y = |x+5|-|x-5|, we get: y = |5+5| - |5-5| = 10-0 = ...”
December 19, 2018
GMATGuruNY posted a reply to One woman and one man can build a wall together in two hours in the Problem Solving forum
“One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. Since replacing 1 man with 2 girls does not change the amount of time required to complete the job, 1 man is the equivalent of 2 ...”
December 19, 2018
GMATGuruNY posted a reply to At garage sale, all of the prices of the items sold were in the Problem Solving forum
“Since the radio = 15th highest price, 14 prices are HIGHER: RADIO-----14 higher prices-----> Since the radio = the 20th lowest price, 19 prices are LOWER: <-----19 lower prices-----RADIO-----14 higher prices----> Total number of items = 19 + RADIO + 14 = 34. The correct answer is ...”
December 19, 2018
GMATGuruNY posted a reply to x and y are positive integers. Is y an even integer? in the Data Sufficiency forum
“The product of two consecutive integers is always EVEN: 1*2 = 2 2*3 = 6 3*4 = 12 Statement 1: y+2 = x² + x y+2 = x(x+1) y+2 = product of 2 consecutive integers y+2 = EVEN y = EVEN - 2 y = EVEN - EVEN y = EVEN SUFFICIENT. Statement 2: No information about y. INSUFFICIENT. The ...”
December 18, 2018
GMATGuruNY posted a reply to (0.0004)(0.000005)/200,000 is equal to which of the followin in the Problem Solving forum
“I believe that the answer choices should appear as shown below: The blue values below cancel out, leaving only the red values: (4 * 10¯⁴)(5 * 10¯⁶) / (20 * 10⁴) = 10¯¹⁰/10⁴ = 10¯¹⁴. The correct answer is B.”
December 18, 2018
GMATGuruNY posted a reply to Sanjana jogged uphill for a while at an average speed of 3 m in the Problem Solving forum
“This is a MIXTURE problem. Two speeds (3 mph and 8 mph) are combined to form a mixture with an average speed of 4 mph. To determine how much time must be spent at each speed, we can use ALLIGATION. Let U = the uphill speed and D = the downhill speed. Step 1: Plot the 3 speeds on a number ...”
December 18, 2018
GMATGuruNY posted a reply to If 2 and 17 are factors of positive integer n, then which of in the Problem Solving forum
“2 and 17 have no factors in common. Since n must be divisible by both 2 and 17 -- and 2*17 = 34 -- n must be a MULTIPLE OF 34. Thus, n must be divisible by I. Eliminate any answer choice that does not include I. Eliminate B and E. If n=34, then n is not divisible by II or III. Eliminate any ...”
December 17, 2018
GMATGuruNY posted a reply to Seven students are trying out for the school soccer team, on in the Problem Solving forum
“To keep track of the number of options for each position, draw a TREE. Start with the MOST RESTRICTED position, which is SWEEPER. If Sweeper = 3, then Goalie = 5. If Sweeper = 4, then Fullback = 2. Here''s the tree so far: http://s11.postimage.org/laxnlsbof/soccer_half_tree.jpg Now complete ...”
December 17, 2018
GMATGuruNY posted a reply to In a network of car dealerships, a group of d sales director in the Data Sufficiency forum
“A group...EACH has a team. The wording above does not convey a logical meaning. When each serves as an adverb, it cannot refer to a singular noun such as a group. When each serves as an adverb, it may refer only to a PLURAL noun. The prompt seems intended to convey the following: Since ...”
December 16, 2018
GMATGuruNY posted a reply to If one manual weighs 400 grams, how many kilograms does a in the Problem Solving forum
“48 manuals * (400 grams)/(1 manual) * (1 kilogram)/(1000 grams) = (48*400)/1000 = 192/10 = 19.2 kilograms.”
December 16, 2018
GMATGuruNY posted a reply to When the positive integer x is divided by 9, the remainder in the Problem Solving forum
“Let x=5, since dividing 5 by 9 yields a remainder of 5: 5/9 = 0 R5. When 3x=15 is divided by 9, we get: 15/9 = 1 R6. The correct answer is E.”
December 16, 2018
GMATGuruNY posted a reply to The main ingredient in a certain prescription drug capsule in the Problem Solving forum
“Each capsule contains 600 milligrams of ingredient. 10⁶ milligrams = 1 kilogram. 1 kilogram of ingredient = 500 dollars. To determine the cost per capsule, we must use the relationships above to convert 600 milligrams into dollars: (600 milligrams) * (1 kilogram)/(10⁶ milligrams) * (500 ...”
December 15, 2018
GMATGuruNY posted a reply to Each Machine of type A has 3 steel parts and 2 chrome parts. in the Problem Solving forum
“(3 steel parts in each type A machine) + (4 steel parts in each type B machine) = 20 steel parts: 3A + 4B = 20 3A = a multiple of 3 less than 20. Options for 3A: 3, 6, 9, 12, 15, 18 4B = a multiple of 4 less than 20. Options for 4B: 4, 8, 12, 16 Only the two values in blue yield a sum ...”
December 15, 2018
GMATGuruNY posted a reply to Did Jeff record more sales revenue this month than Dan did? in the Data Sufficiency forum
“Statement 1: For every $100 commission that Dan earns, Jeff earns $120 in commission. Since the commission rates for Dan and Jeff are unknown, no way to determine whether Jeff recorded more sales revenue than Dan. INSUFFICIENT. Statement 2: Since Jeff''s sales and Dan''s sales can be any ...”
December 14, 2018
GMATGuruNY posted a reply to If sets A and B have the same number of terms, is the standa in the Data Sufficiency forum
“Standard deviation describes how much the values in a set deviate from the mean. A larger standard deviation indicates that the values are deviating more -- getting farther away from -- the mean. So the question can be rephrased: Do the values in set A deviate more from the mean than the do ...”
December 14, 2018
GMATGuruNY posted a reply to Is (y−10)^2>(x+10)^2? ----Veritas in the Data Sufficiency forum
“x² < y² can be rephrased as follows: |x| < |y| Thus, the question stem can be rephrased as follows: Is |x+10| < |y-10|? |a-b| = the distance between a and b |a+b| = |a-(-b)| = the distance between a and -b Thus, the question stem can be further rephrased as follows: Is the ...”
December 14, 2018
GMATGuruNY posted a reply to Three congruent circles overlap in such a way that each circ in the Problem Solving forum
“The statement above is incorrect. https://i.postimg.cc/jL1NMjTL/three-congruent-circles-shaded-region.png The shaded region encompassing the equilateral triangle is not a circle.”
December 13, 2018
GMATGuruNY posted a reply to Three congruent circles overlap in such a way that each circ in the Problem Solving forum
“Area of an equilateral triangle = (s²/4)√3. √3 ≈ 1.7. https://i.postimg.cc/1gCbnSTK/three-congruent-circles.png Each circle has a radius of 8, yielding the equilateral triangle above. Area of the equilateral triangle = (8²/4)√3 = 16√3 ≈ (16)(1.7) = 27. The three circles form ...”
December 13, 2018
GMATGuruNY posted a reply to A baseball team’s season consists of playing 162 games. At in the Problem Solving forum
“The team has won 58 percent of the games it has played. 58% = 58/100 = 29/50. The fraction in blue implies that the number of wins must be a MULTIPLE OF 29: If 50 games are played, the number of wins = (29/50)(50) = 29. If 100 games are played, the number of wins = (29/50)(100) = 58. If 150 ...”
December 12, 2018
GMATGuruNY posted a reply to Effect of several Tsunamis in the Sentence Correction forum
“A method is a PROCEDURE for accomplishing a particular goal. Since the clause in red does not discuss a procedure, it cannot be summed up as a METHOD.”
December 11, 2018
GMATGuruNY posted a reply to Effect of several Tsunamis in the Sentence Correction forum
“The SC above is modeled -- not altogether successfully -- after SC30 in the OG12: https://www.beatthegmat.com/not-sure-about-the-answer-of-a-question-from-og12-t265701.html Rather than study the SC above, stick to the official SC.”
December 11, 2018
GMATGuruNY posted a reply to The table above shows the number of students in three clubs in the Problem Solving forum
“The values in the chart DOUBLE-COUNT any student who belongs to 2 of the 3 clubs. The totals for chess and drama -- 40 and 30 -- double-count the 10 students who belong to both chess AND drama. The totals for chess and math -- 40 and 25 -- double-count the 5 students who belong to both chess AND ...”
December 11, 2018
GMATGuruNY posted a reply to This year, a woman has a lucrative one-year position. During in the Problem Solving forum
“Let r=9, with the result that 1+r = 10. Her husband can turn each dollar she gives him into 1+r, which will be deposited in a bank account. Let the wife give the husband $1, implying that the husband turns this $1 into 1+r = $10. Thus, the amount deposited into the account = $10. The ...”
December 11, 2018
GMATGuruNY posted a reply to Line DB divides Rectangle ABCD into two equal triangles. Is in the Data Sufficiency forum
“Yes, the line will be a diagonal, but the four angles created by this diagonal will each be 45 degrees only if the rectangle is a square.”
December 10, 2018
GMATGuruNY posted a reply to What is the solution set of (1+|x|)(1+x) > 0? in the Problem Solving forum
“x=0 satisfies (1+|x|)(1+x) > 0. Since x=0 is not included in B, C, D or E, eliminate B, C, D and E. The correct answer is A.”
December 10, 2018
GMATGuruNY posted a reply to Tom drives from town A to town B, driving at a constant spee in the Problem Solving forum
“Let the distance between A and B = 120 miles. Since the 120-mile distance between A and B is twice the distance between B and C, the distance between B and C = 60 miles, implying that the total distance = 120+60 = 180 miles. Since the average speed for the 120-mile leg between A and B = 60 ...”
December 10, 2018
GMATGuruNY posted a reply to If the average (arithmetic mean) of five consecutive negativ in the Problem Solving forum
“The value of k is irrelevant. For any set of 5 consecutive integers, the difference between the greatest and least will always be 4. The correct answer is A.”
December 9, 2018
GMATGuruNY posted a reply to Three photographers, Lisa, Mike and Norm, take photos of a w in the Problem Solving forum
“The sum for Lisa and Mike is 50 less than the sum for Norm and Mike. Since Mike is common to both sums, the 50-photo difference must be yielded solely by Lisa and Norm. Implication: Lisa took 50 fewer photos than Norm. We can PLUG IN THE ANSWERS, which represent the number of photos taken ...”
December 9, 2018
GMATGuruNY posted a reply to Andrew sells vintage clothing at a flea market at which he in the Problem Solving forum
“Let h=3. Since an average of $78 is sold per hour, the total revenue for 3 hours = 3*78 = 234. Since the cost for the day is composed of $150 for the table rental and $10 per hour for the assistant, the cost for the day = 150 + 3*10 = 180. P = profit = revenue - cost = 234 - 180 = 54. The ...”
December 9, 2018
GMATGuruNY posted a reply to OG2019 -Logical flow in the Critical Reasoning forum
“It takes for granted that X implies that X is an ASSUMPTION: a statement that must be true for the conclusion to hold. Thus, when X is negated, the conclusion must be invalidated. B: It takes for granted that the volunteers with the highest levels of self-esteem had better social skills than did ...”
December 8, 2018
GMATGuruNY posted a reply to OG2019 -Logical flow in the Critical Reasoning forum
“Premise: Volunteers with the highest levels of self-esteem consistently rated themselves as having much better social skills than did the volunteers with moderate levels. Conclusion: Attaining an exceptionally high level of self-esteem greatly improves one’s social skills. The correct answer ...”
December 8, 2018
GMATGuruNY posted a reply to 2k years ago Frank was 3k years old. In k years Frank's age, in the Problem Solving forum
“Let k=10. 2k years ago Frank was 3k years old. Since k=10, 20 years ago Frank was 30 years old, implying that his age now = 30+20 = 50. In k years Frank''s age, in years, will be: Since Frank is now 50 years old, Frank''s age in 10 years = 50+10 = 60. The correct answer must yield a value ...”
December 7, 2018
GMATGuruNY posted a reply to Which of the following equations is satisfied by x=1+√2? in the Problem Solving forum
“Alternate approach: For any quadratic in the form x² + bx + c = 0, where b and c are rational numbers: If one of the roots is m+√n, then the other root is m-√n. Sum of the roots = -b Product of the roots = c Here, since one of the roots is 1+√2, the other root is 1-√2. Thus: -b ...”
December 7, 2018
GMATGuruNY posted a reply to Each day at Dan’s new job, he earns $10 more than the day in the Data Sufficiency forum
“Since each payday is $10 more than the preceding payday, the list of 15 paydays constitutes an EVENLY SPACED SET. Statement 1: For any evenly spaced set: Median = Sum/Quantity. Thus: Pay on the 14th day = median of the 3 most recent days = sum/quantity = 690/3 = 330. Since the pay on the ...”
December 6, 2018
GMATGuruNY posted a reply to Tom saved $10,000 at a constant compound interest rate of r in the Problem Solving forum
“Original deposit: 10,000. The balance doubles every 10 years. After 10 years, we get: 2*10,000 = 20,000. After 20 years, we get: 2*20,000 = 40,000. After 30 years, we get: 2*40,000 = 80,000. The correct answer is E.”
December 6, 2018
GMATGuruNY posted a reply to If a, b, and c are positive integers such that a < b < in the Data Sufficiency forum
“Does (a/100) * (b/100) * c = integer? Test integer values such that a < b < c. Statement 1: b = (a/100)¯¹ Thus, b = 100/a. Test the smallest possible value for a. Case 1: a=1 Here, b =100/1 = 100. In this case, (a/100) * (b/100) * c = 1/100 * 100/100 * c = c/100. If c ...”
December 5, 2018
GMATGuruNY posted a reply to If a, b, and c are positive integers, what is the remainder in the Data Sufficiency forum
“Statement 1: No information about b. INSUFFICIENT. Statement 2: No information about a. INSUFFICIENT. Statements combined: Case 1: c=3, with the result that a=3³=27 and that b=(3-2)³=1 In this case, a-b = 27-1 = 26. Dividing 26 by 6, we get: 26/6 = 4 R2 Case 2: c=4, with the ...”
December 5, 2018
GMATGuruNY posted a reply to If w, x, and y are consecutive odd positive integers and w & in the Problem Solving forum
“Test easy cases: 5-3-1 = 1 7-5-3 = -1 The case in green indicates that -1 is a possible value of y-x-w. The correct answer is C.”
December 5, 2018
GMATGuruNY posted a reply to x is a positive number. What is the median of x, √x and x^ in the Data Sufficiency forum
“To determine the median of x, √x and x², we need to know the value of x. Statement 1: Since x is positive, we can safely divide both sides by x: x²/x = x/x x = 1 SUFFICIENT. Statement 2: x² + x + 1 = 3x x² - 2x + 1 = 0 (x-1)² = 0 x = 1 SUFFICIENT. The correct answer is D.”
December 5, 2018
GMATGuruNY posted a reply to A triangle is formed by connecting three randomly chosen ver in the Problem Solving forum
“Let the 6 vertices = A, B, C, D, E and F. P(the triangle includes AT LEAST 1 side of the hexagon) = 1 - P(the triangle includes NO sides of the hexagon). From the 6 vertices, the number of ways to choose 3 to form a triangle = 6C3 = (6*5*4)/(3*2*1) = 20. Of these 20 triangles, only 2 include ...”
December 5, 2018
GMATGuruNY posted a reply to Working together, Machine A and Machine B can produce a in the Data Sufficiency forum
“Since A+B take 4 hours to produce 200 widgets, the combined rate for A+B = w/t = 200/4 = 50 widgets per hour. To determine A''s time to produce 200 widgets, we need to know A''s rate. Question stem, rephrased: What is A''s rate? Statement 1: Since B takes 5 hours to produce 50 widgets, B''s ...”
December 4, 2018
GMATGuruNY posted a reply to How many positive two-digit integers have a remainder of 1 w in the Problem Solving forum
“A quick lesson on remainders: Onto the problem at hand: a remainder of 1 when divided by 2 x = 2a + 1 = 1, 3, 5, 7... In other words, x must be ODD. a remainder of 4 when divided by 5 x = 5b + 4 = 4, 9, 14, 19... Since x must be odd, we get: x = 9, 19, 29.... a remainder of ...”
December 4, 2018
GMATGuruNY posted a reply to If there are 4 pairs of twins, and a committee will be in the Problem Solving forum
“Number of options for the 1st person = 8. Number of options for the 2nd person = 6. (Of the 7 people left, we can''t use the twin of the 1st person chosen, leaving 7-1= 6 choices.) Number of options for the 3rd person = 4. (Of the 6 people left, we can''t use the twins of the 2 people already ...”
December 3, 2018
GMATGuruNY posted a reply to For each of her sales, a saleswoman receives a commission in the Problem Solving forum
“The first $500 of the $800 sale earns 20% commission, while the remaining $300 earns 30%. Average commission percentage per $800 = (500*20 + 300*30)/800 = (5*20 + 3*30)/8 = 190/8 = 23.75 ≈ 24. The correct answer is B.”
December 1, 2018
GMATGuruNY posted a reply to When a certain tree was first planted, it was 4 feet tall in the Problem Solving forum
“Let x = the yearly increase. Height after 4 years = 4 + 4x. Height after 6 years = 4 + 6x. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. The phrase in red implies the following: The height in the 6th year was 6/5 of the height in the 4th ...”
December 1, 2018
GMATGuruNY posted a reply to If k is a positive integer and n=(k-1)k(k+1), is n a multipl in the Data Sufficiency forum
“Every other even integer is a MULTIPLE OF 4: 2, 4, 6, 8, 10, 12... Thus, the product of two consecutive even integers = product of a multiple of 4 and an even non-multiple of 4 = MULTIPLE OF 8: 2*4 = 8 4*6 = 2*2*2*3 = 8*3 10*12 = 2*5*2*2*3 = 8*15 Statement 1: Since k is odd, k-1 and k+1 ...”
November 30, 2018
GMATGuruNY posted a reply to If x^2=x+1, then x^4=? in the Problem Solving forum
“Squaring both sides, we get: (x²)² + (x+1)² x⁴ = x² + 2x + 1 Substituting x²=x+1 into x⁴ = x² + 2x + 1, we get: x⁴ = (x+1) + 2x + 1 x⁴ = 3x + 2 The correct answer is A.”
November 30, 2018
GMATGuruNY posted a reply to Is the positive integer p a multiple of 50? in the Data Sufficiency forum
“Any integer that is a multiple 10 is also a multiple of 5. Implication: Any integer that satisfies Statement 1 will also satisfy Statement 2. Both statements are satisfied by the following cases: Case 1: p=10, which is a multiple of 10 (and thus is also a multiple of 5) In this case, p is NOT a ...”
November 30, 2018
GMATGuruNY posted a reply to The point A, B, C, and D are on the number line, not in the Data Sufficiency forum
“The drawings below satisfy both statements: http://s4.postimage.org/1yjxdhskk/ABCD_number_line.jpg Since in the first case BD=1 and in the second case BD=17, the two statements combined are insufficient. The correct answer is E.”
November 30, 2018
GMATGuruNY posted a reply to In a business school case competition, the top three teams in the Problem Solving forum
“Case 1: Team A wins a prize, with the result that Team B must win a prize Number of prizes that could be won by A = 3. Number of remaining prizes that could be won by B = 2. Number of teams that could win the third prize = 4. (Any of the 4 remaining teams.) To combine these options, we ...”
November 30, 2018
GMATGuruNY posted a reply to The juice stall at the circus stocked just 2 brands of in the Problem Solving forum
“Let n=50, implying that 50% of the sold juice packs are A, while the other half are B. In other words, the store sells an EQUAL NUMBER of each type of juice pack. Let the store sell 2 OF EACH TYPE of juice pack. Revenue from two $1 packs of A = 2*1 = 2. Revenue from two $1.5 packs of B = ...”
November 29, 2018
GMATGuruNY posted a reply to James started from his home and drove eastwards at a in the Problem Solving forum
“Let James'' rate = 3 mph. James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James ...”
November 29, 2018
GMATGuruNY posted a reply to The equation of a circle in the x-y coordinate plane is x^2 in the Problem Solving forum
“The equation for a circle with its center at the origin and a radius of r is as follows: x² + y² = r². Thus, x² + y² = 25 is a circle with its center at the origin and a radius of 5. A point on this circle will have integer coordinates in three cases: Case 1: The radius is horizontal ...”
November 29, 2018
GMATGuruNY posted a reply to On a partly cloudy day, Derek decides to walk back from work in the Problem Solving forum
“The average speed -- 2.8 miles per hour -- must be BETWEEN the two individual rates (s and s+1). Thus, s = 2 miles per hour and s+1 = 3 miles per hour. We can PLUG IN THE ANSWERS, which represent the fraction traveled at 2 miles per hour. When the correct fraction is plugged in, the average ...”
November 28, 2018
GMATGuruNY posted a reply to Eight consecutive integers are selected from the integers 1 in the Data Sufficiency forum
“When consecutive positive integers are divided by positive integer x, the resulting remainders also are consecutive: If x=4: 16/4 = 4 R0. 17/4 = 4 R1. 18/4 = 4 R2. 19/4 = 4 R3. 20/4 = 5 R0. From here, the cycle of remainders will repeat: 0,1,2,3,0,1,2,3... The smallest remainder is 0. The ...”
November 28, 2018
GMATGuruNY posted a reply to A club has 10 members. One president and two vice-presidents in the Problem Solving forum
“Number of options for president = 10. (Any of the 10 members.) From the remaining 9 members, the number of ways to choose 2 to serve as vice-president = 9C2 = (9*8)/(2*1) = 36. To combine these options, we multiply: 10*36 = 360. The correct answer is E.”
November 28, 2018
GMATGuruNY posted a reply to Twelve identical machines, running continuously at the same in the Problem Solving forum
“One approach is to use the following equation: (machines)(time) / output = (machines)(time) / output In the equation above: Machines and time are INVERSELY PROPORTIONAL. As the number of machines increases, the amount of time required to produce the same output decreases. Machines and ...”
November 24, 2018
GMATGuruNY posted a reply to In a plane, there are two parallel lines. One line has 5 in the Problem Solving forum
“One approach: Good Cases = Total Cases - Bad Cases. Total Cases: From 9 points, the number of ways to choose 3 = 9C3 = (9*8*7)/(3*2*1) = 84. Bad Case 1: Choosing 3 collinear points from the 5-point line, with the result that a triangle cannot be formed From the 5 points on this line, the ...”
November 24, 2018
GMATGuruNY posted a reply to Find x^4 + 1/x^4 if x – 1/x = 2. in the Problem Solving forum
“(x – 1/x)² = 2² x² + 1/x² - 2(x)(1/x) = 4 x² + 1/x² - 2 = 4 x² + 1/x² = 6 (x² + 1/x²)² = 6² x⁴ + 1/x⁴ + (2)(x²)(1/x²) = 36 x⁴ + 1/x⁴ + 2 = 36 x⁴ + 1/x⁴ = 34. The correct answer is D.”
November 23, 2018
GMATGuruNY posted a reply to If n is an integer greater than 1, what is the value of n? in the Data Sufficiency forum
“Since the prompt indicates that n is an integer greater than 1, the case in red is not possible. The only value that satisfies Statement 2 is n=2, making Statement 2 SUFFICIENT. The correct answer thus is not C but B.”
November 23, 2018
GMATGuruNY posted a reply to What is the sum of the prime factors of 2^8-1? in the Problem Solving forum
“Alternate approach: 2⁸ - 1 = 256 - 1 = 255 = 5*51 = 5*3*17. Sum of the prime factors = 5+3+17 = 25. The correct answer is E.”
November 22, 2018
GMATGuruNY posted a reply to June 25, 1982, fell on a Friday. On which day of the week in the Problem Solving forum
“Between 1982 and 1987 are 4 non-leap years and 1 leap year. Each non-leap year is composed of 365 days; a leap year is composed of 366 days. Thus, from June 25, 1982 to June 25, 1987, the total number of days = 4(365) + 366. Since June 25, 1982 is a Friday, every passing of 7 days will yield ...”
November 22, 2018
GMATGuruNY posted a reply to A man walking at a constant rate of 4 miles per hour is pass in the Problem Solving forum
“(man''s rate)/(woman''s rate) = (4 mph)/(20 mph) = 1/5. Between the moment when the woman passes the man and the moment when she stops to wait, the woman and the man each travel for 5 minutes. During these 5 minutes, the woman travels x miles. Since the man''s rate is 1/5 the woman''s rate, the ...”
November 21, 2018
GMATGuruNY posted a reply to Six countries in a certain region sent a total of 75 in the Data Sufficiency forum
“Let the 6 countries be A, B, C, D, E and F. The question stem asks whether A≥10. Plug in A=10 (which satisfies statement 2 and is at least 10) and A=9 (which also satisfies statement 2 but is NOT at least 10). To save time, let F=41, which satisfies statement 1. Case 1: Total = 75, ...”
November 21, 2018
GMATGuruNY posted a reply to If n is an integer greater than 1, what is the value of n? in the Data Sufficiency forum
“Statement 1: Here, n can be any prime number. INSUFFICIENT. Statement 2: (n+2)/n = n/n + 2/n = 1 + 2/n. Given that n must be an integer, 1 + 2/n will yield an integer value only if n is a FACTOR OF 2. Factors of 2: 1 and 2. Since n must be greater than 1, n=2. SUFFICIENT. The correct ...”
November 21, 2018
GMATGuruNY posted a reply to A number when divided by 4 and 5 leaves remainders 1 and 4 in the Problem Solving forum
“Please fix the prompt, which has been transcribed incorrectly. It should include the word in red:”
November 20, 2018
GMATGuruNY posted a reply to A woman has seven cookies - four chocolate chip and three in the Problem Solving forum
“Alternate approach: Case 1: Deborah and Kim each receive an oatmeal cookie In this case, 4 chocolate chip cookies and 1 oatmeal cookie remain. The remaining oatmeal cookie has 5 options: Nicole, Ronit, Mark, Terrance, or no one. Total ways = 5. Case 2: Deborah and Kim each receive a ...”
November 20, 2018
GMATGuruNY posted a reply to The Lewiston Road Race is how many kilometers long? in the Data Sufficiency forum
“Statement 1: Rate and time have a RECIPROCAL relationship. A rate ratio of (40kph) : (50kph) = 4:5 implies a time ratio of 5:4 = 10:8. The time ratio in blue implies that -- for the time at 40kph to be 2 hours more than the time at 50kph -- the time at 40kph must be 10 hours, while the time at ...”
November 17, 2018
GMATGuruNY posted a reply to Tim and Glenn are running laps around a circular track. in the Data Sufficiency forum
“Statement 1: The TIME RATIO for Tim and Glenn = 48:60 = 4:5. Since time and rate have a RECIPROCAL relationship, the RATE RATIO for Tim and Glenn = 5:4. Implication: For every 5 laps that Tim runs, Glenn runs only 4 laps. Thus, after running 5 laps, Tim will have run 1 more lap than Glenn. ...”
November 16, 2018
GMATGuruNY posted a reply to At the Trenchard Oaks apartment complex, a two-bedroom in the Problem Solving forum
“Let the one-bedroom rent = $2 per month, implying that the two-bedroom rent = 2 + (50% of 2) = 2 + 1 = $3 per month. Since the rent for a one-bedroom apartment = $2 per month, the total amount to rent a one-bedroom apartment for 12 months = 2*12 = $24. For $24, the number of months yielded for a ...”
November 16, 2018
GMATGuruNY posted a reply to A certain store will order 25 crates of apples. The apples in the Problem Solving forum
“Let W = Winesap crates, M = McIntosh crates, and R = Roma crates. Since a total of 25 crates are ordered, we get: W + M + R = 25. To MINIMIZE the value of W, we must MAXIMIZE the values of M and R. Since the store is to order more crates of Winesap than crates of McIntosh and more crates of ...”
November 15, 2018
GMATGuruNY posted a reply to A marzipan factory has two machines producing marzipan. in the Data Sufficiency forum
“The prompt states: Every day, the two machines operate constantly from 08:00 to 18:00. As shown in my post above, Statement 2 yields the following rate ratio: (W alone) : (W and D together) = 1:5. The rate ratio indicates that -- of every 5 kg produced when W and D work together from 8:00 to ...”
November 15, 2018
GMATGuruNY posted a reply to Organized in 1966 by the Fish and Wildlife in the Sentence Correction forum
“Generally, for + VERBing is an ADJECTIVE serving to modify a NOUN. A: The Breeding Bird Survey uses annual roadside counts along established routes for monitoring. Here, for monitoring seems to be an ADJECTIVE modifying routes, implying that the ROUTES were designed FOR MONITORING. Not the ...”
November 15, 2018
GMATGuruNY posted a reply to A marzipan factory has two machines producing marzipan. in the Data Sufficiency forum
“Statement 1: Let N = 50 kg. Since W and D produce the entire 50 kg over the 10 hours between 8:00 and 18:00, the combined rate for W and D = 50/10 = 5 kg per hour. Since W takes 25 hours to produce N/2 = 25 kg, W''s rate alone = w/t = 25/25 = 1 kg per hour. Of every 5 kg produced each hour ...”
November 14, 2018
GMATGuruNY posted a reply to If x and y are unknown positive integers, is the mean of the in the Data Sufficiency forum
“Known values, in ascending order: 1, 5, 6, 7 Statement 1: x+y = 7 Mean = sum/quantity = (1+5+6+7+x+y)/6 = (1+5+6+7+7)/6 = 26/6 = 13/3 = 4.33. Text EXTREMES. Case 1: x and y are far from each other If x=1 and y=6, we get: 1, 1. 5, 6, 6, 7 Median = (5+6)/2 = 11/2 = 5.5 Case 2: x and y ...”
November 14, 2018
GMATGuruNY posted a reply to How many positive two-digit numbers yield a remainder of 1 in the Problem Solving forum
“Let x = the two-digit number. Since dividing by 4 leaves a remainder of 1, x is equal to one more than a multiple of 4: x = 4k + 1 Since dividing by 14 leaves a remainder of 1, x is equal to one more than a multiple of 14: x = 14m + 1 Since the two expressions in blue must be equal, we ...”
November 14, 2018
GMATGuruNY posted a reply to On a wedding catering service, An experienced chef can in the Problem Solving forum
“Let service = 24 units. Rate for each experienced chef = w/t = 24/8 = 3 units per hour. Rate for each novice chef = w/t = 24/12 = 2 units per hour. Combined rate for 1 experienced chef and 1 novice chef working together = 3+2 = 5 units per hour. To produce 24 units in 1.6 hours, rate = w/t = ...”
November 13, 2018
GMATGuruNY posted a reply to Jake and Ryan worked together on a job for which they were in the Problem Solving forum
“Let the hourly wage = $1 per hour. Let Ryan''s time = 10 hours, implying that Jake''s time = 10 + (20% of 10) = 10 + 2 = 12 hours. Thus: Total number of work hours = 10+12 = 22 hours. Total pay = (hourly wage)(total number of work hours) = 1*22 = $22. Since the total pay = 10+12 = $22, and ...”
November 13, 2018
GMATGuruNY posted a reply to A store purchased 20 coats that each cost an equal amount in the Data Sufficiency forum
“Statement 1: If the selling price per coat had been twice as much , the store’s gross profit on the 20 coats would have been $2,400 When the selling price per coat is doubled, the resulting profit per coat = (total profit)/(number of coats) = 2400/20 = 120. Case 1: Double the selling price = ...”
November 13, 2018
GMATGuruNY posted a reply to If 60! is written out as an integer, with how many in the Problem Solving forum
“60! = 60*59*58*....*3*2*1. Since 10=2*5, EVERY COMBINATION OF 2*5 contained within the prime-factorization of 60! will yield a 0 at the end of the integer representation of 60!. The prime-factorization of 60! is composed of FAR MORE 2''S than 5''s. Thus, the number of 0''s depends on the ...”
November 13, 2018
GMATGuruNY posted a reply to In the figure AB and CD are two diameters of circle. in the Problem Solving forum
“An INSCRIBED ANGLE is formed by two chords. A CENTRAL ANGLE is formed by two radii. When an inscribed angle and a central angle intercept the same two points on a circle, the inscribed angle is 1/2 the central angle. https://i.postimg.cc/qgbxWKdW/Angle-CEB-1.png Here, inscribed angle CFB and ...”
November 12, 2018
GMATGuruNY posted a reply to If x and y are positive integers such that x = 8y + 12, what in the Data Sufficiency forum
“Statement 1: x=12u, where u is an integer and x=8y+12. In other words, x is a multiple of 12. For x to be a multiple of 12, 8y must be a multiple of 12. If y=3, then x = 8*3 + 12 = 36. The GCD of 3 and 36 is 3. If y=6, then x = 8*6 + 12 = 60. The GCD of 6 and 60 is 6. Since the ...”
November 11, 2018
GMATGuruNY posted a reply to Eight women and two men are available to serve on a in the Problem Solving forum
“P(at least 1 man) = 1 - P(no men). P(no men): P(1st person selected is a woman) = 8/10. (Of the 10 people, 8 are women.) P(2nd person selected is a woman) = 7/9. (Of the 9 remaining people, 7 are women.) P(3rd person selected is a woman) = 6/8. (Of the 8 remaining people, 6 are women.) To ...”
November 11, 2018
GMATGuruNY posted a reply to A gardener is going to plant 2 red rosebushes and 2 white in the Problem Solving forum
“Moving LEFT TO RIGHT along the row: P(1st rosebush is white) = 2/4. (Of the 4 rosebushes, 2 are white.) P(2nd rosebush is red) = 2/3. (Of the 3 remaining rosebushes, 2 are red.) P(3rd rosebush is red) = 1/2. (Of the 2 remaining rosebushes, 1 is red.) P(4th rosebush is white) = 1/1. (The one ...”
November 10, 2018
GMATGuruNY posted a reply to Every day at noon, a bus leaves for Townville and travels at in the Problem Solving forum
“Time and rate have a RECIPROCAL RELATIONSHIP: 2 times as fast implies 1/2 the time. 3 times as fast implies 1/3 the time. Let t = the normal time. Since the bus travels today at 7/6 its normal rate, the time today is equal to 6/7 of the normal time: (6/7)t. Since the bus leaves 1/2 hour late ...”
November 9, 2018
GMATGuruNY posted a reply to There are 27 different three-digit integers that can be in the Problem Solving forum
“Given any set that is symmetrical about the median: Sum = (quantity)(median) The set of 3-digit integers that can be formed from the digits 1,2 and 3 is symmetrical about the median (222): ...212, 213, 221, 222, 223, 231, 232... Thus: Sum of the 27 integers = (quantity)(median) = 27*222 = ...”
November 7, 2018
GMATGuruNY posted a reply to Is x^2>xy? in the Data Sufficiency forum
“For the purposes of a Y/N DS problem, the rephrase is the equivalent of the original question stem. Original question stem: Is x² > xy? The answer will be YES if y/x is less than 1.. The answer will be NO if y/x is NOT less than 1. Thus, the original question stem can be rephrased as ...”
November 5, 2018
GMATGuruNY posted a reply to Is x^2>xy? in the Data Sufficiency forum
“x² > xy is true only if x is NONZERO, in which case we can safely divide by x², since the square of a nonzero value must be positive: x²/x² > (xy)/x² 1 > y/x Question stem, rephrased: Is y/x < 1? Statement 1: x > y If x=2 and y=1, then y/x =1/2. so the answer to the ...”
November 5, 2018
GMATGuruNY posted a reply to | 1 - | 2 - | 3 - | 4 – π | | | | in the Problem Solving forum
“Let π=3 in the original expression and simplify the blue portion below: | 1 - | 2 - | 3 - | 4 – 3 | | | | Simplify the red portion below; | 1 - | 2 - | 3 - 1 | | | Simplify the green portion below: | 1 - | 2 - 2 | | = | 1 - 0 | = 1 The correct answer choice must yield a value of ...”
November 5, 2018
GMATGuruNY posted a reply to Working alone, three persons P, Q, and R can do a certain in the Problem Solving forum
“Let the job = the LCM of the 3 times = 60 widgets. Maximum time: The maximum time is yielded when the slowest person -- R -- works alone. Since R takes 15 hours to complete the 60-widget job, the maximum time = 15 hours. Minimum time: The minimum time is yielded when all 3 people work ...”
November 4, 2018
GMATGuruNY posted a reply to Triplets Adam, Bruce, and Charlie enter a triathlon. If ther in the Problem Solving forum
“One approach: P(good outcome) = 1 - P(bad outcome). Bad outcome #1: Exactly 1 triplet wins. P(triplet wins 1st place) = 3/9. (Of the 9 competitors, 3 are triplets) P(non-triplet wins 2nd place) = 6/8. (Of the 8 remaining competitors, 6 are non-triplets) P(non-triplet wins 3rd place) = 5/7. ...”
November 4, 2018
GMATGuruNY posted a reply to Ryunosuke Akutagawa in the Sentence Correction forum
“Nicely done! Because the comparison in D allows for more than one logical interpretation, eliminate D. In fact, the ambiguity cited above is the most compelling reason to eliminate D.”
November 2, 2018
GMATGuruNY posted a reply to Ryunosuke Akutagawa in the Sentence Correction forum
“X led to Y implies that X did not directly cause Y but that X was a factor that helped to yield Y. SC755 in the OG17: An inability to adapt led to their extinction. Here, an inability to adapt did not directly cause the extinction but was a factor that helped to yield the extinction. A cause ...”
November 2, 2018
GMATGuruNY posted a reply to Ryunosuke Akutagawa in the Sentence Correction forum
“Generally, COMMA + as-clause implies that the clause after as LEADS to the preceding clause, with the result that the two clauses happen concurrently. An OA in GMATPrep: The steel industry has changed radically over the last two decades, as large, integrated companies such as Bethlehem Steel have ...”
November 2, 2018
GMATGuruNY posted a reply to Barry walks from one end to the other of a 30-meter long in the Problem Solving forum
“Let B = Barry''s rate and W = the walkway''s rate. The distance can be ANY VALUE. Let the distance = 240 meters. WITH the walkway, the time = 30 seconds: Here, Barry and the walkway WORK TOGETHER, so we ADD their rates: B+W = d/t = 240/30 = 8 meters per second. AGAINST the walkway, the ...”
November 2, 2018
GMATGuruNY posted a reply to At a family summer party, each of the x members of the in the Problem Solving forum
“Let the x family members = the product of the two denominators = 3*7 = 21. Number who chose to have a hamburger = (1/3)(21) = 7. Since 1/7 of the hamburger-eaters also had a hot dog, the number who had both = (1/7)(7) = 1. Thus, the number who did NOT have both = (total members) - (number who had ...”
November 1, 2018
GMATGuruNY posted a reply to How many positive five-digit integers contain the digit in the Problem Solving forum
“I believe that the prompt above is outdated; regardless, it does not list a correct answer. The prompt below appears in Manhattan''s 5 lb. Book of GRE Practice Problems: Case 1: 57XXX Number of options for the hundreds digit = 10. (Any digit 0-9.) Number of options for the tens digit = 10. ...”
November 1, 2018
GMATGuruNY posted a reply to Two teachers, Ms. Ames and Mr. Betancourt, each had N in the Data Sufficiency forum
“Since the N cookies can be divided evenly among 24 or 18 students, N must be divisible by both 24 and 18. One way to determine the LCM of two integers is to take multiples of the LARGER integer until we get a multiple of the SMALLER integer. Multiples of 24: 24, 48, 72... We can stop here: the ...”
November 1, 2018
GMATGuruNY posted a reply to Did one of the 3 members of a certain team sell at least 2 in the Data Sufficiency forum
“Statement 1: If NONE of the members sells at least 2 tickets, then the 3 members sell a maximum of 1 ticket each, yielding the following total: 1+1+1 = 3. Too small, since the total number of tickets sold = 6. Implication: For a total of 6 tickets to be sold, one of the 3 members must sell at ...”
October 31, 2018
GMATGuruNY posted a reply to A football team averaged 35 points per game over the first in the Problem Solving forum
“This is a weighted average/mixture problem. Average score for the first N games = 35. Score for the final game = 28. Average score for the MIXTURE of all the games = 34. Step-by-step instruction for the alligation approach: Step 1: Plot the 3 averages on a number line, with the average ...”
October 31, 2018
GMATGuruNY posted a reply to 3, 6, 9, 12, … are multiples of 3. How many multiples of 3 in the Problem Solving forum
“The difference between the endpoints of the range = 200-10 = 190. Since neither endpoint is a multiple of 3, we can count the multiples of 3 simply by dividing 3 into 190: 190/3 ≈ 63. The correct answer is D.”
October 31, 2018
GMATGuruNY posted a reply to A group of 20 friends formed an investment club, with each in the Problem Solving forum
“Let d=100. After the value of the stock increases by 40% to $140, the share received by each of the 20 friends = 140/20 = 7. The correct answer must yield a value of 7 when d=100. Only E works: (7d)/100 = (7*100)/100 = 7. The correct answer is E.”
October 30, 2018
GMATGuruNY posted a reply to The average weight of a class is x pounds. When a new in the Problem Solving forum
“We can PLUG IN THE ANSWERS and use alligation. To learn about alligation, check my posts here: https://www.beatthegmat.com/statistics-average-question-t288903.html https://www.beatthegmat.com/alligation-method-t293459.html https://www.beatthegmat.com/mean-t266852.html Let O = the original ...”
October 30, 2018
GMATGuruNY posted a reply to Machines X and Y can work at their respective constant rates in the Data Sufficiency forum
“Statement 1: Time and rate have a RECIPROCAL relationship. Since X and Y together take 2/3 as long as Y alone, X and Y together work 3/2 as fast as Y alone. Thus, if Y''s rate alone = 2 units per hour, then X and Y''s combined rate = (3/2)(2) = 3 units per hour, implying that X''s rate alone = ...”
October 30, 2018
GMATGuruNY posted a reply to Set S contains nine distinct points in the coordinate plane. in the Problem Solving forum
“To form a triangle, we must select 3 points such that at most 2 are collinear. Case 1: Select 3 points not on the x-axis From the 4 points not on the x-axis, the number of ways to choose 3 = 4C3 = (4*3*2)/(3*2*1) = 4. Case 2: Select 1 point on the x-axis and two points not on the x-axis From ...”
October 29, 2018
GMATGuruNY posted a reply to Employees at a company will vote for an executive team of in the Problem Solving forum
“Number of options for president = 8. (Any of the 8 candidates.) Number of options for treasurer = 7. (Any of the 7 remaining candidates.) From the 6 remaining people, the number of ways to choose 3 to serve as warrant officers = 6C3 = (6*5*4)/(3*2*1) = 20. To combine these options, we multiply: ...”
October 29, 2018
GMATGuruNY posted a reply to A set of pencils can be evenly shared between 2, 3, 4, 5 and in the Problem Solving forum
“For the set of pencils to be shared evenly, the total number of pencils must be divisible by the total number of children. Thus, the correct answer must be divisible by 2, 3, 4, 5 and 6. Of the five answer choices, only E is divisible by 2, 3, 4, 5 and 6. The correct answer is E.”
October 29, 2018
GMATGuruNY posted a reply to (x^2-3x+2)(y^2-5y+6)=? in the Data Sufficiency forum
“Statement 1: Substituting x=1 into (x² - 3x + 2)(y² - 5x + 6), we get: (1 - 3*1 + 2)(y² - 5x + 6) = (0)(y² - 5x + 6) = 0. SUFFICIENT. Statement 2: Substituting y=1 into (x² - 3x + 2)(y² - 5x + 6), we get: (x² - 3x + 2)(1² - 5*1 + 6) = (x² - 3x + 2)(2). Since the value of x is ...”
October 29, 2018
GMATGuruNY posted a reply to How many integers are there between, but not including, in the Data Sufficiency forum
“Statement 1: Case 1: r=0 and s=10 Integers between r and s: 1, 2, 3, 4, 5, 6, 7, 8, 9 --> 9 integers Case 2: r=1 and s=11 Integers between r and s: 2, 3, 4, 5, 6, 7, 8, 9, 10 --> 9 integers Case 3: r=2 and s=12 Integers between r and s: 3, 4, 5, 6, 7, 8, 9, 10, 11 --> 9 ...”
October 28, 2018
GMATGuruNY posted a reply to Both Betty and Wilma earn annual salaries of more than $5000 in the Data Sufficiency forum
“Statement 1: Betty''s annual salary is closer to $50000 than Wilma''s is. On a number line: -----50,000---B---W Thus, W > B. SUFFICIENT. Statement 2: Betty''s annual salary is closer to $35000 than it is to Wilma''s annual salary. Case 1: -----35,000-----50,000---B---W Case 2: ...”
October 28, 2018
GMATGuruNY posted a reply to In a right triangle, the longer leg is two more than three in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the length of the shorter leg. When the correct answer is plugged in, the area = 400. B: 20 Longer leg = two more than three times the shorter leg = 2 + 3*20 = 62. Area = (1/2)(20)(62) = 620. Since the area is too great, a smaller answer choice is ...”
October 27, 2018
GMATGuruNY posted a reply to A framed picture is shown above. The frame, shown shaded, is in the Data Sufficiency forum
“Statement 1: Test one case that also satisfies Statement 2. Case 1: The frame is 8 inches tall, with the result that the total area of the frame and picture combined = 6*8 = 48 Area of the picture = (total area) - (shaded region) = 48-24 = 24. Implication: The width of the frame is 1 inch, ...”
October 27, 2018
GMATGuruNY posted a reply to What is the largest prime factor of the expression 3^8 − 2 in the Problem Solving forum
“A general rule: Given x^(even power) - y^(even power), where x and y are distinct positive integers, we can always simplify by applying the difference of two squares. Each time we apply the difference of two squares to the expression in blue, the exponents are reduced by 1/2. For example: x⁸ - ...”
October 26, 2018
GMATGuruNY posted a reply to Jazz and blues recordings accounted for 6 percent of the in the Data Sufficiency forum
“Let J = jazz and blues revenue in 1998. Statement 1: Case 1: Total revenue in 1998 = 100 In this case, J = 5% of 100 = 5. Case 2: Total revenue in 1998 = 1000 In this case, J = 5% of 1000 = 50. Since J can be different values, INSUFFICIENT. Statement 2: In other words: (jazz and blues ...”
October 26, 2018
GMATGuruNY posted a reply to x and y are non-negative integers. If xy+2x+3y=0, then y=? in the Problem Solving forum
“NONNEGATIVE implies that we should test ZERO. Let x=0. Substituting x=0 into xy + 2x + 3y = 0, we get: 0*y + 2*0 + 3y = 0 3y = 0 y = 0 The correct answer is A.”
October 26, 2018
GMATGuruNY posted a reply to Set S contains consecutive natural numbers from 1 to 100, in in the Problem Solving forum
“For any evenly spaced set: sum = (count)(median) Sum of the first n even numbers = n * median of the first n even numbers Sum of the last n odd numbers = n * median of the last n odd numbers Since the ratio of the two sums = 16/85, we get: (n * median of the first n even numbers) / (n * ...”
October 26, 2018
GMATGuruNY posted a reply to Quentin's income is 60% less than Rex's income, and Sam's in the Problem Solving forum
“Let Rex''s income = 100. Since Quentin''s income is 60% less than Rex''s, Quentin''s income = 100 - (60% of 100) = 100-60 = 40. Since Sam''s income is 25% less than Quentin''s, Sam''s income = 40 - (25% of 40) = 40-10 = 30. After Rex gives 60% of his income to Sam, Sam''s new income = 30 + (60% ...”
October 25, 2018
GMATGuruNY posted a reply to If |x-6|=2x, then x=? in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the value of x. Since an absolute value cannot be equal to a negative value, the correct answer cannot be A or B. D: x=2 If we plug x=2 into |x-6|=2x, we get: |2-6| = 2*2 |-4| = 4 4 = 4. Success! The correct answer is D.”
October 25, 2018
GMATGuruNY posted a reply to Tom drives from town A to town B, driving at a constant in the Problem Solving forum
“Let the distance between A and B = 120 miles. Since the 120-mile distance between A and B is twice the distance between B and C, the distance between B and C = 60 miles, implying that the total distance = 120+60 = 180 miles. Since the average speed for the 120-mile leg between A and B = 60 mph, ...”
October 25, 2018
GMATGuruNY posted a reply to gmat prep 2 in the Critical Reasoning forum
“The negation test is not recommended for Evaluate CRs. It can be applied to Assumption CRs and Inference CRs.”
October 24, 2018
GMATGuruNY posted a reply to Computer-based activities in the Critical Reasoning forum
“The answer choices are already phrased as statements. The OA is a statement that weakens the conclusion. OA: Computer owners in the United States predominately belong to a demographic group that have long been known to spend less time watching television. This statement indicates that a lack of ...”
October 24, 2018
GMATGuruNY posted a reply to Noelle walks from point A to point B at an average speed of in the Problem Solving forum
“Let the distance between A and B = the LCM of the two speeds = 5*6 = 30 kilometers, implying that the distance for the entire round trip = 60 kilometers. At a rate of 5 kph, the time to travel the 30 kilometers from A to B = d/r = 30/5 = 6 hours. At a rate of 6 kph, the time to travel the entire ...”
October 24, 2018
GMATGuruNY posted a reply to What is the median number of employees assigned per project in the Data Sufficiency forum
“In ascending order of EMPLOYEES PER PROJECT, let the projects be numbered 1 through 100: 1, 2, 3.....49, 50, 51, ....98, 99, 100. Projects 50 and 51 determine the MEDIAN number of employees: Question rephrased: How many employees are assigned to PROJECTS 50 and 51? Looking at the two ...”
October 24, 2018
GMATGuruNY posted a reply to Three photographers , Lisa, Mike and Norm, take photos of a in the Problem Solving forum
“The sum for Lisa and Mike is 50 less than the sum for Norm and Mike. Since Mike is common to both sums, the 50-photo difference must be yielded solely by Lisa and Norm. Implication: Lisa took 50 fewer photos than Norm. We can PLUG IN THE ANSWERS, which represent the number of photos taken by ...”
October 24, 2018
GMATGuruNY posted a reply to Circle ABCD in the diagram above is defined by the equation in the Problem Solving forum
“Circle ABCD: The equation for a circle with a center at the origin and a radius of r is x² + y² = r². The equation for circle ABCD is x² + y² = 5². Thus, circle ABCD has a radius of 5. Line EF: 3y = 4x + 25 y = (4/3)x + 25/3 Slope = 4/3. A radius drawn to a point of tangency forms ...”
October 24, 2018
GMATGuruNY posted a reply to A factory has three types of machines, each of which works in the Problem Solving forum
“In many cases, similar or identical solutions are posted when two experts respond at virtually the same time, with the result that the second poster is not aware of the first. The time stamps for the two solutions here indicate that both solutions were posted at 11:45am.”
October 23, 2018
GMATGuruNY posted a reply to A factory has three types of machines, each of which works in the Problem Solving forum
“Rates can be ADDED TOGETHER. 7 Machine As and 11 Machine Bs can produce 250 widgets per hour. 7A + 11B = 250 8 Machine As and 22 Machine Cs can produce 600 widgets per hour. 8A + 22C = 600 4A + 11C = 300 Adding together 7A + 11B = 250 and 4A + 11C = 300, we get: 11A + 11B + 11C = 550 A ...”
October 23, 2018
GMATGuruNY posted a reply to 25 integers are written on a board. Are there at least two in the Data Sufficiency forum
“The wording in Statement 1 does not convey a clear meaning: For every value in the list, if the value is increased by 1, the number of distinct values in the list does not change. Here, the term in red could convey to some test-takers that EVERY VALUE in the list is to be increased by 1. Not the ...”
October 23, 2018
GMATGuruNY posted a reply to The annual rent collected by a corporation from a certain in the Data Sufficiency forum
“Let the 1997 rent = 100. Increase in 1998 = (x/100)(100) = x. Thus, rent in 1998 = 100+x. Decrease in 1999 = (y/100)(100+x) = y + xy/100 For the rent to be greater in 1999 than in 1997, the increase in 1998 (x) must be greater than the decrease in 1999 (y + xy/100). Question stem, ...”
October 21, 2018
GMATGuruNY posted a reply to During a 3 year period, the profits of company X changed by in the Data Sufficiency forum
“Statement 1: If profits increase by $X from the first year to the second year, then they must increase by $0 from the second year to the third year, with the result that the increase in profits from the first year to the third year (X+0 = $X) is the same as the increase in profits from the first ...”
October 21, 2018
GMATGuruNY posted a reply to OG The estimated number of homeschooled students in the Problem Solving forum
“Percent greater or percent increase: (bigger value - smaller value)/(smaller value) * 100 Percent less or percent decrease: (bigger value - smaller value)/(bigger value) * 100”
October 21, 2018
GMATGuruNY posted a reply to Mark has fewer than 9 coins. Each coin is either a quarter in the Data Sufficiency forum
“Statement 1: 25Q + 10D = 170 5Q + 2D = 34 To minimize the number of coins, we must maximize the value of Q. If Q=6, then D=2, with the result that 5Q + 2D = (5*6) + (2*2) = 34. In this case, the total number of coins = 6+2 = 8. If the value of Q decreases, then the total number of coins will ...”
October 20, 2018
GMATGuruNY posted a reply to doubt 3 in the Sentence Correction forum
“having + VERBed is a viable construction. An introductory HAVING + VERBed modifier implies PRIOR ACTION: an action completed before the main verb. HAVING FINISHED his dessert, John LEFT the table. Here, HAVING FINISHED implies PRIOR ACTION -- an action completed before John LEFT the table. ...”
October 20, 2018
GMATGuruNY posted a reply to All attendees at a university gathering are faculty or in the Data Sufficiency forum
“Neither statement offers any information about the number of attendees who are alumni. Thus, the two statements combined are INSUFFICIENT. The correct answer is E.”
October 20, 2018
GMATGuruNY posted a reply to If n is an integer, which of the following must be divisible in the Problem Solving forum
“Test n=0. A --> n³ - 4n = 0³ - (4*0) = 0 B --> n³ + 4n = 0³ + (4*0) = 0 C --> n² + 1 = 0² + 1 = 1 D --> n² - 1 = 0² - 1 = -1 E --> n² - 4 = 0² - 4 = -4 Only the options in green yield a multiple of 3. Eliminate C, D and E. Test n=1 in the remaining answer ...”
October 20, 2018
GMATGuruNY posted a reply to At a certain industrial manufacturer, an open tank contains in the Problem Solving forum
“Since 6% of the 1000-gallon tank is fluorine, the amount of fluorine = (6/100)(1000) = 60 gallons. Since the total volume decreases at a rate of 10 gallons per day for 25 days, the decrease in the total volume = 10*25 = 250 gallons. Remaining total volume = 1000-250 = 750 gallons. Since 60 of the ...”
October 20, 2018
GMATGuruNY posted a reply to Is 1+x+x^2+x^3+x^4+x^5+x^6 < 1/(1-x)? in the Data Sufficiency forum
“CRITICAL POINTS in an equality occur when the two sides are EQUAL or the inequality is undefined. Here, the two statements provide the critical points for the inequality in the prompt: When x=0, the two sides are equal. When x=1, the inequality is undefined. To determine the range(s) where the ...”
October 20, 2018
GMATGuruNY posted a reply to Did Jeff record more sales revenue this month than Dan did? in the Data Sufficiency forum
“Statement 1: For every $100 commission that Dan earns, Jeff earns $120 in commission. Since the commission rates for Dan and Jeff are unknown, no way to determine whether Jeff recorded more sales revenue than Dan. INSUFFICIENT. Statement 2: Since Jeff''s sales and Dan''s sales can be any ...”
October 19, 2018
GMATGuruNY posted a reply to If a rectangle’s length is a+b and its area is (1/a)+(1/b) in the Problem Solving forum
“Let a=b=0.5, implying that the rectangle''s length = a+b = 0.5+0.5 = 1 and that its area = (1/0.5) + (1/0.5) = (10/5) + (10/5) = 2+2 = 4. Since the rectangle has an area of 4 and a length of 1, its width = 4. The correct answer must yield a value of 4 when a=b=0.5. Only E works: 1/ab = 1/(0.5 * ...”
October 19, 2018
GMATGuruNY posted a reply to When positive integer N is divided by positive integer J, in the Problem Solving forum
“N/J = 134.08 = 13408/100 = 3352/25. The resulting ratio indicates that N must be multiple of 3352 and that J must be a multiple of 25. Of the five answer choices, only E is a multiple of 25. The correct answer is E.”
October 19, 2018
GMATGuruNY posted a reply to A container contains 4 red marbles and 8 blue marbles. in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the number of blue marbles in the second container. When the correct answer is plugged in, the probability of selecting 2 red marbles OR 2 blue marbles = 1/2. B: 4 blue marbles, implying a total of 10 marbles in the second container Case1: 2 red ...”
October 19, 2018
GMATGuruNY posted a reply to Two printing presses begin printing currency at the same in the Problem Solving forum
“Since F produces 1000 5-dollar bills each minute, the dollar amount produced by F each minute = 1000*5 = $5000. Since T produces 200 20-dollar bills each minute, the dollar amount produced by T each minute = 200*20 = $4000. Thus, every minute F surpasses T by $1000. Since F surpasses T by $1000 ...”
October 18, 2018
GMATGuruNY posted a reply to Brian purchased a bouquet of 40 flowers for his mother for in the Problem Solving forum
“= We can PLUG IN THE ANSWERS, which represent the number of tulips. When the correct answer is plugged in, the total cost = $48. D: 24 tulips, implying 16 roses, for a total of 40 flowers Since each of the 24 tulips costs $1, and each of the 16 roses costs $1.50, we get: Total cost = (24*1) ...”
October 18, 2018
GMATGuruNY posted a reply to A certain NYC taxi driver has decided to start charging a in the Problem Solving forum
“Let r=100 cents. For 3 people, the cost per mile = 3*100 = 300 cents = 3 dollars. Let x = 2 miles. Regular cost for 3 people to travel 2 miles = 3*2 = 6 dollars. With a 50% discount, the cost in dollars = 3. This is the target. Plug x=2 and r=100 into the answers to see which yields the ...”
October 16, 2018
GMATGuruNY posted a reply to (1-1/10)(1-1/11)(1-1/12)…(1-1/100) =? in the Problem Solving forum
“(1-1/10)(1-1/11)(1-1/12)…(1-1/99)(1-1/100) = (9/10)(10/11)(11/12)....(98/99)(99/100). The values in blue all cancel out, leaving only the values in red: 9/100. The correct answer is C.”
October 16, 2018
GMATGuruNY posted a reply to A rectangular garden is to be twice as long as it is wide. in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the length. When the correct answer is plugged in, perimeter = 360. B: 140 Since the length is twice the width, W = 70, with the result that the perimeter = 140+140+70+70 = 420. Since the perimeter is too great, a SMALLER answer choice is needed. ...”
October 16, 2018
GMATGuruNY posted a reply to Is the sum of 7 different positive integers greater than or in the Data Sufficiency forum
“Statement 1: Least possible case: 1+2+3+9+10+11+12 = 48. Since the least possible case is greater than or equal to 48, the answer to the question stem is YES. SUFFICIENT. Statement 2: Least possible case: 1+2+3+4+5+6+12 = 33. Greatest possible case: 6+7+8+9+10+11+12 = 63. Since the answer ...”
October 16, 2018
GMATGuruNY posted a reply to If x, y, and z are all nonzero numbers, and x = y + z, which in the Problem Solving forum
“x = y + z is valid if x=2, y=1 and z=1. The correct answer must yield a value of 1 when x=2, y=1 and z=1. Only E works: (x-z)/y = (2-1)/1 = 1. The correct answer is E.”
October 16, 2018
GMATGuruNY posted a reply to If |x+1|=2|x-1|, x=? in the Data Sufficiency forum
“Case 1: Signs unchanged x+1 = 2(x-1) x+1 = 2x-2 3 = x Case 2: Signs changed on ONE SIDE -x-1 = 2(x-1) -x-1 = 2x-2 1 = 3x 1/3 = x Resulting solutions: x=3 or x=1/3 Statement 1: Since x < 1, only x=1/3 is a viable solution. SUFFICIENT. Statement 2: Since x>0, both x=1/3 ...”
October 15, 2018
GMATGuruNY posted a reply to Lindsay can paint 1/x of a certain room in one hour. If in the Problem Solving forum
“Let the room = 20 units. Let x = 4. Since Lindsay paints 1/x of the room in 1 hour, Lindsay''s rate = (1/4) * 20 = 5 units per hour. Since Lindsay and Joseph paint the entire room in 1 hour, their combined rate = 20 units per hour. Thus, Joseph''s rate = (combined rate) - (Lindsay''s rate) ...”
October 15, 2018
GMATGuruNY posted a reply to The principal feature of the redesigned checks is a series o in the Sentence Correction forum
“Generally, a COMMA + VERBing modifier serves to modify the nearest preceding action and the agent of this action. C: instructions that...will help merchants confirm a check''s authenticity, by including reminders to watch the endorsement. .Here, COMMA + by including seems to modify merchants ...”
October 15, 2018
GMATGuruNY posted a reply to What is the remainder if 7^10 is divided by 100? in the Problem Solving forum
“When a positive integer is divided by 100, the remainder is yielded by the last two digits: 123/100 = 1 R23 548/100 = 5 R48 692/100 = 6 R92 Thus: The remainder when 7¹⁰ is divided by 100 is equal to the last two digits of 7¹⁰. Calculate the last two digits for consecutive powers of 7 ...”
October 14, 2018
GMATGuruNY posted a reply to Alice, Barbara, and Cynia work on identical tasks at differe in the Data Sufficiency forum
“TIME and RATE have a reciprocal relationship. Statement 1: The time ratio for Barbara and Alice = (14 hours)/(21 hours). The rate ratio for Barbara and Alice is equal to the reciprocal of the time ratio: (B''s rate)/(A''s rate) = 21/14 = 3/2. Let B = 3 units per hour and A = 2 units per ...”
October 13, 2018
GMATGuruNY posted a reply to James started from his home and drove eastwards at a in the Problem Solving forum
“Let James'' rate = 3 mph. James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James ...”
October 13, 2018
GMATGuruNY posted a reply to A certain club has 10 members, including Harry. One of the 1 in the Problem Solving forum
“Each of the 10 members has an EQUAL chance of being elected secretary. P(Harry is elected secretary) = 1/10. Each of the 10 members has an EQUAL chance of being elected treasurer. P(Harry is elected treasurer) = 1/10. Since EITHER outcome is favorable, we ADD the fractions: 1/10 + 1/10 = 2/10 = ...”
October 13, 2018
GMATGuruNY posted a reply to Challenge question: What is the sum of all in the Problem Solving forum
“x^(2/3) - x^(1/3) - 2 = 4 x^(2/3) - x^(1/3) - 6 = 0 D.”
October 12, 2018
October 12, 2018
GMATGuruNY posted a reply to Hard Assumption - Manhattan in the Critical Reasoning forum
“The conclusion is constrained to the case at hand: Of the 10 babies recently placed with parents, 8 were given to friends of the staff. The assumption is that the premise (the parents given babies -- including the 8 friends --all far surpassed the agency''s criteria) is sufficient to prove the ...”
October 11, 2018
GMATGuruNY posted a reply to If every boy in a kindergarten class buys a soda and every in the Problem Solving forum
“Let: b = the number of boys g = the number of girls s = the number of cents for each soda j = the number of cents for each juice box Note: All of the values above must be POSITIVE INTEGERS. Case One: If every boy in a kindergarten class buys a soda and every girl in the same class buys a ...”
October 11, 2018
GMATGuruNY posted a reply to Julie opened a lemonade stand and sold lemonade in two in the Data Sufficiency forum
“Let X = the number of 52¢ lemonades and Y = the number of 58¢ lemonades. Since the question stem asks for the number of 52¢ lemonades, we get: What is the value of X? Statement 1: X+Y = 9 Since X can be any value between 0 and 9, inclusive, INSUFFICIENT. Statement 2: 52X + 58Y = 492 ...”
October 11, 2018
GMATGuruNY posted a reply to For the students in a Physical Fitness Class Section #1, the in the Data Sufficiency forum
“Range = highest - lowest. Thus: Lowest = highest - range. In Section 1, lowest = highest - range = X-R. In Section 2, lowest = highest - range = Y-S. If the lowest weight in Section 1 is greater than the lowest weight in Section 2, we get: X-R > Y-S X+S > Y+R. Question ...”
October 11, 2018
GMATGuruNY posted a reply to Angela’s grade was in the 90th percentile out of 80 grades in the Problem Solving forum
“Percentile means the percentage below: (total below)/(total grades) * 100. Angela''s 80-student class: Since Angela''s grade was in the 90th percentile, 90% of the grades were below Angela''s: (90/100)(80) = 72. 100-student class: Since 19 grades were higher than Angela''s, the remaining ...”
October 10, 2018
GMATGuruNY posted a reply to There are 5 cars to be displayed in 5 parking spaces with in the Problem Solving forum
“Alternate approach: The 3 red cars must occupy a combination of 3 spaces. From 5 spaces, the number of ways to choose a combination of 3 for the red cars = 5C3 = (5*4*3)/(3*2*1) = 10. Number of options for the blue car = 2. (Either of the 2 remaining spaces.) Number of options for the yellow ...”
October 10, 2018
GMATGuruNY posted a reply to Hard Assumption - Manhattan in the Critical Reasoning forum
“Premise: All of the applicants given babies far surpassed the adoption criteria. Conclusion: In placing 8 of the 10 babies with friends, the staff was not guilty of favoritism. Apply the NEGATION TEST. When the correct answer is negated, the conclusion will be invalidated. B, negated: Of ...”
October 10, 2018
GMATGuruNY posted a reply to A group of medical interns at Bohemus Medical School want to in the Problem Solving forum
“In other words: How many ways can 5 girls and 5 guys be divided into pairs, if each pair must consist of one girl and one guy? Number of options for the first girl = 5. (Any of the 5 guys.) Number of options for the second girl = 4. (Any of the 4 remaining guys). Number of options for the ...”
October 9, 2018
GMATGuruNY posted a reply to If x, y, and z are positive numbers, Is z between x and y? in the Data Sufficiency forum
“Statement 1: x < 2z < y Let x=2 and y=10. In this case: 2 < 2z < 10 1 < z < 5. If z=4, then it is between x=2 and y=10. If z=1.5, then it is not between x=2 and y=10. INSUFFICIENT. Statement 2: 2x < z < 2y Let x=2 and y=10. In this case: 2*2 < z ...”
October 9, 2018
GMATGuruNY posted a reply to If s is an integer between 0 and 10, is t less than the av in the Data Sufficiency forum
“The average of s and 10 lies HALFWAY between s and 10 on the number line: s------------AVERAGE------------10 Statement 1: Since t closer to 10 than to s, t must be greater than the average of s and 10, as shown here: s-----------AVERAGE---t----------10 Thus, the answer to the question stem is ...”
October 9, 2018
GMATGuruNY posted a reply to A group of 10 people consists of 3 married couples and 4 si in the Problem Solving forum
“Good committees = total committees - bad committees. Total committees: From 10 people, the number of ways to choose 4 = 10C4 = (10*9*8*7)/(4*3*2*1) = 210. Bad committees: Since a good committee includes at most 1 married couple, a bad committee is composed of 2 married couples. From 3 ...”
October 9, 2018
GMATGuruNY posted a reply to Problem solving: Difficulty level: 700, Source: Princeton in the Problem Solving forum
“For any evenly spaced set: sum = (number)(median) We can PLUG IN THE ANSWERS, which represent the sum. Since the number of integers can be 5 or 7, the sum must be a multiple of both 5 and 7. Eliminate A, which is not divisible by 5. Eliminate D, which is not divisible by 7. The equation in ...”
October 7, 2018
GMATGuruNY posted a reply to Health insurance Plan A requires the insured to pay $1000 or in the Problem Solving forum
“THE INSURED is the person covered by the insurance. Plan A: If $1000 is LESS than 50% of the cost level, then THE INSURED pays $1000, and PLAN A pays the remainder. If $1000 is MORE than 50% of the cost level, then THE INSURED pays 50% of the cost level, and PLAN A pays the remainder. Plan ...”
October 6, 2018
GMATGuruNY posted a reply to John tossed a fair coin 3 times. What is the probability in the Problem Solving forum
“P(TTH) = 1/2 * 1/2 * 1/2 = 1/8. Since H can occur on the 1st, 2nd or 3rd flip, we multiply by 3: 3*(1/8) = 3/8. The correct answer is C.”
October 6, 2018
GMATGuruNY posted a reply to Mixture Problem DS in the Data Sufficiency forum
“Yes -- each statement conveys the same information, since doubling the total volume is the equivalent of reducing the acid concentration by 1/2.”
October 6, 2018
GMATGuruNY posted a reply to The value of a share was 25% less in the 2nd quarter over in the Problem Solving forum
“Let the 1st-quarter value = 100. Since 2nd-quarter value is 25% less, the 2nd-quarter value = 100 - (25% of 100) = 100 - 25 = 75. Since the 3rd-quarter value is 20% more than the 2nd-quarter value, the 3rd-quarter value = 75 + (20% of 75) = 75 + 15 = 90. Since the 4th-quarter value must equal 120 ...”
October 6, 2018
GMATGuruNY posted a reply to Mixture Problem DS in the Data Sufficiency forum
“Statement 1 indicates that 80 grams of water are added to the 80 grams of original solution, DOUBLING the total volume from 80 grams to 160 grams Statement 2 indicates that the added water reduces the acid concentration by 1/2. Doubling the total volume will reduce the acid concentration by 1/2 ...”
October 6, 2018
GMATGuruNY posted a reply to Each year for 4 years, a farmer increased the number of in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the original number of trees. Since the number of trees increases by 1/4 each year, the correct answer must be a multiple of 4. The last 2 digits of a multiple of 4 must themselves form a multiple of 4. Eliminate A (1250) and C (2250), since 50 is ...”
October 5, 2018
GMATGuruNY posted a reply to A chessboard is an 8×8 array of identically sized squares. in the Problem Solving forum
“Case 1: Every 6-block rectangle with a base of 2 and a height of 3 yields 4 possible L-shapes: https://i.postimg.cc/1gJCfb5J/chessboard_L_shape_1.png Chessboard: https://i.postimg.cc/LYJThXW8/chessboard_whole.png The base for the 6-block rectangle shown above can appear in rows 1 through 6, ...”
October 5, 2018
GMATGuruNY posted a reply to Amit and Ian paint a wall in alternating shifts. First Amit in the Problem Solving forum
“During each of Amit''s 4 shifts, he paints 1/2 of the room, leaving 1/2 the room unpainted. Since 1/2 of the room is left unpainted FOUR TIMES, the total fraction left unpainted as a result of Amit''s 4 shifts = (1/2)⁴. Since Ian works after each of Amit''s first 3 shifts, Ian paints a total ...”
October 5, 2018
GMATGuruNY posted a reply to A thin piece of wire 40 meters long is cut into two pieces. in the Problem Solving forum
“Since the answer choices are in terms of a variable -- the value of r -- we can PLUG IN. Let the ENTIRE WIRE be used to form the square. Then: Perimeter of the square = 40. Side = 10. Area = 100. Circle area + square area = 0 + 100 = 100. This is our target. Since the circle has no ...”
October 4, 2018
GMATGuruNY posted a reply to If x and y are positive integers, is x^2*y^2 even ? in the Data Sufficiency forum
“x²y² will be even unless both x and y are ODD. Question stem, rephrased: Are x and y both odd? Statement 1: x+5 is prime number greater than 2 and thus must be ODD. Implication: x+5 = ODD x = ODD - 5 = ODD - ODD = EVEN. Since x is even, x and y cannot both be odd. SUFFICIENT. ...”
October 4, 2018
GMATGuruNY posted a reply to A hiker walking at a constant rate of 4 miles per hour is in the Problem Solving forum
“Rate and time have a RECIPROCAL RELATIONSHIP. The RATE RATIO for the hiker and cyclist = 4 mph : 20 mph = 1:5. Thus: The TIME RATIO for the hiker and cyclist = the reciprocal of the rate ratio = 5:1. Implication: The hiker will take 5 TIMES AS LONG as the cyclist to travel the same ...”
October 4, 2018
GMATGuruNY posted a reply to How many ounces of water must be added to 10 ounces of 3 % in the Problem Solving forum
“Alcohol percentage in the original solution: 3%. Alcohol percentage in the added water: 0%. Alcohol percentage in the mixture: 1%. Let S = the original solution and W = the added water. The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS. Step 1: ...”
October 3, 2018
GMATGuruNY posted a reply to Vivian drives to her sister's house and back. She takes the in the Problem Solving forum
“When the same distance is traveled at two different speeds, the average speed for the entire trip will be a bit LESS than the average of the two speeds. Since (70+50)/2 = 60, the average speed for Vivian''s''s entire trip must be a bit less than 60. The correct answer is B.”
October 3, 2018
GMATGuruNY posted a reply to Tom’s Mom is five times as old as him. In 6 years, Tom’ in the Problem Solving forum
“An alternate approach is to PLUG IN THE ANSWERS, which represents Tom''s current age. When the correct answer is plugged in, Mom''s age in 6 years will be 3 times Tom''s age in 6 years. D: Tom = 6 Since Mom is currently 5 times as old as Tom, Mom = 5*6 = 30. Tom''s age in 6 years = 6+6 = 12. ...”
October 3, 2018
GMATGuruNY posted a reply to If 3 different numbers are selected from the first 8 prime n in the Problem Solving forum
“First 8 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19. The sum will be even if 2 is among the three numbers selected, with the result that the sum = EVEN PRIME + ODD PRIME + ODD PRIME = EVEN. Since 3 NUMBERS are selected from 8 OPTIONS, the probability that 2 will be among the three numbers selected = ...”
October 2, 2018
GMATGuruNY posted a reply to In a certain office, 50 percent of the employees are college in the Data Sufficiency forum
“Let T = the total number of employees. Since 60% of the employees are over 40, we get: Over 40 = 0.6T 30% of those over 40 -- in other words, 30% of the expression in blue -- have master''s degrees. Thus: Over 40 with master''s = 0.3(0.6T). To calculate the value of the expression in ...”
October 2, 2018
GMATGuruNY posted a reply to On a 20 mile course, Pat bicycled at an average rate of 30 in the Problem Solving forum
“Since Pat travels at 30 miles per hour for the first 12 minutes -- the equivalent of 1/5 hour -- the distance traveled in the first 12 minutes = (30)(1/5) = 6 miles. Since the remaining 14 miles are traveled at 8 miles per hour, the time to travel the remaining 14 miles = 14/8 = 7/4 hours = 1 hour ...”
October 2, 2018
GMATGuruNY posted a reply to 190 students go to a school bake sale. 95 buy a chocolate in the Problem Solving forum
“Total = Group 1 + Group 2 - Both + Neither Here: Total = 190. Group 1 = 95 who buy chocolate chip. Group 2 = 75 who buy peanut butter. Plugging these values into the equation above, we get: 190 = 95 + 75 - Both + Neither 20 + Both = Neither Neither = 20 + Both. To minimize the value of ...”
October 2, 2018
GMATGuruNY posted a reply to Is x^3-x>0? in the Data Sufficiency forum
“Question stem, rephrased: Is x³ > x? Statement 1: x > 1 When a positive value greater than 1 is cubed, the result is greater than the original number: x=2 --> 2³ > 2 x=3 --> 3³ > 3 x=4 --> 4³ > 4 In every case, x³ > x. Thus, the answer to the rephrased ...”
October 2, 2018
GMATGuruNY posted a reply to The greatest common factor of 16 and the positive integer n in the Problem Solving forum
“The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Draw a VENN DIGRAM showing where the prime factors of n, 16 and 45 overlap: https://i.postimg.cc/xkyNCFg7/GCF_Venn_n_16_and_45.jpg The diagram implies the following: Since n and ...”
October 2, 2018
GMATGuruNY posted a reply to Five letters A, P, P, L and E are listed in a row. How many in the Problem Solving forum
“Good arrangements = total arrangements - bad arrangements. Total arrangements: Number of ways to arrange 5 elements = 5!. But when an arrangement includes IDENTICAL elements, we must divide by the number of ways each set of identical elements can be ARRANGED. The reason: When the ...”
October 1, 2018
GMATGuruNY posted a reply to If a, b, c, d, e are consecutive positive integers such that in the Problem Solving forum
“For any set of consecutive integers, average = median. Let the five integers = 1, 2, 3, 4, 5. Average of 2, 3, 4 and 5 = 3.5. Average of 1, 2, 3, and 4 = 2.5. Difference between the averages = 3.5 - 2.5 = 1. The correct answer is D.”
September 30, 2018
GMATGuruNY posted a reply to If a, b, c, d, e are integers such that a<b<c<d< in the Data Sufficiency forum
“Statement 1: For any set of consecutive integers, average = median. Case 1: 1, 2, 3, 4, 5 Average of 2, 3, 4 and 5 = 3.5. Average of 1, 2, 3, and 4 = 2.5. Difference between the averages = 3.5 - 2.5 = 1. Case 2: 2, 3, 4, 5, 6 Average of 3, 4, 5, and 6 = 4.5. Average of 2, 3, 4 and 5 = ...”
September 30, 2018
GMATGuruNY posted a reply to If x is the greatest common factor of 36 and 96, what is the in the Problem Solving forum
“36 = 2*2*3*3 96 = 2*2*2*2*2*3 GCF = the product of the factors in blue = 2*2*3 = 12. Sum of the digits = 1+2 = 3. The correct answer is B.”
September 30, 2018
GMATGuruNY posted a reply to Bob invested $2000 in fund A and $1000 in fund B. Over the in the Problem Solving forum
“Fund A after 2 years: 2000 + (10% of 2000) + (2)(1% of 2000) = 2000 + 200 + 2(20) = 2240. Fund B after 1 year: 1000 + (30% of 1000) = 1000 + 300 = 1300. Fund B after 2 years: 1300 + (30% of 1300) = 1300 + 390 = 1690. Difference after two years: 2240 - 1690 = 550. The correct answer is ...”
September 30, 2018
GMATGuruNY posted a reply to If a photocopier makes 2 copies in 1313 second, then, at the in the Problem Solving forum
“Using ratios, convert 4 minutes into copies: (4 minutes) * (60 seconds)/(1 minute) * (2 copies)/(1/3 second) = 1440 copies. The correct answer is E.”
September 30, 2018
GMATGuruNY posted a reply to Lindsay can paint 1/x of a certain room in 20 minutes. What in the Problem Solving forum
“Let the room = 20 units. Let x = 4. Since Lindsay paints 1/x of the room in 20 minutes -- the equivalent of 1/3 hour -- Lindsay''s rate = (1/4) * 20 = 5 units per 1/3 hour = 15 units per hour. Since Lindsay and Joseph paint the entire room in 1 hour, their combined rate = 20 units per hour. ...”
September 29, 2018
GMATGuruNY posted a reply to 50% of students' study science and 30% of science students in the Problem Solving forum
“Let the total number of students = 100. Since 50% of the students study science, the number of science students = (50/100)(100) = 50, implying that the number of non-science students = 100-50 = 50. Since 30% of the 50 science students score more than 80%, the number of science students who ...”
September 29, 2018
GMATGuruNY posted a reply to A garden center sells a certain grass seed in 5-pound bags in the Problem Solving forum
“5-pound bags = ($13.85)/5 ≈ $3 per pound. 10-pound bags = ($20.43)/10 = more than $2 per pound. 25-pound bags = ($32.25)/25 = less than $1.50 per pound. To minimize the cost, we must maximize the number of 25-pound bags, which offer seed at the lowest price per pound. Two 25-pound bags = 50 ...”
September 29, 2018
GMATGuruNY posted a reply to Which of the following equations is NOT equivalent to in the Problem Solving forum
“If we plug y=-3 into 4x² = y²-9, we get: 4x² = (-3)² - 9 4x² = 0 x = 0. Test x=0 and y=-3 in the answer choices. When the question stem includes the phrase which of the following, the correct answer is likely to be D or E. D: 2x = y-3 Plugging in x=0 and y=-3, we get: 2*0 = -3-3 0 = ...”
September 28, 2018
GMATGuruNY posted a reply to If non- negative integers n & p are not both odd, in the Problem Solving forum
“If n=p=0, options A, B, C and D each yield a even value, indicating that these options do NOT have to be odd. Eliminate A, B, C and D. The correct answer is E.”
September 28, 2018
GMATGuruNY posted a reply to Is |x+y|<|x|+|y|? in the Data Sufficiency forum
“Since an absolute value cannot be negative, both sides of the question stem are NONNEGATIVE, enabling us to safely square the inequality: (|x+y|)²< (|x|+|y|)² x² + y² + 2xy < x² + y² + 2|x||y| xy < |xy| The resulting inequality is valid only if x and y have DIFFERENT SIGNS. ...”
September 28, 2018
GMATGuruNY posted a reply to The shaded portion of the rectangular lot shown above in the Problem Solving forum
“ALWAYS KEEP YOUR EYES ON THE ANSWER CHOICES. C, D and E imply that the flower bed is probably a 6-8-10 triangle in which y=6, x = y+2 = 6+2 = 8, and z=10. Check whether this triangle satisfies the condition that the flower bed has an area of 24 square yards: Area of a 6-8-10 triangle = ...”
September 27, 2018
GMATGuruNY posted a reply to Anna wants to distribute chocolates among her four children in the Problem Solving forum
“Let the total number of chocolates = the LCM of the four denominators 2, 5, 6 and 12 = 60. Number of chocolates given to the four children: (1/2)(60) = 30 (1/5)(60) = 12 (1/6)(60) = 10 (1/12)(60) = 5 Total number of chocolates = 30+12+10+5 = 57. The correct answer is C.”
September 27, 2018
GMATGuruNY posted a reply to In 2004, 2,400 condos sold, 15% of the total housing units in the Problem Solving forum
“Of the units sold, non-condos constitute 85% = 85/100 = 17/20. Implication: Of every 20 units sold, 17 are non-condos, with the result that the number of non-condos must be a multiple of 17. A. 16000 B. 13600 C. 12400 D. 11200 E. 8600 Only the portion in green is a multiple of 17: ...”
September 27, 2018
GMATGuruNY posted a reply to If the probability of Ronaldo will score at least 3 goals in in the Problem Solving forum
“Let G = at least 3 goals and NG = not at least 3 goals. Let W = win the match and NW = not win the match. Use a DOUBLE-MATRIX to organize the data: https://i.postimg.cc/JHLj6Tyr/matrix_goals_wins_0.png The probability that Ronaldo will score at least 3 goals in the match is 0.59. The ...”
September 27, 2018
GMATGuruNY posted a reply to A set of numbers has an average of 50. If the largest elemen in the Problem Solving forum
“Let S = the smallest number of L = the largest number. Since the largest number is 4 more than 3 times the smallest number, we get: L = 3S + 4 L-4 = 3S (L-4)/3 = S. Since the average is 50 -- and the numbers are not all the same -- S must be LESS THAN 50, while L must be greater than 50. ...”
September 26, 2018
GMATGuruNY posted a reply to What is the sum of the solutions of the equation (x-1)^2=|x- in the Problem Solving forum
“If we replace x-1 with a, we get: a² = |a|. The resulting equation is valid only if a -- in other words, the value of x-1 -- is equal to -1, 0, or 1: x-1 = -1 --> x=0 x-1 = 0 ---> x=1 x-1 = 1 ---> x=2 Sum of the solutions = 0+1+2 = 3. The correct answer is E.”
September 26, 2018
GMATGuruNY posted a reply to If H = [(x^3) - 6(x^2) - x + 30] / (x-5)and x ≠ 5, then H in the Problem Solving forum
“Let x=0, with the result that H = 30/-5 = -6. Now plug x=0 in the answers to see which yields a value of -6. Only A works: x² - x - 6 = 0² - 0 - 6 = -6. The correct answer is A.”
September 26, 2018
GMATGuruNY posted a reply to Robin split a total of $24,000 between 2 investments, X and in the Data Sufficiency forum
“Statement 1: Test one case that also satisfies Statement 2. Case 1: X = 5% and Y = 7% For 5% interest and 7% percent interest to yield the same dollar amount, $7 must be invested at 5% interest for every $5 invested at 7% interest: X --> $7(0.05) = $0.35. Y --> $5(0.07) = $0.35. Thus: ...”
September 25, 2018
GMATGuruNY posted a reply to In how many ways four men, two women and one child can sit a in the Problem Solving forum
“Once the child has been placed at the table: Number of ways to arrange the 2 women in the 2 seats adjacent to the child = 2! = 2. Number of ways to arrange the 4 men in the remaining 4 seats = 4! = 24. To combine these options, we multiply: 2*24 = 48. The correct answer is C.”
September 24, 2018
GMATGuruNY posted a reply to W, X, Y and Z each represent a different number. If the sum in the Problem Solving forum
“Sum of all 4 rows = 3 + 6 + 9 + 0 = 18. Sum of all 4 columns = -2 + 7 + n + 5 = n + 10. The values in blue must be EQUAL, since each represents the sum of all 16 values in the table. Thus: n+10 = 18 n=8. The correct answer is C.”
September 24, 2018
GMATGuruNY posted a reply to How many 3 digit numbers can we make such that two of the in the Problem Solving forum
“Number of digit options for the repeated digit = 9. (Any digit but 0.) Number of digit options for the non-repeated digit = 8. (Any digit but 0 and the digit already used.) Number of position options for the non-repeated digit = 3. (The hundreds place, the tens place, or the units place.) To ...”
September 24, 2018
GMATGuruNY posted a reply to Is 10m > 5n - k? in the Data Sufficiency forum
“Statement 1: n=2m Substituting n=2m into 10m > 5n-k, we get: 10m > 5(2m) - k ? 10m > 10m - k ? 0 > -k ? k > 0 ? No way to determine whether k>0. INSUFFICIENT. Statement 2: |k| = -k This equation is valid only if k≤0. No information about m or n. INSUFFICIENT. ...”
September 23, 2018
GMATGuruNY posted a reply to Machine A and Machine B can produce 1 widget in 3 hours work in the Problem Solving forum
“Algebra: Machine A and Machine B can produce 1 widget in 3 hours working together at their respective constant rates. (A+B)(3) = 1 widget. If Machine A''s speed were doubled, the two machines could produce 1 widget in 2 hours working together at their respective rates. (2A+B)(2) = 1 widget. ...”
September 23, 2018
GMATGuruNY posted a reply to Machine A and Machine B can produce 1 widget in 3 hours work in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent A''s time to produce 1 widget. Since A and B working together take 3 hours to produce 1 widget, A working alone must take MORE than 3 hours. Eliminate A, B and C. Let the value of each widget = 30 units. Since A and B together take 3 hours to produce ...”
September 23, 2018
GMATGuruNY posted a reply to In an office that employs 120 people, m% of the employees in the Data Sufficiency forum
“Use a DOUBLE-MATRIX to organize the data. Statements combined: Case 1: m=25% and c=25% Total number of males = (25/100)(120) = 30. Total number of custodial employees = (25/100)(120) = 30. The following matrix is yielded: https://i.postimg.cc/H88Lq5zN/matrix_custodial_1.png In this case, ...”
September 22, 2018
GMATGuruNY posted a reply to In these difficult economic times, those who have---Veriats in the Sentence Correction forum
“The default referent for a subject pronoun is the subject of the preceding INDEPENDENT CLAUSE. A: Those who have public pensions are being pursued strongly by pension advance companies that operate without much oversight from banking regulators, but they are now drawing scrutiny. Here, the default ...”
September 21, 2018
GMATGuruNY posted a reply to GMATPREP Question - what is the subject in the Sentence Correction forum
“This interpretation is not valid. The comparative in blue is clearly an ADJECTIVE describing a city.. Since as big as refers not to China but to A CITY. no comparison between China and Singapore is implied. The sentence unambiguously compares A CITY to Singapore, as discussed below. ...”
September 21, 2018
GMATGuruNY posted a reply to If m > 0, y > 0, and x is m percent of 2y, then, in te in the Problem Solving forum
“Let y=100, implying that 2y = 200. Let m=100. x is m percent of 2y. Since m=100 and 2y=200, x = 100% of 200 = 200. m is what percent of x? m/x = 100/200 = 1/2 = 50%. This is our target. Now plug y=100 into the answers to see which yields the target value of 50. Only E works: 5000/y = ...”
September 21, 2018
GMATGuruNY posted a reply to If 7 < m < 11 and −2 < n < 5, then which of th in the Problem Solving forum
“To determine the lower limit and the upper limit of mn, calculate mn using every combination of endpoints (7 and 11 for m, -2 and 5 for n): mn = (7)(-2) = -14. mn = (7)(5) = 35. mn = (11)(-2) = -22. mn = (11)(5) = 55. The LOWER limit is the LEAST of the results above: -22. The UPPER ...”
September 21, 2018
GMATGuruNY posted a reply to The square ACEG shown below has an area of 36 units squared. in the Problem Solving forum
“Almost no math is needed here. Answer choice A implies the following: BCD is a 45-45-90 triangle in which each leg has a length of 1. DEF is a 45-45-90 triangle in which each leg has a length of 5. Answer choice E implies the following: BCD is a 45-45-90 triangle in which each leg has a ...”
September 20, 2018
GMATGuruNY posted a reply to If Albert can travel 200 miles in 4 hours, how many hours in the Problem Solving forum
“Since Albert travels 200 miles in 4 hours, his rate = 200/4 = 50 mph. When the correct answer is divided into 350 miles, the resulting rate must be 50 mph. Only C works: 350/7 = 50. The correct answer is C.”
September 20, 2018
GMATGuruNY posted a reply to In four years, Andy will be twice as old as Betsy. How old in the Data Sufficiency forum
“In four years, Andy will be twice as old as Betsy. Since Andy''s age in 4 years is twice Betsy''s age in 4 years, we get: A+4 = 2(B+4) A+4 = 2B+8 A-2B = 4. Statement 1: Since Andy''s age 4 years ago is twice Betsy''s current age, we get: A-4 = 2B A-2B = 4. Same equation as given in the ...”
September 20, 2018
GMATGuruNY posted a reply to How many multiples of 33 lie between 101 and 1,000, inclusiv in the Problem Solving forum
“Since 1000 - 101 ≈ 900 -- and the answer choices are a bit spread out -- we can count the multiples of 33 simply by dividing 33 into 900: 900/33 = 300/11 = a bit more than 27. Thus, there are 27 multiples of 33 between 101 and 1000. The correct answer is B.”
September 20, 2018
GMATGuruNY posted a reply to Comparison - GMAT paper test in the Sentence Correction forum
“OA: A neutron star, as small as 12 miles in diameter but containing half as much matter as the Sun, has a gravitational force at its surface about 67 billion times greater than that on Earth. The green portion conveys the following meaning: The words in brackets are omitted so that the green ...”
September 19, 2018
GMATGuruNY posted a reply to Rasheed bought two kinds of candy bars, chocolate and toffee in the Data Sufficiency forum
“I believe that the problem has been transcribed incorrectly. Statement 1 should indicate that Rasheed bought not 2 fewer packages but only 1 fewer package, as shown in the following screen shot: https://i.postimg.cc/t7bcm77Z/rasheed_Gprep-ds-2.jpg If we know the number of chocolate BARS that ...”
September 19, 2018
GMATGuruNY posted a reply to √3-2|+|3-√2|+|5+√3|+|1-√2|=? in the Problem Solving forum
“|a-b| = the distance between a and b. |a+b| = |a-(-b| = the distance between a and -b. |√3-2| + |3-√2| + |5+√3| + |1-√2| = |5+√3| + |√3-2| + |1-√2| + |3-√2| = |√3+5| + |√3-2| + |1-√2| + |3-√2| = |√3-(-5)| + |√3-2| + |1-√2| + |3-√2| The red terms ...”
September 19, 2018
GMATGuruNY posted a reply to On the number line shown, the distance between 0 and a, a in the Problem Solving forum
“In the number line shown, the distance between 0 and a, a and b, and a and c is in the ratio of 1:2:3. To determine the ratio of a to b to c, TEST AN EASY CASE. Let a=1. Since a is ONE PLACE to the right of 0, b must be TWO PLACES to the right of a (implying that b=3), while c must be THREE ...”
September 18, 2018
GMATGuruNY posted a reply to If 12 men and 16 women can do a piece of work in 5 days and in the Problem Solving forum
“Let M = the rate for each man and W = the rate for each woman. The TIME RATIO for 12 men and 16 women to 13 men and 24 women is 5 days to 4 days. Since time and rate are RECIPROCALS, the RATE RATIO for 12M+16W and 13M+24W is equal to the reciprocal of the time ratio: (12M+16W)/(13M+24W) = ...”
September 18, 2018
GMATGuruNY posted a reply to A certain investment grows at an annual interest rate of 8%, in the Problem Solving forum
“When a value increases repeatedly by r%: Final amount = Original amount * (1 + r/100)^number of changes. Let original amount = 1. Since the original amount increases by a factor of 16: Final amount = 16. Since the investment increases by 2% every quarter: r = 2. Since x = the number of ...”
September 18, 2018
GMATGuruNY posted a reply to Grandmother's Punch hangover cure is a mix of two in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the amount of cider. When the correct answer is plugged in, the amount of alcohol in the 750 ml bottle = 87 ml. Since the alcohol percentage in the cider = 5% = 1/20, the correct answer is almost certain to be a multiple of 20. Of the five answer ...”
September 17, 2018
GMATGuruNY posted a reply to A tank has 5 inlet pipes. Three pipes are narrow and two are in the Problem Solving forum
“Let the rate of each wide pipe = 2 liters per hour. Combined rate for 2 wide pipes = 2*2 = 4 liters per hour. Since each narrow pipe works at 1/2 the rate of each wide pipe, the rate of each narrow pipe = (1/2)(2) = 1 liter per hour. Combined rate for 3 narrow pipes and 2 wide pipes = (3*1) + ...”
September 16, 2018
GMATGuruNY posted a reply to Gunther, the pizza delivery boy, went out from the store in the Problem Solving forum
“Average = sum/quantity. In this case: Average speed = (sum of the minutes spent at each speed)/(total number of minutes). Total time spent at 15mph = 30 minutes. Total time spent delivering pizzas at 0mph = 30 minutes. Total time spent at 30mph = 15 minutes. Average speed = (15*30 + 0*30 + ...”
September 15, 2018
GMATGuruNY posted a reply to A basket contains 5 apples, of which 1 is spoiled and the in the Problem Solving forum
“P(spoiled apple is selected) = 1 - P(spoiled apple is NOT selected). P(1st apple is not spoiled) = 4/5. (Of the 5 apples, 4 are not spoiled). P(2nd apple is not spoiled) = 3/4. (Of the 4 remaining apples, 3 are not spoiled). Since we want both events to happen, we multiply the fractions: ...”
September 15, 2018
GMATGuruNY posted a reply to Point P is the point of the circle x^2 + y^2 -2x -4y = 4 wit in the Problem Solving forum
“(x-h)² + (y-k)² = r² is a circle with a center at (h, k) and a radius of r. x² + y² - 2x - 4y = 4 x² - 2x + y² - 4y = 4 x² - 2x + 1 + y² - 4y + 4 = 4 + 1 + 4 (x-1)² + (y-2)² = 9 (x-1)² + (y-2)² = 3³ The equation above constitutes a circle with a center at (1, 2) and a ...”
September 14, 2018
GMATGuruNY posted a reply to At what speed was Erik running when he was at the halfway in the Data Sufficiency forum
“Statements combined: Each statement conveys the same information: that the average speed for the whole trip was 5 miles per hour. The AVERAGE speed for the whole trip does not constrain the speed AT THE HALWAY POINT. At the halfway point, the speed could be ANY NONNEGATIVE VALUE. Thus, the ...”
September 13, 2018
GMATGuruNY posted a reply to (1^2+2^2+3^3+…+20^2) / (1+2+3+ …+20)=? in the Problem Solving forum
“The answer choices represent the ratio between the numerator and the denominator of the given expression. Option A implies that the numerator is about 14 times the denominator Option B implies that the numerator is less than 7 times the denominator. Option C implies that the numerator is 41 times ...”
September 13, 2018
GMATGuruNY posted a reply to (1^2+2^2+3^3+…+20^2) / (1+2+3+ …+20)=? in the Problem Solving forum
“Since the answer choices are very spread out, we can BALLPARK -- and we can be somewhat lax with our estimations. Numerator: If the 11 greatest terms were 10²=100, the sum of the 11 greatest terms = 11*100 = 1100. If the 11 greatest terms were 20²=400, the sum of the 11 greatest terms = ...”
September 13, 2018
GMATGuruNY posted a reply to If the interior angles of a triangle are in the ratio 3 to in the Problem Solving forum
“The sum of the 3 angles of a triangle = 180. The sum of the parts of the ratio = 3+4+5 = 12. Since 180/12 = 15, the multiplier for the ratio is 15, implying that the largest angle = 5*15 = 75. The correct answer is D.”
September 12, 2018
GMATGuruNY posted a reply to During a one day sale, a store sold each sweater of a in the Data Sufficiency forum
“Statement 1: Case 1: 1 sweater is sold for $270 Case 2: 3 sweaters are sold for $90 each Since the number of sweaters sold can be different values, INSUFFICIENT. Statement 2: Since the $30 markup is 1/2 the cost of each sweater, the cost of each sweater = 60. Thus, the selling price of ...”
September 12, 2018
GMATGuruNY posted a reply to Three boys are ages 4, 6 and 7 respectively. Three girls are in the Problem Solving forum
“Since only a few cases are possible, we can list them out: 4+6+5+8 = 23 4+6+5+9 = 24 4+6+8+9 = 27 4+7+5+8 = 24 4+7+5+9 = 25 4+7+8+9 = 28 6+7+5+8 = 26 6+7+5+9 = 27 6+7+8+9 = 30 Of the 9 cases above, the four in red are ODD, implying that the remaining five cases are EVEN. Since 5/9 of ...”
September 12, 2018
GMATGuruNY posted a reply to The perimeter of a rectangular garden is 360 ft. What is the in the Data Sufficiency forum
“The GRE is administered by ETS, which also used to administer the GMAT. The GRE Quantitative Guide states that any side of a triangle or parallelogram can be used as a base. The GMAT is likely to abide by this definition. But the terms length and long seem to connote a different meaning when ...”
September 11, 2018
GMATGuruNY posted a reply to The perimeter of a rectangular garden is 360 ft. What is the in the Data Sufficiency forum
“Definitions of length: Merriam-Webster: The LONGER OR LONGEST dimension of an object. American Heritage: The measurement of something along its GREATEST dimension.”
September 11, 2018
GMATGuruNY posted a reply to a family has 5 children, what is the probability that there in the Problem Solving forum
“The problem should make clear that P(boy) = P(girl) = 1/2: P(exactly n times) = P(one way) * total possible ways. Let B = boy and G = girl. P(one way): One way to get exactly 3 boys and 2 girls is BBBGG. P(BBBGG) = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32. Total possible ways: Any ...”
September 11, 2018
GMATGuruNY posted a reply to The sum of the ages of Doris and Fred is y years. If Doris in the Problem Solving forum
“Since Doris is 12 years older than Fred, let Fred = 2 and Doris = 2+12 = 14. y = sum of their ages = 2+14 = 16. Since Fred = 2 and y=16, Fred''s age y years from now = 2+16 = 18. This is our target. Now plug y=16 into the answers to see which yields the target value of 18. Only D works: 3y/2 - ...”
September 11, 2018
GMATGuruNY posted a reply to The rate of a certain chemical reaction is directly in the Problem Solving forum
“The trick is translate the chemical relationship into the following equation: R = A²/B Here''s why the equation above works: 1)The problem states that R is directly proportional to A². Directly proportional means that as one value increases, the other value also increases by a ...”
September 10, 2018
GMATGuruNY posted a reply to In a certain pond, 50 fish were caught, tagged, and returned in the Problem Solving forum
“Of the 50 fish caught in the second catch, 2 were tagged: 2/50 = 4/100 = 4%. Since the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, the total number of tagged fish -- 50 -- must be equal to about 4% of the total number of fish in the pond: 50 = ...”
September 10, 2018
GMATGuruNY posted a reply to If 5^{m-2}2^{m+2} is an n-digit integer, where m is an inte in the Problem Solving forum
“Since m=2 will yield an integer value for the given expression and will make the math easier, ignore the condition that m>2 and let m=2. Plugging m=2 into 5^(m-2) * 2^(m+2), we get: 5⁰2⁴ = 1*16 = 16. Since the result is a 2-digit integer, n=2. The correct answer must work for n=m=2. Only ...”
September 10, 2018
GMATGuruNY posted a reply to Sam's car was fined when he gave Joe and Peter a ride, so in the Problem Solving forum
“Thanks for the heads up. I''ve revised my post accordingly.”
September 9, 2018
GMATGuruNY posted a reply to What is the probability of n(n+1)(n+2) being evenly divisibl in the Data Sufficiency forum
“Statement 1: Since n is an integer, n(n+1)(n+2) = the product of 3 consecutive integers. WRITE IT OUT and LOOK FOR A PATTERN. 1*2*3 2*3*4 3*4*5 4*5*6 5*6*7 6*7*8 7*8*9 8*9*10 9*10*11 10*11*12 11*12*13 12*13*14 13*14*15 14*15*16 15*16*17 16*17*18 Each of the products in red ...”
September 9, 2018
GMATGuruNY posted a reply to Twenty-four men can complete a work in sixteen days.Thirty in the Problem Solving forum
“Let the rate for each man = 1 widget per day, implying that the rate for 24 men = 24 widgets per day. Since 24 men complete the job in 16 days, the total amount of work = rt = 24*16 widgets. Since 32 women require 24 days, the rate for 32 women = w/t = (24*16)/24 = 16 widgets per day. Since ...”
September 9, 2018
GMATGuruNY posted a reply to Sam's car was fined when he gave Joe and Peter a ride, so in the Problem Solving forum
“Given that the answers choices are integers, I believe that the following reflects the problem''s intent: The three fractions in the prompt -- 1/4, 1/3 and 1/2 -- imply that the fine must be divisible by 4, 3 and 2. Smallest possible case: Total fine = 4*3*2 = 24. Since Sam paid $4 less ...”
September 9, 2018
GMATGuruNY posted a reply to GMATPREP Question - what is the subject in the Sentence Correction forum
“Option B for SC18 in the OG12: Plants are more efficient at acquiring carbon than fungi. Logical interpretation 1: Plants are more efficient at acquiring carbon than Logical interpretation 2: Plants are more efficient at acquiring carbon than fungi Since B allows for more than one logical ...”
September 8, 2018
GMATGuruNY posted a reply to The bear alarm at Grizzly's Peak ski resort sounds an in the Problem Solving forum
“The alarm sounds for 3 of EVERY 4 BEARS that actually appear, If 4 bears appear, then the number of alarms = 3. Since the alarm sounds only 3 times for 4 bears, 1 of these 4 bears is undetected. Since there are 10 false alarms for every 1 undetected bear, the number of false alarms = 10. Thus, ...”
September 7, 2018
GMATGuruNY posted a reply to If a mixture of ground meat consists of 2 pounds of veal in the Problem Solving forum
“The answer choices represent the price per pound: (total cost)/(total number of pounds). Since 7 pounds are purchased, the correct answer must have a denominator of 7. A, C and D lack denominators and thus can be eliminated. Since the denominator in B does not have to be 7, eliminate B. The ...”
September 7, 2018
GMATGuruNY posted a reply to How many hours did it take Dale to drive from A-town to B-to in the Data Sufficiency forum
“Statement 1: Time and rate have a RECIPROCAL relationship. 3 TIMES AS FAST implies 1/3 THE TIME. Thus, the 2 hours that would be spent traveling 3 times as fast must be equal to 1/3 the actual time: 2 = (1/3)t t = 6 hours. SUFFICIENT. Statement 2: Here, the time can be any nonnegative ...”
September 7, 2018