royrijit1

“Target question: What is the value of term 500? Given: Each term after the first term is 5 more than the preceding term. Statement 1: Term 515 of sequence X is -98. Since each term is 5 more than the preceding term, we know that term 514 = -103 term 513 = -108 term 512 = -113 term ...”

“Our goal is to find P(M and N both selected) Method #1: P(M and N both selected) = P(one of them is selected 1st AND the other selected 2nd) = P(one of them is selected 1st) x P(the other selected 2nd) = (2/5)(1/4) = 1/10 = 0.1 Aside: P(one of them is selected 1st) = 2/5 because I''m ...”

“Statements combined: Since dividing by 3 or 2 leaves a remainder of 1, j must be 1 more than a multiple of 3 and 2: j = (3*2)a + 1 = 6a + 1, where a is a positive integer Options for j: 7, 13, 19, 25... If j=7, then the answer to the question stem is YES. If j=25, then the answer to the ...”

“Approach 1; P = (good pair)/(all possible pairs) Good pair = Marnie and Noomi = 1 option. All possible pairs = the number of ways to select 2 managers from 5 options = 5C2 = (5*4)/(2*1) = 10 options. Thus: P = 1/10 = 0.1 Approach 2: P(M or N is selected first) = 2/5. (Of the 5 managers, 2 ...”

“Target question: What is the perimeter of quadrilateral Q? If we recognize that each statement alone is not sufficient, we can jump straight to...... Statements 1 and 2 combined There are several quadrilaterals satisfy BOTH statements. Here are two: Case a: Q is a rectangle with width 1 ...”

“I suggest that we choose some nice values that meet the given conditions. Tim''s income is 40 percent less than Juan''s income. Let Juan''s income = $100 40% of $100 = $40 This means Tim''s income = $100 - $40 = $60 Mary''s income is 60 percent more than Tim''s income 60% of $60 = $36 So ...”

“Since, the question asks "Which of the following must be true?", we can eliminate any answer choice that is not necessarily true. So let''s test some values that satisfy the given conditions For integers x and y, when x is divided by y, the remainder is odd. One possible case is that ...”

“1st day - $0.10 2nd day - $0.20 or $0.40 (double or add $0.30) $0.20 is the lesser amount 3rd day - $0.40 or $0.50 (double or add $0.30) $0.40 is the lesser amount 4th day - $0.80 or $0.70 (double or add $0.30) $0.70 is the lesser amount The correct answer is B Cheers, Brent”

“List the numbers in ASCENDING ORDER to get: 19, 24, 27, 29, 31. So 27 is the median. Average = (19 + 24 + 27 + 29 + 31)/5 = 130/5 = 26. The median (27) is 1 greater than the average (26). Answer: A Cheers, Brent”

“Here, the phrase in blue implies that people were trying to drive on the freeway but that the process was made challenging by the rain. This meaning is logical. Here, the phrase in red implies that nuclear plants are trying to generate electricity but that the process is made more expensive ...”

“An effect is a CHANGE brought about by an event. The Earth ALWAYS has a temperature. Since temperature does not constitute a change, it cannot be an effect. In the OA, EXTREMES are the change brought about by greenhouse emissions. This meaning is logical. The temperature of the Earth is not ...”

“Statement 1: Case 1: x=0, with the result that -|x| = - |0| = 0 In this case, |x| = 0. Case 2: x=-1, with the result that -|-1| = -1 In this case, |x| = 1. Since |x| can be different values, INSUFFICIENT. Statement 2: Thus, x=2 or x=-2. In each case, |x|=2. SUFFICIENT. The correct ...”

“Let J=100. Since Tim''s income is 40% less than Juan''s, T = 100 - (40% of 100) = 100 - 40 = 60. Since Mary''s income is 60% greater than Tim''s, M = 60 + (60% of 60) = 60 + 36 = 96. What percent of Juan''s income is Mary''s income? M/J = 96/100 = 96%. The correct answer is C.”

“IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in the video below. Target question: What ...”

“If y > 16, (16 # y) = 16, so we need only check the values from 1 to 15 Also, we need not check the FACTORS of 16, since they will all yield a remainder of 0 We''re left with: (16 # 3) = 1 KEEP! (16 # 5) = 1 KEEP (16 # 7) = 2 (16 # 9) = 7 (16 # 10) = 6 (16 # 11) = 5 (16 # 12) = 4 (16 # ...”

“Target question: Is x²y² even ? Statement 1: x + 5 is a prime number So, x+5 is a prime number greater than 5, which means x+5 must be ODD (since 2 is only even prime) If x+5 is ODD, then x must be EVEN If x is EVEN, then x²y² must be even The answer to the target question is YES, ...”

“Let x = the width Let y = the length Let z = the height So, the volume = xyz Area of one face = 12 We can write: xy = 12 Area of one face = 15 We can write: xz = 15 Area of one face = 20 We can write: yz = 20 Combine to get: (xy)(xz)(yz) = (12)(15)(20) Simplify: x²y²z² = 3600 ...”

“If it earns $360 in a month, it earns $360 *12 in a year, if there''s no compounding. Dividing by the amount invested, we''ll get the interest rate for the year: (12)(360)/48000 = 1*360/4000 = 36/400 = 9/100 = 9%”

“Lots of ways to do this, for example: x^2 - x - 1 = x(x-1) - 1 Notice x(x-1) is the product of two consecutive integers, so it is the product of one odd and one even integer, and must therefore be even. When we subtract 1 from this product, we get an odd number, so x(x-1) - 1 is odd.”

“Statement 1 is automatically true, so it really only tells us that it is possible to divide the number of baskets by 2. But we might have 2 baskets with 10 oranges each, or 20 baskets with 1 orange each, for example, so that information is not sufficient. If Statement 2 is true, then when we ...”

“Using only Statement 1, we might be picking only from 15 employees in total, in which case it''s not likely, but also not nearly impossible, that Lisa and Philip sit together. But we might be picking from 15,000,000 employees in total, and the probability might be almost zero that we even pick Lisa ...”

“The OGs vary by very little with each edition. So, you can just use an earlier edition (see https://www.beatthegmat.com/official-guide-question-library-t296759.html) Cheers, Brent”

“Sorry, but there are no plans to update BTG''s 60-Day Study Guide to include OG2019 questions.”

“Here''s one more approach: First notice that 4x² - 4x - 8 looks a lot like (2x - 1)² (2x - 1)² = (2x - 1)(2x - 1) = 4x² - 4x + 1 Now take: f(2x - 1) = 4x² - 4x - 8 Rewrite as: f(2x - 1) = 4x² - 4x + 1 - 9 = (2x - 1)² - 9 In other words, f(something) =something² - 9 In general, ...”

“We can also test the answer choices.... (A) x = 200 means y = 248 - 398(200) = some number LESS THAN 248 (B) x = 100 means y = 248 - 398(100) = some number LESS THAN 248 (C) x = 0.5 means y = 248 - 398(0.5) = some number LESS THAN 248 (D) x = 0 means y = 248 - 398(0) = some number EQUAL TO ...”

“Target question: What is the 105th term of S? Given: Sequence S has 120 terms Statement 1: The first term of S is −8. We have no information about the nature of the sequence. So, knowing the value of term 1 won''t help is determine the value of term 105 Since we cannot answer the ...”

“NOUN + VERBing implies that the VERBing is a restrictive modifier. The purpose of a restrictive modifier is to SPECIFY the type of noun being discussed. Here, the restrictive modifier in blue implies the following: There are many types of planets. The sentence is not referring to all these ...”

“Target question: Does x + c = y + c ? This is a good candidate for rephrasing the target question. Take the equation x + c = y + c, and subtract c from both sides to get: x = y REPHRASED target question: Does x = y ? Aside: Here’s a video with tips on rephrasing the target question: ...”

“Choose ANY prime number greater than 3, and test it. If n = 5, then n² = 5² = 25 When 25 is divided by 12, the quotient is 2 and the remainder is 1 Answer: B Cheers, Brent”

“Target question: Is integer x odd? Statement 1: 2x + 1 is odd There are several values of x that satisfy statement 1. Here are two: Case a: x = 1. Notice that 2x + 1 = 2(1) + 1 = 3, which is odd. In this case, the answer to the target question is YES, x IS odd Case b: x = 2. Notice that 2x ...”

“Statement 1: x=2 \(2^y =2^{2y-3} \) Since each side has the same base, the two exponents must be equal: y = 2y-3 3 = y Since the values of x and y are known, the value of \(x^y\) can be determined. SUFFICIENT. Statement 2: Thus, x=2. Same information as in Statement 1. Since Statement ...”

“List of 10 pet values implied by the chart: 0, 0, 1, 1, 1, 2, 2, 3, 3, 3 Since the answer choices are all 3 or greater, the addition of the manager''s pet value will yield the following list of 11 values: 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, M Since the new average must be equal to the median value ...”

“Target question: How many of the children developed inflammation but not fever? One approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). ...”

“Target question: Is xy > 0? Statement 1: x - y > -2 Let''s TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 5 and y = 1. In this case, xy = (5)(1) = 5. So, the answer to the target question is YES, xy IS greater than 0 Case b: ...”

“GIVEN: x = 10y + 5 Factor out 5 to get: x = 5(2y + 1) We can see that x is a multiple of 5, which also means x is divisible by 5, which means the remainder will by ZERO when x is divided by 5 Answer: A Cheers, Brent”

“As with all VIACs (Variables In the Answer Choices questions), we can solve this via the INPUT-OUTPUT approach (as Mitch has done) or via an ALGEBRAIC approach. Typically, when the answer choices look complex (as they do here), I find the INPUT-OUTPUT approach easier. However, the algebraic ...”

“In a strengthen CR, the OA SUPPORTS THE PASSAGE. In an inference CR, the PASSAGE SUPPORTS THE OA. Here, the OA supports the passage. The result is a strengthen CR. Since the OA supports the conclusion, its negation naturally will weaken the conclusion.”

“This is the comparison conveyed by the green sentence above. Here, each blue portion has a subject (the company) and a verb (had) and thus constitutes a clause. The result is a logical comparison. This is the comparison implied by the incorrect red sentence above. The first blue portion ...”

“Here''s another approach.... Take: $$\frac{x+y}{3}-\frac{x-y}{4}$$ Find common denominator: $$\frac{4(x+y)}{12}-\frac{3(x-y)}{12}$$ Expand numerators: $$\frac{4x+4y}{12}-\frac{3x-3y)}{12}$$ Combine fractions: $$\frac{(4x+4y)-(3x-3y)}{12}$$ Simplify numerator: $$\frac{x+7y}{12}$$ ...”

“Let H = price of one hamburger Let C = price of one cola A man spends $48 to buy 6 hamburgers and 8 colas for his office workers. 6H + 8C = 48 The next day, he buys 5 hamburgers and 4 colas and spends $32. 5H + 4C = 32 Assuming the prices of hamburgers and colas remain constant, what ...”

“P(exactly 2 win) = P(A wins and B wins and C loses OR B wins and C wins and A loses OR A wins and C wins and B loses) = P(A wins and B wins and C loses) + P(B wins and C wins and A loses) + P(A wins and C wins and B loses) Let''s calculate each probability P(A wins and B wins and C loses) = ...”

“D:M:N = 3:5:8. The sum of the parts of the ratio = 3+5+8 = 16. The values in red indicate the following: Nicole''s fraction of the total = 8/16 = 1/2. Since Nicole''s $28,000 is 1/2 of the total, the total = $56,000. The correct answer is E.”

“Let the job = 44 units. Since 15A+7B take 4 hours to complete the 44-unit job, the rate for 15A+7B = w/t = 44/4 = 11 units per hour. Since 8B+15C take 11 hours to complete the 44-unit job, the rate for 8B+15C = w/t = 44/11 = 4 units per hour. Adding together 15A+7B=11 and 8B+15C=4, we get: ...”

“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 ...”

“√12 + (√9 * √12) + (√4 * √12) = √12 + 3√12 + 2√12 = 6√12 = 6 * √4 * √ 3 = 12√3 The correct answer is A.”

“Approach 1: Since n is greater than 6, and the statements refer to n², make a list of perfect squares greater than 6²: n² = 49, 64, 81, 100, 121, 144, 169, 196, 225. Subtracting 1 from these values, we get the following options for n² - 1: n² - 1 = 48, 63, 80, 99, 120, 143, 168, 195, ...”

“Let x=2 and y=1, with the result that (x+y)/3 - (x-y)/4 = 1 - 1/4 = 3/4. The correct answer must yield 3/4 when x=2 and y=1. Only D works: (7y+x)/12 = (7*1 + 2)/12 = 9/12 = 3/4 The correct answer is D.”

“Target question: Is (100 - n)/n an integer? Statement 1: n > 4 Let''s TEST some values There are infinitely many values of n that satisfy statement 1. Here are two: Case a: n = 5. In this case, (100 - n)/n = (100 - 5)/5 = 95/5 = 19. So, the answer to the target question is YES, (100 - ...”

“GIVEN: f(x) = x² - x So, f(8) = 8² - 8 = 56 I. a = -7 So, f(-7) = (-7)² - (-7) = 56 This means f(a) ≥ f(8) Check the answer choices. . . ELIMINATE B and C II. a = -8 So, f(-8) = (-8)² - (-8) = 72 This means f(a) ≥ f(8) Check the answer choices. . . ELIMINATE A II. a = -9 ...”

“98 = (2)(7)(7) = (2^1)(7^2) So, 98^98 = (2^1)(7^2)]^98 = (2^98)(7^196) What is the largest value of integer n such that 98^98 is divisible by 7^n? Since 98^98 = (2^98)(7^196), the largest value of n is 196 Answer: E Cheers, Brent”

“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 ...”

“Every time Dwight does 1/4 of the remaining work, 3/4 of the work remains. Every time Mose does 1/6 of the remaining work, 5/6 of the work remains. When Mose starts his third shift, Dwight has completed 3 shifts, while Mose has completed 2 shifts. Thus, the remaining work at the start of Mose''s ...”

“Let the total number of employees = 100, implying that the total number of associates = 72% of 100 = 72 and that the number of senior associates = 54% of 100 = 54. The prompt should make clear that every associate is either a junior associate or senior associate, yielding the following equation: ...”

“Since the answer choices are PERCENTS, the total number of books can be ANY POSITIVE VALUE. 30% = 3/10, implying a denominator of 10. Let the total number of books = the product of the three denominators 10, 3 and 3 = 10*3*3 = 90. Since 30% of the books are fiction, the number of fiction books ...”

“I''m not crazy about this question. Typically, when we talk about series, Sn represents the SUM of the first n terms of that series. However, based on the official answer, Sn seems to represent the value of TERM n. Cheers, Brent”

“that-clause includes its own subject and verb and thus does not require an additional agent. In the blue that-clause above, the subject for will meet (verb) is a system of import relief laws. Since it is clear that A SYSTEM will meet the strategic needs, no additional agent is required. An ...”

“Hi VJesus12, We''re told that a teacher wants to select a team of 5 players from a group of 9 players. However, she needs to keep the following constraints in mind: If Jane is in the team, Sue should also be included in the team and vice versa. We''re asked for the number of different ways that ...”

“Hi swerve, We''re told that the time it took car A to travel 400 miles was 2 hours LESS than the time it took car B to travel the same distance and car A''s average speed was 10 miles per hour GREATER than that of car B. We''re asked for car B''s average speed in miles per hour. This question ...”

“Hi All, We''re told that a newly-opened retail store made $400 profit on the initial expenditure of $25000, and then made $1200 profit on the next $80000 expenditure. We''re asked for the approximate percentage change in the ratio of profit to expenditure change from the first $25000 expenditure ...”

“Hi All, We''re told that the architects of a certain type of building estimate construction costs to be $2.0 million per floor for each of the first 5 floors, $2.5 million per floor for each of the next 3 floors, and $3.5 million per floor for any additional floors. We''re asked what the ...”

“Hi All, We''re told that X people won a medal for water competitions. Of those X people, 1/3 won a medal for swimming; of those who won a medal for SWIMMING, 1/4 also won a medal for diving. This question can be solved by TESTing VALUES (and taking a few notes). The common denominator between ...”

“Hi shoc064, Forming a study group could be quite helpful, but you''ll still need a proper Study Plan to hit your Score Goal. From your post, it''s not clear whether you''re just beginning your studies or if you''ve put in some significant study time already, so if you''re interested in any advice ...”

“Hi realcanario, That''s OUTSTANDING news! Your 690 was already a fantastic Score, but pushing that up to a 720 (with a Q50) is a noteworthy improvement! With this 720/Q50, you can comfortably apply to ANY Business Schools that interest you! You have plenty of time to work on your applications ...”

“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: ...”

“To get a better idea of what''s happening, let''s sketch the set-up: https://i.imgur.com/SwHzFJD.png Mary is faster than Kate, we can say that Kate has a 250 meter head start. In other words, when Mary closes that 250-meter gap, she will pass Kate for the FIRST time. ...”

“The bad weather makes it difficult to work outdoors. Here, the infinitive in blue is not immediately preceded by an agent: the sentence does not specify WHO is intended TO WORK. The implication is that the agent for the blue infinitive is not a specific person but people IN GENERAL, as follows: ...”

“Let''s look for a pattern 1³ = 1 = 1² 1³ + 2³ = 9 = 3² 1³ + 2³ + 3³ = 36 = 6² 1³ + 2³ + 3³ + 4³ = 100 = 10² 1³ + 2³ + 3³ + 4³ + 5³ = 225 = 15² See the pattern yet? 1 + 2 = 3 3 + 3 = 6 6 + 4 = 10 10 + 5 = 15 First we add 2, then we add 3, then 4, then 5, etc ...”

“We need to examine powers of 10 that are smaller than AND greater than 0.00012345 We know that: 0.0001 < 0.00012345 < 0.001 Rewrite as FRACTIONS to get: 1/10,000 < 0.00012345 < 1/1,000 Rewrite as POWERS OF 10 to get: 1/10⁴ < 0.00012345 < 1/10³ We''re told that 0.00012345 ...”

“ Given: wx = y Target question: What is the value of xy ? Statement 1: wx²= 16 We can rewrite this as: (wx)(x) = 16 Since wx = y, we can replace wx with y to get: (y)(x) = 16 So, the answer to the target question is xy = 16 Since we can answer the target question with certainty, ...”

“2 of them are priced at $10.45 each, 2 at $12.05 each, 1 at $17.50 TOTAL cost when purchased individually = (2 x $10.45) + (2 x $12.05) + (1 x $17.50) = $20.90 + $24.10 + $17.50 = $62.50 The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased ...”

“To MINIMIZE machine B''s operating time, we must MAXIMIZE the time machine A''s operating time. So, let machine A operate for the full 8 hours. In 8 hours, machine A produces 72,000 pencils So, the number of pencils machine B must make = 100,000 - 72,000 = 28,000 Time = output/rate So, ...”

“https://i.postimg.cc/Z0xg3MXX/lattice.png To form a rectangle, we must combine as HORIZONTAL LENGTH with a VERTICAL LENGTH: Horizontal length: Number of ways to choose a horizontal length of 1: AB, BC, CD, DE, EF = 5 Number of ways to choose a horizontal length of 2: AC, BD, CE, DF = 4 ...”

“\(3^x + 1\) will yield a remainder of 0 when divided by 10 if it has a units digit of 0. 3¹ --> units digit of 3. 3² --> units digit of 9. (Since the product of the preceding units digit and 3 = 3*3 = 9.) 3³ --> units digit of 7. (Since the product of the preceding units digit and ...”

“30! = 30*29*28*....*3*2*1. Statement 1: To determine the greatest possible value for d, we need to know the number of 10''s contained within 30! Since 10=2*5, EVERY COMBINATION OF 2*5 contained within the prime-factorization of 30! will yield a 10. The prime-factorization of 30! is composed ...”

“The price of a jar of peanut butter at a certain store was P dollars and the price of a jar of jelly at the same store was J dollars, where J=2P. Let P = 10 and J = 20 This year, the price of peanut butter increased by 20% and the price of jelly decreased by 20% New P = 10 + (20% of 10) = 10 + ...”

“Target question: Is r/s a terminating decimal? Statement 1: 90 < r < 100 There are several pairs of values that meet this condition. Here are two: Case a: r = 91 and s = 2, in which case r/s = 91/2 = 45.5 = a terminating decimal Case b: r = 91 and s = 3, in which case r/s = 91/3 = ...”

“Target question: What is the wholesale price of a bolt of fabric X? Given: Each bolt contains 50 meters of fabric X Statement 1: The store sells fabric X for $6.25 per meter. No information about the relationship between the WHOLESALE price and the RETAIL price Statement 1 is NOT ...”

“Let''s use the complement. That is, P(Event A happening) = 1 - P(Event A not happening) So, here we get: P( 2 different languages) = 1 - P(NOT 2 different languages) So, we can write: P(2 different languages) = 1 - P(the 2 languages are the SAME) P(the 2 languages are the SAME) P(the 2 ...”

“In ascending order, let the four numbers = a, b, c, d. Since the average of the 4 numbers = 10, we get: (a+b+c+d)/4 = 10 a+b+c +d = 40 Since the median of the 4 numbers = 10, we get: (b+c)/2 = 10 b+c = 20 Subtracting the blue equation from the red equation, we get: (a+b+c+d) - (b+c) = 40-20 ...”

“Sorry - I know almost nothing about that company. Cheers, Brent”

“Data Sufficiency lesson #6: - Rephrasing the Target Question Video : https://www.youtube.com/watch?v=MyG1K3ee69w Cheers, Brent”

“Target question: What is the probability that Katelyn wins at least one of the 3 games? This is a good candidate for rephrasing the target question. In order to determine P(Katelyn wins at least one of the 3 games), we need to know the probability that Katelyn wins if they play ONE game. We ...”

“A fast approach is to use some estimation. E = 1/2 + 1/4 + 1/6 + 1/8 + 1/10 + 1/12 + 1/14 + 1/16 + 1/18 + 1/20 ≈ 0.5 + 0.25 + 0.15 + 0.1 + 0.1 + 0.1 + 0.05 + 0.05 + 0.05 + 0.05 ≈1.4 Which of the following can be a possible value of the reciprocal of E? The reciprocal of E ...”

“A = 15% alcohol B = 50% alcohol The MIXTURE of A and B = 30% alcohol To determine the ratio of A to B, use ALLIGATION -- a very efficient way to handle mixture problems. Step 1: Plot the 3 percentages on a number line, with the percentages for A and B (15% and 50%) on the ends and the ...”

“Let G = the number of general tickets. Since a total of 30 tickets are sold, the number of special exhibit tickets = 30-G. Since general tickets = $10 each and special exhibit tickets = $70 each, we get: Total revenue = 10G + 70(30-G) = 10G + 2100 - 70G = 2100 - 60G. Statement 1: 1570 < ...”

“Statements combined: Case 1: X=460, with the result that 500 is the multiple of 100 closest to X Y=360, with the result that 400 is the multiple of 100 closest to Y In this case, X+Y=820, so the multiple of 100 closest to X+Y is 800. Case 2: X=490, with the result that 500 is the multiple of ...”

“Say Harry earns $H, and has $E in expenses, while Ron earns $R, and spends $S. Then Harry saves H-E dollars, and Ron saves R-S dollars. Statement 1 tells us: H + S > R + E H - E > R - S or in other words, Harry''s savings exceed Ron''s savings. Now, it''s not clear what is meant ...”

“If you look at the units digits of various powers of 9, you''ll see they alternate between 1 and 9: 9^0 ends in 1 9^1 ends in 9 9^2 ends in 1 9^3 ends in 9 and so on. So if we add 9^0 + 9^1 + 9^2 + ... + 9^n, we''ll get something ending in 0 when n is even, and something ending in 1 when n ...”

“OA=E Target question: Is x an even number? Jump straight to..... Statements 1 and 2 combined There are infinitely many values of x that satisfy BOTH statements. Here are two: Case a: x = 32. In this case, the answer to the target question is YES, x IS an even number Case b: x = 17. ...”

“Let x = the number of miles Rafael drove Average = 80 So, (72 + 78 + 83 + x)/4 = 80 Multiply both sides by 4 to get: 72 + 78 + 83 + x = 320 Simplify: 233 + x = 320 Solve: x = 87 Answer: D”

“Target question: How many minutes will it take to run the cartoon? Given: cartoon consists of a total of 17,280 frames Statement 1: The cartoon runs without interruption at the rate of 24 frames per second. Time = (output)/(rate) So, time = (17,280 frames)/(24 frames per second) NOTE: ...”

“..... paid a neighborhood boy $11 per week to mow their lawn... So, in 3 weeks, the amount the family paid for lawn-moving = (3 weeks)($11/week) = $33 ...the family paid $4 per DAY to feed and walk their dog... 3 weeks = 21 DAYS So, the amount the family paid for dog care = (21 days)($4/day) = ...”

“Each owner received 3 times as much as each employee Let E = the amount (in dollars) that ONE employee received So, 3E = the amount (in dollars) that ONE owner received Last year $48,000 of a certain store''s profit was shared by its 2 owners and their 10 employees. In other words: 3E + 3E + ...”

“GIVEN: Alice is a years old Alice is twice as old as Brian This also means Brian is HALF as old as Alice So, Brian''s age = a/2 Cathy is 6 years younger than Brian So, Cathy''s age = (Brian''s age) - 6 So, Cathy''s age = (a/2) - 6 How old is Cathy in terms of a ? Cathy''s age = (a/2) - ...”

“GOAL: Find the value of 4?3 GIVEN: m?n = (2m - n)(m+ n) So, 4?3 = (2(4) - 3)(4+ 3) = (5)(7) = 35 Answer: A Cheers, Brent”

“Target question: What is the value of x + y? Statement 1: 6 is halfway between x and y. KEY CONCEPT: The average (arithmetic mean) of 2 numbers is HALFWAY between those 2 numbers. For example, the average of 1 and 9 is 5. Notice that 5 is HALFWAY between 1 and 9. So, statement is ...”

“---------ASIDE-------------------- A little extra background on standard deviations above and below the mean If, for example, a set has a standard deviation of 4, then: 1 standard deviation = 4 2 standard deviations = 8 3 standard deviations = 12 1.5 standard deviations = 6 0.25 ...”

“Let''s first determine the equation of line k A quick approach is the write the equation of line k in slope y-intercept form: y = mx + b, where m = slope and b = y-intercept. We''re told that the slope = 0.5 and the point (0,5) tells us that the y-intercept is 5 So, the equation of line k is: ...”

“Another approach: Let M = number of men CURRENTLY in the office Let W = number of women CURRENTLY in the office In a certain office, the ratio of men to women is CURRENTLY 3/4. We can write: M/W = 3/4 Cross multiply to get: 4M = 3W Rewrite as: 4M - 3W = 0 If 10 men were added to the ...”

“In a certain office, the ratio of men to women is 3/4. This tells us that, out of EVERY 7 people in the office, 3 are men and 4 are women. It also tells us that the TOTAL number of men and women currently in the office is divisible by 7 When we check the answer choices, we see that A, B and E ...”

“Generally, a when-clause refers to an action performed at a particular moment: When Mary entered the room, John smiled. Here, the usage of when implies that the action in blue happened at a particular moment. An as-clause refers to an action performed over an extended period of time: Adam sang ...”

“There is no reason to repeat which in the OA. Even if more than one verb is attributed to COMMA + WHICH, the usage of one which should suffice.”

“Let N=12. Number who answered yes to question 1 = (1/4)12 = 3. Number who also answered yes to question 2 = (1/3)3 = 1. Number who didn''t answer yes to both questions = 12-1 = 11. This is our target. Now we plug N=12 into the answers to see which yields our target of 11. Only E works: ...”

“C.”

“points A, B, C, D, and E represent the five teams in a certain league in which each team must play each of the other teams exactly once. Let''s first determine the total number of games that will be played. There are 5 teams, so each team will play 4 games (since a team can''t play itself) So, ...”

“BG is the height of triangle ABC (when we use AC as our base), and EC is the height of triangle DEF (when we use DF as our base). It''s confusing to use all those capital letters, so let''s use ''h'' for the height BG, and ''j'' for the height EC. We also have three important lengths along the ...”

“Statement 1 tells us our number is 30 greater than some multiple of 45, so our number is equal to 45q + 30, for some integer q. But 45q + 30 = 5(9q + 6), which is clearly divisible by 5, so the remainder is 0 when we divide our number by 5, and Statement 1 is sufficient, even without using any ...”

“If you knew that the seemingly-vertical line of length ''h'' was at right angles to the line MO, then it would be easy, with both statements, to use Pythagoras to find the lengths of all of the sides. But without knowing if we have a right angle there, we can''t do much, and the answer is E. ...”

“One approach: Salary Mary''s NET salary was x - y dollars (because Mary gave John y dollars) John''s NET salary was x + y dollars Hours worked Mary worked 8 hours John worked 10 hours In the end, John and Mary received the SAME hourly wage. So, John''s hourly wage = Mary''s ...”

“Let W = # of women Let M = # of men Let C = # of children Target question: What is the value of M? Given: The ratio of the number of women to the number of children was 5 to 2 In other words, W : C = 5 : 2 Statement 1: On the sight-seeing tour, the ratio of the number of children to ...”

“Take the task of feeding the 5 friends and break it into stages. We’ll begin with the most restrictive stage(s). Stage 1: Select a pizza for Phoebe Since Phoebe will only eat Margherita pizza, there''s only 1 pizza we can serve her. So, we can complete stage 1 in 1 way Stage 2: ...”

“Let''s draw a bunch of lines with a negative slope AND have a y-intercept of 4 (ie, passes through the point (0,4)) We get: http://i1168.photobucket.com/albums/r500/GMATPrepNow/x-int_zpsswbinqns.png As we can see, the x-intercept can have ANY POSITIVE value. So, the x-intercept COULD be 6, ...”

“Statement 1: x³ < -1 The cube of x will be negative only if x itself is negative. Thus, x < 0. SUFFICIENT. Statement 2: x³ + x < -1 x(x² + 1) < -1 Since the square of a value cannot be negative, x² ≥ 0, with the result that the factor in blue must be POSITIVE. ...”

“The GMAT would list the answer choices in ascending or descending order, as follows: We can PLUG IN THE ANSWERS, which represent the number of small pizzas. The average cost per pizza = 5050/500 ≈ $10. Since the average cost ($10) is much closer to the price of a large pizza ($12.50) than ...”

“Here''s a very similar (official) practice question: https://www.beatthegmat.com/volume-of-rectangular-solid-t273956.html Cheers, Brent”

“Target question: Is x < 0? Two important rules: ODD exponents preserve the sign of the base. So, (NEGATIVE)^(ODD integer) = NEGATIVE and (POSITIVE)^(ODD integer) = POSITIVE An EVEN exponent always yields a positive result (unless the base = 0) So, (NEGATIVE)^(EVEN integer) = ...”

“term1 = 3 term2 = (3)(2) = (3)(2¹) term3 = (3)(2)(2) = (3)(2²) term4 = (3)(2)(2)(2) = (3)(2³) term5 = (3)(2)(2)(2)(2) = (3)(2⁴) . . term14 = (3)(2^13) term15 = (3)(2^14) term16 = (3)(2^15) What is the sum of the 14th, 15th, and 16th terms in sequence S? Sum = (3)(2^13) + ...”

“ Given: x, y, and d are integers and d is odd Target question: Are both x and y divisible by d? Statement 1: x+y is divisible by d. Let''s TEST some values. There are several values of x, y and d that satisfy statement 1. Here are two: Case a: x = 6, y = 9 and d = 3. Notice that 6+9 = ...”

“ Given: m and n are positive integers. Target question: Are m and n consecutive integers? Statement 1: m² + n² = 5 Since m and n are positive integers, there are only two possible solutions: Solution #1: m = 1 and n = 2 Solution #2: m = 2 and n = 1 In BOTH possible cases, the ...”

“A general truth is something that is true not just at a particular moment but is true IN GENERAL. Mary plays the saxophone. Here, the portion in blue expresses a general truth about Mary. To express a GENERAL TRUTH, we use the simple present tense. The SC above is intended to express a general ...”

“Distance traveled in the first 5 hours = 5m. Distance traveled in the remaining 4 hours = 4n. Average speed for the entire 9-hour trip = (5m + 4n)/9. To determine the average speed for the entire trip, we need to know the value of 5m+4n. Question stem, rephrased: What is the value of 5m+4n? ...”

“The OA does not make a comparison. to double X = to increase X by 100% OA: Personal spending in the Julv-September quarter would more than double the...growth rate. Conveyed meaning: Personal spending in the July-September quarter would increase the growth rate by more than 100%.”

“We can solve this question by applying equivalent ratios For every 30 seconds that elapse, Norbert can cut up 1 plastic six-pack container In other words, for every 0.5 MINUTES that elapse, Norbert can cut up 1 plastic six-pack container Let t = the time (in MINUTES) to cut up 512 plastic ...”

“OA: Plants are more efficient than fungi at acquiring carbon, in the form of carbon dioxide. Here, the modifier in green is an adverb in that it describes UNDER WHAT CIRCUMSTANCE the preceding blue action happens. Under what circumstance ARE plants MORE EFFICIENT at acquiring carbon? Under the ...”

“I just want to point out that Jay has done a perfect job employing a technique known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it. Here, we have a population of patients, and the ...”

“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 ...”

“I imagine there''s a typo in the question somewhere, because as written, the statements aren''t consistent, and the answer is not D (it would be A). It seems more likely the question is meant to say something like: What is $$10^x 10^y$$ ? 1. 2^(x+y) = 16 2. 5^(x+y) = 625 Since 10^x * 10^y ...”

“If s is his speed, and w the speed of the walkway, then when he walks with the walkway, his net speed is s+w, and when he walks against the walkway, his net speed is s-w. Using the familiar S = D/T equation for both cases, we have: s+w = 30/30 = 1 s-w = 30/120 = 1/4 and adding these two ...”

“For any sequence question, it is usually a good idea to work out the first few terms until you understand the structure of the sequence. Here, if s_n = x^(2n - 1) then plugging in n =1, 2 and 3 we find: s_1 = x^1 s_2 = x^3 s_3 = x^5 and so on. We want to multiply these terms together, ...”

“The digits long after the decimal point are not going to matter here, since they only make a minuscule contribution to the sum, and we only need a rough estimate. If we work out the first seven terms, truncating each to one decimal place, we have: 1.2 2.4 3.6 4.8 5.1 6.1 7.1 When we ...”

“xy > 0 will be true if x and y have the same sign, so if both are positive, or if both are negative. x^2 is always positive or zero, so Statement 1 tells us almost nothing (it only tells us x is not zero). In Statement 2, we can divide by y^2 on both sides, because we know y^2 is positive (so ...”

“If two lines are perpendicular, their slopes are negative reciprocals, so if one line has a slope of m, the other has a slope of -1/m. So from Statement 1, if line m has a slope of -1/4, the perpendicular line z must have a slope of 4, and Statement 1 is sufficient. Knowing about one point on a ...”

“2⁸ = 256 2⁷ = 128 Thus: 2⁸ + 2⁷ + 2⁶ + 2⁵ + 2⁴ + 2³ + 2² + 2 + 2 = 256 + 128 + (around 100) ≈ 500. Only A is viable: 2⁹ = 512. The correct answer is A.”

“Target question: What is the number of cans that can be packed in a certain carton? Let''s head straight to..... Statements 1 and 2 combined Consider these two conflicting cases (that satisfy BOTH statements): Case a: the dimensions of the box are numbers are 1 x 1 x 2304 (inches), in ...”

“Let''s look for a pattern... We want: 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = ? 2 + 2 + 2^2 = 4 + 4 = 8 = 2^3 So, 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 2^3 + 2^3 = 2(2^3) = 2^4 So, 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 2^4 + ...”

“There''s a nice rule says: The product of k consecutive integers is divisible by k, k-1, k-2,...,2, and 1 So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1 Likewise, the product of any 11 consecutive integers will be divisible by 11, 10, 9, . . . 3, ...”

“Target question: What is the number on the card? Given: A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9. Statement 1: The units digit of the sum of the numbers on the remaining 35 cards is 6. 1+2+3+4+5+6+7+8+9=45 Since there are 4 sets of ...”

“Target question: What is the value of z? Given: x = 1 – 2y Statement 1: 5x + 10y + z = 5 Replace x with 1 – 2y to get: 5(1 – 2y) + 10y + z = 5 Expand: 5 - 10y + 10y + z = 5 Simplify: 5 + z = 5 Solve: z = 0 Since we can answer the target question with certainty, statement 1 is ...”

“Target question: Is x > 0? Statement 1: x² > 0 This statement doesn''t feel sufficient, so I''ll TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = 1. In this case, the answer to the target question is YES, it is the case that x > ...”

“Key concept: The prime factorization of a perfect square (the square of an integer) will have an EVEN number of each prime. For example, 36 = (2)(2)(3)(3) And 400 = (2)(2)(2)(2)(5)(5) Likewise, 3150y must have an EVEN number of each prime in its prime factorization. So, 3150y = ...”

“Hi Joy Shaha, This question can be solved by TESTing THE ANSWERS. We''re given several facts to work with: 1) Total number of books = 140 and there are only 3 types of books. 2) Paperback Nonfiction = 20 + Hardcover Nonfiction 3) Paperback Fiction = 2(Paperback Nonfiction) We''re ...”

“Hi dee1711s, To start, the GMAT is NOT going to test you on the concept of "negative factors", as an example - if you are asked for the factors of 6, then those factors are 1, 2, 3 and 6. If you''re told that A is a factor of B, then that means that A is a positive integer that ...”

“Hi deralexandre, First off, a 680/Q47 is a strong score, so it could be enough to get you into your first-choice School. As such, a retest might not be necessary. You''re ultimately asking a series of Admissions questions though, so you would likely find it beneficial to speak with an Admissions ...”

“When you subtract y-coordinates of two points, you''re just finding the distance between them purely in the vertical direction. That''s sometimes called the "rise". Similarly when you subtract x-coordinates of two points, you''re finding the purely horizontal distance between them, ...”

“Using both statements, k can be 2, and thus prime, or -1, and not prime, so the answer is E.”

“Using Statement 2 alone, if she bought x stamps at 30 cents, and x stamps at 40 cents, she spent 70x cents in total just on those stamps. If she only spent 420 cents overall, then x clearly is no greater than 6. But if she also bought some 35 cent stamps, x must be strictly less than 6. And ...”

“n-1, n and n+1 are three consecutive integers. If, as Statement 1 tells us, n is odd, then n-1 and n+1 are both even -- in fact, they are consecutive even numbers. If you take any two consecutive even integers, one of them will always be a multiple of 4, so Statement 1 guarantees that (n-1)(n+1) is ...”

“Statement 1 is clearly insufficient. Using Statement 2, maybe her speed was 8 km/hr, and the total distance was 16 km, so took 2 hours. Then if her speed was 8 km/hr greater, so was 16 km/hr, she would have saved an hour. But we know there must also be a solution where her speed was 72 km/hr, ...”

“If you connect a diameter of a circle to a point C on the circle, you always form a right angle at C, so Statement 2 tells us nothing new, and is useless. Using only Statement 1, since we know we have a right triangle, and we know two of its sides (the hypotenuse is twice the radius, so is 4), we ...”

“The perimeter of the figure is identical to the perimeter of a rectangle with sides a and b (if you just draw the two lines in the top right corner that you''d need to draw to make that rectangle, you''ll see that you''re adding a line of length v to the top side, and a line of length u to the ...”

“Let x be the number 3 less than twice a certain number is equal to 2 more than 3 times the number We can write: 2x - 3 = 3x + 2 So: -3 = x + 2 Solve: -5 = x 5 less than 5 times the number is 5 times the number = 5(-5) = -25 So, 5 less than 5 times the number = -25 - 5 = -30 Answer: A ...”

“When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know: Rule #1: If |something| < k, then –k < something < k Rule #2: If |something| > k, then EITHER something > k OR something < -k Note: these rules assume that k is positive (A) |x| ≤ 3 ...”

“We can PLUG IN THE ANSWERS, which represent the number of cars in the left lane. Answer choice C: 1700 If 700 cars per hour were diverted from the left lane to the right lane, the number of cars entering the right lane per hour would be twice as big as the number of cars entering the left lane ...”

“Take the task of creating a cricket team and break it into stages. Stage 1: Select 5 batsmen Since the order in which we select the batsmen does not matter, we can use combinations. We can select 5 batsmen from 7 batsmen in 7C5 ways (21 ways) So, we can complete stage 1 in 21 ways ...”

“Target question: What percentage of his bills did Stanley pay before their due dates last month? This is a great candidate for rephrasing the target question. Aside: We have a free video with tips on rephrasing the target question: Let P = # of bills PAID before due date Let T = TOTAL # of ...”

“ Given: r is the remainder when (n² - 1) is divided by 8 Target question: What is the value of r? Statement 1: n is odd Let''s test some ODD values of n If n = 1, then n² - 1 = 1² - 1 = 0, and 0 divided by 8 leaves remainder 0. So, the answer to the target question is r = 0 If n = 3, ...”

“ Given: √k is not an integer Target question: Is k a prime number? Statement 1: k < 10 Let''s TEST some values. There are several values of k that satisfy statement 1. Here are two: Case a: k = 1.3 (√1.3 is not an integer). In this case, the answer to the target question is NO, ...”

“The ratio of boys to girls in Class A is 3 to 4. Let B = number of boys in class A Let G = number of girls in class A We get: B/G = 3/4 Cross multiply to get: 4B = 3G Class A has one more boy and two more girls than class B So B - 1 = number of boys in class B So G - 2 = number of girls in ...”

“Number of options for the first character = 8. (Of the 10 digits, any digit but 0 or 9.) Number of options for the second character = 24. (Of the 26 letters in the alphabet, any but a or z.) Number of options for the third character = (number of options for the first character) + (number of ...”

“We can PLUG IN THE ANSWERS, which represent the number of girls in Class A. Since b:g = 3:4, the number of girls must be a multiple of 4. Eliminate B, C and D. Answer choice A: g = 8. Since b:g = 3:4 = 6:8, b=6. Since Class A has one more boy and two more girls than Class B, in Class B, ...”

“100 = Only Math + Only English + Both + Neither For every student who passed in both the tests, 8 students passed only in Maths and 9 students passed only in English. Let B = both, implying that Only Math = 8B and that Only English = 9B. Thus: 100 = 8B + 9B + B + Neither 100 = 18B + Neither ...”

“Since $150 soft lenses and $85 hard lenses yield $1690 in revenue, we get: 150S + 85H = 1690 30S + 17H = 238 The sum on the left side must yield a units digit of 8. Since 17*4 = 68, it is likely that H=4: 30S + 17*4 = 338 30S + 68 = 238 30S = 170 S=9 S=9 and H=4 satisfy the condition ...”

“D: Laos has a land area comparable to the size of Great Britain, but only four million in population, and many are members of hill tribes ensconced in the virtually inaccessible mountain valleys of the north. Error 1: The intent here is to compare the LAND AREA of Laos to the LAND AREA of Great ...”

“We can PLUG IN THE ANSWERS, which represent the range of x. A: -1 < x < 0 Plugging x=-0.5 into the given inequality, we get: 0 < |-0.5| - 2(-0.5) < 3 0 < 0.5 + 1 < 3 0 < 1.5 > 3 Since x=-0.5 is a valid solution, the correct answer must include x=-0.5 within its ...”

“Data Sufficiency lesson #5: - Summarizing Information Video : https://www.youtube.com/watch?v=cK9PR3SLsSA Cheers, Brent”

“Hi All, This question is a standard "Work Formula" question. When you have 2 entities sharing a task, you can use the following formula to figure out how long it takes for the 2 entities to complete the task together. Work = (A)(B)/(A+B) where A and B are the individual times ...”

“Hi swara31, Yes, you should be able to find online tutoring without too much trouble, but it''s not clear whether you actually need that type of resource yet. Before I can offer you the specific advice that you’re looking for, it would help if you could provide a bit more information on how ...”

“So, let''s say that the volume of the pool is 45 gallons. The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours So, this outlet pumps at a rate of 5 gallons per hour The water from a second outlet, flowing at a constant rate, can fill the same pool in 5 ...”

“Since t is NOT divisible by 5, we need only test t = 1, 2, 3 and 4 If t = 1, then t⁴ = 1, and 1 divided by 5 leaves remainder 1 If t = 2, then t⁴ = 16, and 16 divided by 5 leaves remainder 1 If t = 3, then t⁴ = 81, and 81 divided by 5 leaves remainder 1 If t = 4, then t⁴ = 256, and ...”

“There''s a nice integer properties rule that says: If j is a multiple of d, and k is NOT a multiple of d, then j-k (and j+k) is NOT a multiple of d For example, since 56 is a multiple of 7, and 11 is NOT a multiple of 7, then 56-11 is NOT a multiple of 7 At a certain school, the student to ...”

“Statement 1: For every 2 hours spent at 30 mph and 1 hour spent at 50 mph, 3 hours are spent at 60 mph. Average speed per 6 hours = (2*30 + 1*50 + 3*60)/6 = 290/6. SUFFICIENT. Statement 2: Case 1: NQ = 180 miles, PM = 60 miles and MN = 50 miles Since NQ is traveled at 60 mph, the time for ...”

“https://i.postimg.cc/N2Ky6DSp/square-divided-into-triangles.png Each triangle in the figure above is an isosceles right triangle with sides 1, 1 and √2. Shaded region = 4 triangles. Largest square = 16 triangles. Thus: (shaded region)/(largest square) = 4/16 = 1/4. The correct answer is ...”

“Correctted! And yes - that typo was on purpose ;o.”

“At a certain school, the student to teacher ratio is 52 to 9. If 38 students and 11 teachers leave, which of the following COULD represent the number of students and teachers remaining at the school? A) 532 students and 88 teachers B) 794 students and 162 teachers C) 1106 students and 225 ...”

“Anyone who attended the festival must have attended only Saturday, only Sunday, or both days. Let the total number of attendees = 100. Statement 1: 40% of attendees attended both days. No way to determine how many attendees attended only Saturday. INSUFFICIENT. Statement 2: 70% of attendees ...”

“Let b = boat and t = trailer. What is the value of t? Statement 1: b = 7500+t No way to solve for t. INSUFFICIENT. Statement 2: b+t = 15000 No way to solve for t. INSUFFICIENT. Statements combined: Since we have two variables (b and t) and two distinct linear equations (b=7500+t and ...”

“Statement 1: (pq)² = 36 pq = 6 Case 1: p=2 and q=3 Case 2: p=3 and q=2 Since q can be different values, INSUFFICIENT. Statement 2: (qr)² = 225 qr = 15 Case 1: q=3 and r=5 Case 2: q=5 and r=3 Since q can be different values, INSUFFICIENT. Statements combined: Only one case ...”

“(a+b)² = a² + b² + 2ab √r + 2/√r = 4 (√r + 2/√r)² = 4² (√r)² + (2/√r)² + 2(√r)(2/√r) = 16 r + 4/r + 4 = 16 r + 4/r = 12 The correct answer is A.”

“Thanks Roach! Cheers, Brent - now with 50% less "t"!!”

“This question doesn''t make any sense, at least if the OA is A. I can guess the logic they use to justify ''A'' as the right answer -- using only Statement 1, there are only two primes that sum to 12, namely 5 and 7. If we want to seat 5 people in 7 chairs, there are 7*6/2! = 21 ways to choose the ...”

“Hi myspecialtie, Brent''s explanation is spot-on, so I won''t rehash any of that here. This prompt is an example of a "Symbolism" question - in which the prompt introduces a "made up" math symbol, explains how to use it and asks you to perform a calculation (and sometimes more ...”

“Hi amegupte0410, GMAC has publicly stated that the Official Score that you earn on Test Day is within +/- 30 points of actual ability. Assuming a similar ''swing'' in how your CATs function, your 3 CAT score results show that you essentially performed the same each time (about 550 +/- a few ...”

“TRAILING 0''s = the number of 0''s at the end of a large product. 63! = 63*62*61*....*3*2*1. Since 10=2*5, EVERY COMBINATION OF 2*5 contained within the prime-factorization of 63! will yield a 0 at the end of the integer representation of 63!. The prime-factorization of 63! includes FAR ...”

“GIVEN: f(x)=x³ + 1/x³ So, f(-1/x) = (-1/x)³ + 1/(-1/x)³ = -1/x³ + 1/(-1/x³) = -1/x³ - x³ = -(1/x³ + x³) = -(x³ + 1/x³) = -f(x) Answer: B Cheers, Brent”

“Last year a certain bond with a face value of $5,000 yielded 8 percent of its face value in interest 8% of $5,000 = $400 So, interest = $400 If that interest was approximately 6.5 percent of the bond''s selling price,approximately what was the bond''s selling price? Let x = the bond''s ...”

“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 our target. Now we plug x=2 and r=100 into the answers to see which ...”

“Use a DOUBLE-MATRIX to organize the data. Let P = public transportation, NP = not public transportation, S = science, NS = not science. 60% of all students in a class commute by public transportation. 30% of the students aspire to be scientists. The following matrix is yielded: ...”

“Proposed revision: The sandpipers...are a result of residential and industrial development. This meaning is nonsensical. BIRDS cannot be a RESULT. This line of reasoning is valid: In D and E, the referent for in the northeastern United States is unclear.”

“You can do this mathematically - if you suppose it takes t minutes for A to print n pages, you can then get the same time for each machine: A prints 2n pages in 2t minutes B prints n pages in 2t minutes so A+B together print 3n pages in 2t minutes and A+B together print n pages in 2t/3 ...”

“Target question: Is it true that x > 0? Statement 1: x² = 2x Rewrite as: x² - 2x = 0 Factor: x(x - 2) = 0 So, EITHER x = 0 OR x = 2 Let''s examine each possible case Case a: If x = 0, then the answer to the target question is NO, it is not true that x > 0 Case b: If x = 2, then ...”

“Statement 1: Case 1: P=2 and Q=2, with the result that P divides evenly into Q In this case, P=Q, so the answer to the question stem is YES. Case 2: P=2 and Q=4, with the result that P divides evenly into Q In this case, P≠Q, so the answer to the question stem is NO. INSUFFICIENT. ...”

“Statement 1: Case 1: x=0 In this case, the answer to the question stem is NO. Case 2: x≠0, allowing us to divide both sides by x x²/x = 2x/x x = 2 In this case, the answer to the question stem is YES. INSUFFICIENT. Statement 2: Case 1: x=0 In this case, the answer to the question ...”

“Hi All, We''re told that In a certain bathtub, both the hot and cold water fixtures leak. The cold water leak alone would fill an empty bucket in C hours, and the hot water leak alone will fill the same bucket in H hours, where C < H. If both fixtures began to leak at the same time into the ...”

“It makes no logical sense to ask a DS question like this, because it''s not clear what information would be sufficient to find the "maximum number" of something. That''s easy to see if you imagine a different question: There are 25 boxes, and each box contains one colored tie. What is ...”

“You can say "the average score of admitted applicants was 15 points higher than of rejected applicants" or you can say "the difference between the average score of accepted applicants and rejected applicants was 15 points" but you can''t say both things in the same sentence. The ...”

“Here''s my full solution: https://www.beatthegmat.com/for-all-positive-integers-m-t299496.html Cheers, Brent”

“Statement 1: P(at least one event occurs) = 1 - P(neither event occurs) Thus: P(at least A or B) = 1 - P(neither A nor B) Since P(at least A or B) = 0.84, we get: 0.84 = 1 - P(neither A nor B) P(neither A nor B) = 0.16 P(not A) * P(not B) = 0.16. Since it is given that P(A) = P(B), P(not ...”

“Third-side rule: The third side a triangle must be LESS THAN THE SUM OF and GREATER THAN THE DIFFERENCE OF the other two sides. Here, all the sides must be INTEGER values. In triangle ANS, AS=10 and NS=5. Thus, third side AN must be an integer value less than 10+5 = 15 and greater than 10-5 = ...”

“Hi All, We''re told that neither X nor Y can equal 0 and that 75% of X is equal to 125% of Y. We''re asked which of the following is true. This question can be solved in a couple of different ways, including by TESTing VALUES. IF.... X = 100, then (75% of X) = 75 75 = 125% of Y 75 = ...”

“Hi All, We''re told that neither X nor Y can be 0 and that (2X + 3Y) is 175% of 8X. We''re asked for the value of X/Y. This question can be solved in a number of different ways, including by TESTing THE ANSWERS. Between Answers B and D, Answer D would be an easier Answer to TEST, so let''s try ...”

“Hi All, We''re asked for the range of values of X that satisfy the inequality (X+1)(X-2) > 4. This question can be approached in a couple of different ways, including by TESTing VALUES. IF... X=10, then (11)(8) = 88 which is greater than 4. Thus, X=10 is a possible solution. Eliminate ...”

“(x+1)(x-2) > 4 x^2 - x - 2 > 4 x^2 - x - 6 > 0 (x-3)(x+2) > 0 So either x-3 and x+2 are both positive, which will be true when x > 3, or both x-3 and x+2 are negative, which will be true when x < -2.”

“If we''re taking 175% of something, we''re multiplying it by 1.75, or by 7/4. So 2x + 3y = (7/4)(8x) 2x + 3y = 14x 3y = 12x 1/4 = x/y”

“His smallest bonus is 30% of 20% of his salary, so, multiplying, is 6% of his salary. Statement 1 tells us his smallest bonus, and since we know that''s 6% of his salary, we can find his salary. Statement 2 tells us the difference in his largest and smallest bonuses, and since 20% - 6% = 14%, that ...”

“Am I missing something? Statement 2 tells us the exact answer to the question. I assume it means to ask how many *cat* pictures in charcoal there are. Since we know the 39 pictures mentioned in the stem consist precisely of flower-pencil, flower-charcoal, and cat-charcoal pictures, then once we ...”

“GIVEN: 75 percent of x equals 125 percent of y Rewrite as: 3/4 of x = 5/4 of y Or we can say: (3/4)(x) = (5/4)( y) Multiply both sides by 4 to get: 3x = 5y Divide both sides by 5 to get: 3x/5 = y Rewrite as: y = (3/5)(x) Or y = 3/5 of x Or y = 60/100 of x Or y = 60% of x Answer: C ...”

“ Given: m and n are prime numbers Target question: What is the value of m+n? Statement 1: 15 ≤ m < n ≤ 20 17 and 19 are the only PRIME numbers from 15 to 20 inclusive So, it must be the case that m = 17 and n = 19 So, the answer to the target question is m+n = 17 + 19 = 33 Since ...”

“Test an analogous case with easier values: 2⁴ - 2³ - 2² - 2¹ = 16 - 8 - 4 - 2 = 2¹ The matching blue portions imply the following: 2²⁰ - 2¹⁹ - 2¹⁸ - 2¹⁷ = 2¹⁷ The correct answer is C.”

“Target question: Is n + 1 odd? Some important rules: #1. ODD +/- ODD = EVEN #2. ODD +/- EVEN = ODD #3. EVEN +/- EVEN = EVEN Statement 1: n + 2 is an even integer. In other words: n + EVEN = EVEN In other words: n = EVEN - EVEN By Rule #3, n must be even, which means n+1 is ODD The ...”

“2^20 - 2^19 - 2^18 - 2^17 = 2^17(2^3 - 2^2 - 2^1 - 1) = 2^17(8 - 4 - 2 - 1) = 2^17(1) = 2^17 Answer: C Cheers, Brent”

“(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 ...”

“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. ...”

“Target question: What is the total cost to make 7 long distance telephone calls? When we SCAN the statements, we see the key phrase: at least This allows us to jump straight to... Statements 1 and 2 combined There are infinitely many scenarios that satisfy BOTH statements. Here are two: ...”

“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 ...”

“The ride up the mountain took 135 seconds longer than her run down the mountain Start with a word equation: (time going UP mountain) = (time going DOWN mountain) + 135 time = distance/speed We can now write: 300/(x - 8) = 300/(x + 10) + 135 Multiply both sides by (x - 8) to get: 300 = 300(x - ...”

“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 ...”

“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 ...”

“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 ...”

“x = (2)(4)(6)....(46)(48)(50) = (1)(2)(2)(2)(3)(2).....(23)(2)(24)(2)(25)(2) Notice that: x is divisible by 2. This tells us that x+1 is 1 greater than a multiple of 2. In other words, x+1 is NOT divisible by 2 x is divisible by 3. This tells us that x+1 is 1 greater than a multiple of 3. ...”

“Hi All, We''re told that X is the product of all even numbers from 2 to 50, inclusive. We''re asked to define what the smallest prime factor of (X+1) must be. This particular question is a variation on an Official question that periodically pops up in the forums. The main idea behind this prompt ...”

“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: ...”

“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 ...”

“Here''s one approach. Take the task of selecting the 3 committee members and break it into stages. Stage 1: Select the 3 twins from which we will select 1 spouse each. There are 4 sets of twins, and we must select 3 of them. Since the order in which we select the 3 twins does not matter, ...”

“http://s16.postimg.cc/p2mwbwdpt/triangle_PQR.jpg We can answer this question without performing any calculations. Instead, we can use some visualization. Important point: For geometry DS questions, we are typically checking to see whether the statements "lock" a particular angle or ...”

“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 ...”

“Hi All, We''re told that a furniture store sells only two models of desks, model A and model B. The selling price of model A is $120, which is 30 percent of the selling price of the model B - and the furniture store sells 2,000 desks, 3/4 of which are model B. We''re asked for the TOTAL revenue ...”

“We can also use weighted averages to solve this Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ... Let G = number of girls Let B = number of boys So, G+B = TOTAL number of children ...”

“Hi All, We''re told that Point A is in the xy-coordinate system as shown - and that two other points B (4a, b) and C (2a, 5b) are also in the system. We''re asked for the AREA of triangle ABC in terms of a and b. This question can be approached in a couple of different ways, including by TESTing ...”

“Hi All, We''re told that in a group of children, the average (arithmetic mean) weight of the boys is 60 pounds, the average weight of the girls is 48 pounds and the average weight of ALL of the children in the group is 50 pounds. We''re asked for the ratio of the number of boys to the number of ...”

“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 ...”

“Let x = the 1st (smallest integer) So, x+1 = the 2nd integer x+2 = the 3rd integer x+3 = the 4th integer x+4 = the 5th integer (greatest integer) What is the difference between the greatest and least of the five integers? Difference = ( x+4) - x = 4 Answer: A Cheers, Brent”

“Let''s examine some perfect squares that are close to 1000 30² = 900 31² = 961 32² = 1024 So, 1000 lies between 961 (aka 31²) and 1024 (aka 32²) 1000 is closer to 1024 (aka 32²) than to 961 Answer: D Cheers, Brent”

“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 ...”

“Let L = cost of 1 LARGE LemonHead doll So L-1 = cost of 1 SMALL LemonHead doll If he buys only small LemonHead dolls, which are $1 cheaper than the large LemonHead dolls, he could buy 5 more dolls than if he were to buy only large LemonHead dolls. Let''s first write a "word equation": ...”

“Statement 1 tells us that we want to know if 2p^2 - q is less than 20, which we can''t tell with no information about p or q. Statement 2 is clearly not sufficient alone, because we have no idea what this "$" operation does. Using both Statements, we can clearly evaluate p$q = 2p^2 - q and ...”

“Since we know three values in List S, and we know the mean, and thus the sum, of all five values in List S, then if we''re given a fourth value in list S, we can find the fifth missing value. So from Statement 1 alone, we know exactly what List S contains. Similarly, from Statement 2 alone, we know ...”

“Strange question - you obviously need to know about both x and y, so neither statement could be sufficient alone. But Statement 1 gives us the value of x, and Statement 2 gives us the value of y, so of course we can answer any question in the universe about x and y using both Statements, and the ...”

“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 ...”

“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. ...”

“Once the first day is done, 6/7 of the job is left. We then know that the two workers together do 6/7 of a job in 4 days. So now we know these two things: Carpenter A does 1 job in 7 days Carpenters A+B together do 6/7 jobs in 4 days We can now get the same time for both: A does 4 jobs ...”

“Prime factorize the 450: 450 = 50*9 = 2 * 3^2 * 5^2 To get a perfect cube, we need to multiply by a number that will make every exponent in the prime factorization into some multiple of 3. So the smallest thing we can multiply by is 2^2 * 3^1 * 5^1 = 60, since that will give us 2^3 * 3^3 * ...”

“If you know remainder arithmetic ("modular arithmetic"), this is a three-second question, because if you''re dividing by k, then "k+1" is the same as "1", so (k+1)^3 is the same as 1^3, and our remainder is 1 using Statement 1. But that won''t make any sense to most ...”

“When you''re only selecting one thing from a group, a probability is just a ratio. If you''re asked, say, "if you pick a random student from a class, what is the probability you pick a woman?", that is the same question as "what fraction of the students are women?" So the ...”

“If our sequence contains positive values, and if we''re multiplying by some positive constant (different from one) to produce each subsequent term, the sequence is either constantly increasing (if the constant is greater than 1) or constantly decreasing. (if the constant is less than 1). Either ...”

“If xyz < 0, then at least one of x, y or z must be negative. Notice that means that the smallest of the three numbers is certainly negative, because negative numbers are always smaller than positive numbers. Statement 1 tells us x < y, but maybe they''re both positive and z is negative. ...”

“t_0 = 3 t_1 = 3 + 1 t_2 = 3 + 1 + 2 t_3 = 3 + 1 +2 + 3 t_4 = 3 + 1 + 2 + 3 + 4 and so on, so t_n is just equal to 3 plus the sum of the first n positive integers. The sum of the first n positive integers is just (n)(n+1)/2 (it''s the number of terms, n, times the average term, which, since ...”

“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 ...”

“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.”

“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 ...”

“Let A = number of CDs Al owns Let B = number of CDs Bea owns Target question: What is the value of B - A? Statement 1: If Bea gives 9 of her CDs to Al, then Al will own twice as many CDs as Bea owns. We can create the equation: 2(B - 9) = A+9 Expand left side to get 2B - 18 = A+9 ...”

“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 ...”

“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.”

“Take the task of creating the 3-digit numbers and break it into stages. Stage 1: Select the first digit (hundreds digit) Since the first digit can be 3, 4, 5, 7 or 9, we can complete stage 1 in 5 ways Stage 2: Select the second digit (tens digit) Since the second digit can be 0, 2, 3, 4, ...”

“Hi camitava, This is essentially a rate question. Here''s how to solve it: Single rooms take one person 15 minutes to clean and double rooms take one person 20 minutes to clean. 15 mins. = 1/4 hour 20 mins. = 1/3 hour With 1400 single rooms x 1/4 hour = 350 hours of total work for ...”

“Hi All, We''re told that a cosmetics company would like to market a 6-item gift basket bundle from a set of 10 possible items, but 49 of the potential bundles have already been eliminated from consideration. We''re asked for the total number of potential bundles that are still being considered. ...”

“Hi All, We''re asked for the sum of the integers from 1 to 999, inclusive. This question can be approached in a number of different ways, including by "bunching" The sum of 1 and 999 is 1,000 The sum of 2 and 998 is 1,000 The sum of 3 and 997 is 1,000 Etc. Using the numbers ...”

“Hi All, We''re told that a basketball team’s current roster consists of G guards and F forwards - and 2 guards join and 1 forward leaves. We''re asked for the probability that a player chosen at random is a guard. This question can be approached in a couple of different ways, including by ...”

“In the first half hour, A covers 10 miles. So at 2pm, the cyclists are 135 miles apart. Together they will cover this distance in 3 hours, since they meet at 5pm. Since A covers 60 miles in that time, B must cover the rest, or 75 miles, and so B''s speed must be 25 mph.”

“p and q almost always represent prime numbers in math, so I don''t like their choice of letters here. Statement 1 tells us p is divisible by 8, but not by 16. So for pq to be divisible by 16, we need q to be even, something we don''t know, so Statement 1 is not sufficient alone. Statement 2 gives a ...”

“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 ...”

“Target question: Is n > 24? Given: The cost of delivery for an order of desk chairs was $10.00 for the 1st chair, and $1 for each additional chair in the order. The office manager placed an order for n desk chairs. Statement 1: The delivery cost for the order totaled more than $30.00 ...”

“There''s a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median." Since the consecutive integers are equally-spaced, their mean and median will be equal. Target question: What is the average of eleven consecutive integers? ...”

“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 ...”

“Hi Gmat_mission, We''re told that after multiplying a positive integer A (which has N digits) by (N+2), we get a number with (N+1) digits, all of whose DIGITS are (N+1). We''re asked for the number of possible values of A that ''fit'' this description. To start, this question certainly ...”

“Hi All, This question is really just about basic arithmetic and staying organized. Based on the information in the prompt, there are two ''total costs'' that we have to calculate... Total cost of purchasing 2 Type A machines = Base Price = (2)($20,000) = $40,000 The 20% down payment = ...”

“Hi All, We''re told that in an office of 11 people, everyone but Lauren each contributed D dollars to buy her a surprise gift for her birthday, but the gift cost a total of G dollars, which was an amount that was less than the total collected. We''re asked - if each member who donated is to ...”

“This question is somewhat ambiguous, since it''s hard to say whether "nondrinkers" in statement 1 refers to people who drank neither beer nor wine, or did not drink beer. I''m assuming that it means to not drink beer, so I''ve add that to the question below. One approach is to use ...”

“Target question: What is the arithmetic mean of set X? Given: Set X consists of different positive numbers arranged in ascending order: K, L, M, 5, 7. K, L and M are consecutive integers This means that EITHER K, L, M = 1, 2, 3 respectively, OR K, L, M = 2, 3, 4 respectively Head straight ...”

“Good catch. In my solution, the lone exception (N=29) is now noted.”

“The logic of your answer is perfect, but this is not quite true - when you add 1 to a number, when that number ends in 9, the digit sum drops by 8 (the tens digit goes up by 1, the units digit falls by 8) rather than increases by 1. So here, when N = 29, after adding 1 we don''t get a digit sum of ...”

“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 -- ...”

“Statement 1 is not sufficient, since the sides could be anything. Statement 2 also isn''t sufficient, because you''ll have different perimeters when, say, the quadrilateral is a square and when it isn''t. Using both statements, squaring the equation in statement 1, we learn x^2 + y^2 - 2xy = ...”

“The wording of the question is strange (is it asking if exactly 40% are men, or at least 40%?) but regardless, with no information about how many men or women work at the company, the question clearly can''t be answered even using both statements. If equal numbers of men and women work for the ...”

“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.”

“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 ...”

“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: ...”

“Sure thing. Number of outcomes that OBEY the restriction = (total # of outcomes that IGNORE the restriction) - (# of outcomes that BREAK the restriction) total # of outcomes that IGNORE the restriction Select any 3 people from the 8 people We can do this in 8C3 ways (= 56 ways) # of ...”

“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.”

“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 ...”

“When it comes to remainders, there''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, then we ...”

“The great thing about DS questions is that we aren''t required to perform calculations if we know that we COULD perform those calculations. Here''s what I mean: Target question: What amount must be invested at k percent simple annual interest for one year to yield the same amount of dollars ? ...”

“ Given: xyz ≠ 0 Target question: Is x³y⁴z⁵ > 0? This is a great candidate for rephrasing the target question. Since we know that x² must be POSITIVE, we can safely take the inequality x³y⁴z⁵ > 0 and divide both sides by x² to get: xy⁴z⁵ > 0 Similarly, since ...”

“Set M is composed of the positive even integers up to 100. Set M = {2, 4, 6, 8, . . . . 96, 98, 100} Set N is composed of the odd integers from –1 to 99 Set N = {-1, 1, 3, 5, . . . 95, 97, 99} What is the value of (the sum of Set M) – (the sum of Set N)? SUM of set M = 2 + 4 + 6 + 8 + ...”

“Drop 8 meters Rise 4 meters Drop 4 meters Rise 2 meters Drop 2 meters Rise 1 meters (DONE!) 8 + 4 + 4 + 2 + 2 + 1 = 21 meters Answer: A Cheers, Brent”

“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 ...”

“The hotel has 1,400 single rooms, and one person can clean a single room every 15 minutes So, one person can clean 4 single rooms in ONE HOUR In other words, it takes 1 WORKER HOUR to clean 4 single rooms 1400/4 = 350 So, it takes 350 WORKER HOURS to clean 1400 rooms The hotel has 420 ...”

“The number of candidates rejected in a certain admission process was four times GREATER than the number of candidates accepted. Let x = the number of candidates accepted So, x + 4x = the number of candidates rejected In other words, 5x = the number of candidates rejected So, 6x = TOTAL number ...”

“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.”

“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: ...”

“Hi All, We''re told that a student worked 20 days - and the given table shows the number of days that the student earned each of 5 possible amounts of money. We''re asked for the MEDIAN amount of money earned per day for those 20 days. Since there are 20 total days, the MEDIAN will be the ...”

“Hi All, We''re told that in a group of 24 musicians, some are pianists and the rest are violinists and exactly 1/2 of the pianists and exactly 2/3 of the violinists belong to a union. We''re asked for the LEAST possible number of union members in the group. This question can be approached in a ...”

“In a group of 24 musicians, some are pianists and the rest are violinists. Let x = number of pianists So, 24-x = number of violinists Exactly 1/2 of the pianists and exactly 2/3 of the violinists belong to a union. So, the number of pianists in the union = x/2 And the number of violinists in ...”

“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 ...”

“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 ...”

“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 ...”

“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 ...”

“Hi All, We''re told that a certain reel of film runs at 5/6 of a frame per second. We''re asked how long it will take to run 2580 frames of the film. While this question involves some ''ugly'' numbers, the answer choices are sufficiently ''spread out'' that you can use estimation to get the ...”

“Hi All, We''re told that 5 friends play blackjack in Las Vegas and lose an AVERAGE of $100 each - with the losses of two of the friends totaling $380. We''re asked for the AVERAGE loss of the other 3 friends. This question is a standard Average Formula question and requires just a bit or ...”

“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 ...”

“Hi All, While this question is wordy, and will require some note-taking, it can be solved by TESTing VALUES. Let''s TEST... R = 5 students Y = 50 dollars X = 3 fail to pay So the ''story'' is that 5 students agree to pay an equal amount for a $50 present (that''s $10 per student). We''re ...”

“Hi All, We''re told that a city council will select 2 of 9 available firefighters and 1 of 6 available police officers to serve on an advisory panel. We''re asked for the number of different groups of 3 people that could serve on the panel. This question is essentially a Combination Formula ...”

“Hi All, We''re asked to find the minimum number of identical SQUARES that be cut from an 18 in. x 30 in. board without ''wasting'' any of the space. To accomplish this, we need to find a square whose dimensions will evenly divide into both 18 and 30; to find the LEAST number of squares, we''ll ...”

“ Given: Carmen currently works 30 hours per week Target question: If Carmen''s gross hourly wage were to increase by $1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase? This is a good candidate for rephrasing the target ...”

“ Given: When X is divided by Y, the quotient is Z and the remainder is W. ------ASIDE------- There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 ...”

“Target question: What is the hundredths digit of the decimal z? Statement 1: The tenths digit of 100z is 2 Notice what happens when we take a decimal like 0.123456 and multiply it by 100. We get 12.345 (the tenths digit is 3) In the original decimal, the 3 was in the thousandths place. ...”

“W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. If W = X – 7, what is the sum of all possible values of W? A) 19 B) 20 C) 21 D) 22 E) 23 Source: www.gmatprepnow.com Difficulty level: 650 - 700”

“GIVEN: 4x − 3y = 13 5x + 2y = − 1 Take the TOP equation and multiply both sides by 2 Take the BOTTOM equation and multiply both sides by 3 We get: 8x - 6y = 26 15x + 6y = -3 ADD the two equations to get: 23x = 23 Solve: x = 23/23 = 1 Answer: C Cheers, Brent”

“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 ...”

“Statement 1 is always true, so is useless, while Statement 2 obviously gives you one equation in one unknown, so is sufficient. But test takers don''t need to know anything about ''exterior angles'' for the GMAT, nor what a ''non-convex polygon'' is, not to mention that Statement 2 is problematic ...”

“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 ...”

“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 ...”

“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.”

“Target question: What is the value of Z? Given: When X is divided by Y, the quotient is Z and the remainder is W. ------ASIDE------- There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with ...”

“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 ...”

“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 ...”

“Target question: What is the total number of articles of clothing in the closet? Given: The ratio of the number of shirts to the number of dresses to the number of jackets in the closet is 9:4:5, respectively. If shirts : dresses : jackets = 9 : 4 : 5, then there are infinitely many ...”

“W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. What is the value of Z? 1) W = X – 4 2) W + Z = 4 Difficulty level: 650 – 700 Source: www.gmatprepnow.com”

“Sorry, but there are no plans to update the 60-day guide in the near future. Cheers, Brent”

“This is exactly identical to a GMATPrep question: https://gmatclub.com/forum/in-the-figure-shown-point-o-is-the-center-of-the-semicircle-89662.html”

“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 ...”

“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 ...”

“It makes no sense to ask a DS question in this way. If y is a "number of patrons" in a real GMAT DS question, then y stands for a single unknown value; it doesn''t stand for a variable. You can''t ask "how many values of y are possible?" in DS, because it''s not clear what ...”

“Always check the answer choices BEFORE solving the question!! Since the answer choices are nicely spread apart, we can be quite aggressive in our estimation Let''s add the 5 numbers in each COLUMN COLUMN 1: Sum ≈500 COLUMN 2: Sum ≈-1000 COLUMN 3: Sum ≈1500 COLUMN 4: Sum ≈-2000 ...”

“We can use a nice (and often tested) fraction property that says: (a - b)/c = a/c - bc So, (y-x)/(xy) = y/xy - x/xy = 1/x - 1/y That''s better! So, we''re now looking for a possible value of 1/x - 1/y Let''s look at some EXTREME values. We can MAXIMIZE the value of 1/x - 1/y by MAXIMIZING ...”

“f(24) = 2 x 4 x 6 x 8 x 10 x 12 x 14 x 16 x 18 x 20 x 22 x 24 Rewrite as prime factorization: f(24) = 2 x (2)(2) x (2)(3) x (2)(2)(2) x (2)(5) x (2)(2)(3) x (2)(7) x (2)(2)(2)(2) x (2)(3)(3) x (2)(2)(5) x (2)(11) x (2)(2)(2)(3) Answer: E ASIDE: As you can see from the answer choice, I ...”

“The above solution isn''t right. If we have 100 objects, we have 72 cubes. If 54 of these are blue, the rest, or 18, are red. The question asks "What percent of the cubes are red?", and we have 18 red cubes and 72 cubes in total, so the answer is 18/72 = 1/4 = 25%.”

“In each column, if we list the numbers in increasing order, we get an equally spaced list with a multiple of 100 in the middle. So, for example, the second column contains the numbers: -204, -202, -200, -198, -196 The sum of an equally spaced list is just equal to the average (which, in an ...”

“I don''t like the wording of the question, because it''s not altogether clear if order should matter. But that''s the intention, so we have 8 choices for which person goes in the first seat, 7 for the next seat, and so on, and multiplying our choices gives the answer of (8)(7)(6)(5)(4).”

“Target question: Is xy > 3 ? Statement 1: (7^x) > 729 Since there''s no information about y, we cannot answer the target question with certainty. Statement 1 is NOT SUFFICIENT Statement 2: (9^y) = 7 Since there''s no information about x, we cannot answer the target question with ...”

“It''s a pure ratio/percent problem, so we can freely make up a number, and since we''re asked for a percent in the end, I''d just use 100. Then we have: 50 have blue eyes, of whom: 40 have blue eyes and no glasses 10 have blue eyes and glasses We also know that the ratio of ...”

“Statement 1 says, in words, "k is 5 greater than some multiple of of j". If j > 5, then that''s just another way of saying "the remainder is 5 when we divide k by j". But we don''t know if j > 5, using only Statement 1. If j=2, say, then it''s impossible for the remainder ...”

“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 ...”

“Here''s a very similar (official) question to practice with: https://www.beatthegmat.com/arthemetic-question-on-factors-and-prime-numbers-t275643.html Cheers, Brent”

“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.”

“Let R = REGULAR price of the item Joey and receives an employee discount of 10 percent off the regular price of any item. So, Joey pays 90% of the REGULAR price. In other words, 0.9R = the DISCOUNT price that Joey actually pays What is the regular price of an item that Joey purchases for ...”

“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 ...”

“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.”

“If you know that in any counting situation, when the order of k things doesn''t matter, you can first pretend order does matter and then divide by k!, then you can just: imagine putting all 16 gifts in a row, which you can do in 16! ways. Give the first four gifts to the oldest child, the next four ...”

“Let''s say the children are named A, B, C, and D Stage 1: Select 4 gifts to give to child A Since the order in which we select the 4 gifts does not matter, we can use combinations. We can select 4 gifts from 16 gifts in 16C4 ways (= 16!/(4!)(12!)) So, we can complete stage 1 in ...”

“Another approach is to test some values for x and y that satisfy the given information. Positive two-digit integers x and y have the same digits, but in reverse order So, it COULD be the case that x = 12 and y = 21 Which of the following must be a factor of x + y? x + y = 12 + 21 = 33 ...”

“Each Statement is clearly insufficient alone, because using only one statement, we know almost nothing about one of the two unknowns in the inequality in the question. Using Statement 1, we know when 900 is divided by d, the remainder is 1. That means that 900 is exactly 1 larger than some ...”

“The wording here is problematic for a few reasons - it needs to mention that yard totals must be integers (that''s not going to be intuitive or obvious to someone who doesn''t follow football), it should say ''yards per game'', and it should certainly not ask what Barry needs to do to "keep his ...”

“If AB is a two digit number, where A is the tens digit and B the units digit, then the number is equal to 10A + B. Here we are adding AB and BA, which is the same as adding 10A+B and 10B + A. Adding those we get 11A + 11B, which clearly has 11 as a factor.”

“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, ...”

“Hi All, We''re told that working continuously 24 hours a day, a factory bottles Soda Q at a rate of 500 liters per second and Soda V at a rate of 300 liters per second and that TWICE as many bottles of Soda V as of Soda Q are filled at the factory each day. We''re asked for the ratio of the ...”

“Hi All, This question is a variation of a ''Work Formula'' question (it involves 2 ''entities'' working on the same task together), so we can use the Work Formula to solve it. Work = (A)(B)/(A+B) where A and B are the individual times that it takes the 2 entities to complete the task on their ...”

“Hi All, We''re told that Set X consists of PRIME numbers {3, 11, 7, K, 17, 19}, the integer Y represents the PRODUCT of all elements in Set X and 11Y is an EVEN number. We''re asked for the RANGE of Set X. This question is based on several Number Property rules - and doesn''t actually require ...”

“Hi All, We''re asked to find the number of ways that the letters D, I, G, I, T be arranged so that the two I''s are NOT next to each other. Since the two "I"s cannot be side-by-side, there are a limited number of ways to arrange the 5 letters. As such, with a little permutation math ...”

“Anyone interested in my GMAT math books or problem sets can contact me at the email address below.”

“If we have a set of y INTEGERS, there are two possible cases when it comes to the MEDIAN. Case a: y is an ODD number, in which case the MEDIAN equals the one middle integer (when all of the integers are arranged in ascending order). In this case, the median must be an integer. Case b: y is an ...”

“This is a near-exact replica of an official question. Statement 1 is clearly not sufficient, because there is an infinite number of primes. I think Statement 2 is supposed to read: 11! - 12 < y < 11! - 2 That''s also not sufficient, because each number in that interval has an obvious ...”

“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.”

“If you multiply all of the values in a set by some constant k, you will multiply the mean, median, range and standard deviation of that set by k. So here, if we multiply everything in set A by 1/4, we will make the standard deviation 1/4 of its previous value. Since standard deviation is always zero ...”

“\((2^{(1-x)})^2\) = \(2^{2-2x}\) = \(2^2/2^{2x}\) = \(4/2^{2x}\) 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.”

“Strange question. The ratio of circumference to diameter for every circle in the universe is π, so Statement 1 tells you nothing. Circle A''s radius is half its own diameter, so if it is also half of B''s diameter, they have the same radius, and thus the same area, so Statement 2 is sufficient ...”

“This is a weighted average problem, where 15% and 25% are the averages of each group. We can draw a number line with the three averages: ---15------------A------25--- Since the ratio of boys to girls is 2 to 3, the overall average A will divide the total distance above in a 3 to 2 ratio, so ...”

“Alternatively: 2^(4x) = 3600 2^(2x) = 60 2^x = √60 So (2^(1-x))^2 = (2 / 2^x)^2 = (2/√60)^2 = 4/60 = 1/15”

“2^(4x) = 3600, so (2^2)^2x = 3600, and 4^(2x) = 3600. Taking square roots, 4^x = 60. We want to find the value of (2^(1-x))^2 = (2^2)^(1-x) = 4^(1-x) = 4^1 * 4^(-x) Since 4^x = 60, 4^(-x) is equal to 1/60, so 4^1 * 4^(-x) = 4 * (1/60) = 4/60 = 1/15”

“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 ...”

“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.”

“Posted and answered about a week ago: https://www.beatthegmat.com/andrew-bought-pizzas-for-his-swim-team-pepperoni-pizzas-cos-t306615.html#827261”

“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.”

“Hi All, We''re told that the product of the digits of the four-digit number H is 36 and no two digits of H are identical. We''re asked for the number of different possible values of H. While this question might seem complex, most of the work is based on basic Arithmetic (and some Permutation ...”

“Hi All, We''re told that a motorcycle travels at a speed of X KILOMETERS per P HOURS. We''re asked for the number of METERS it will travel in S SECONDS, in terms of S, P and X. (xps ≠ 0; 1 kilometer = 1000 meters). This question can be solved in a number of different ways, including by TESTing ...”

“Hi All, We''re told that all assets in Karina''s investment portfolio are divided between an IRA, 401k, and two separate taxable accounts and that NO two accounts have the SAME amount of money and all four have at least SOME money in them. If each account has a whole-number percent of Karina''s ...”

“Hi All, We''re told that Vivian drives to her sister''s house and back. She takes the exact same route both ways; on the trip out she drives an average speed of 50 miles per hour and on the trip back she drives an average speed of 70 miles per hour. We''re asked for her approximate average speed ...”

“Hi Rahufalb, To start, the only practical way to properly measure your overall Test-taking skills during the course of your studies is to take a FULL-LENGTH CAT under realistic conditions (meaning that you should take a FULL CAT - with the Essay and IR sections, in a location that is NOT your ...”

“Two positive numbers differ by 12 Let x = the smaller number So x + 12 = the larger number NOTE: our goal is to find the value of x(x + 12) Their reciprocals differ by 4/5 We get: 1/x - 1/(x+12) = 4/5 Multiply both sides by x to get: 1 - x/(x + 12) = 4x/5 Multiply both sides by 5 to get: 5 ...”

“Another approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). Here, we have a population of residents, and the two characteristics are: ...”

“Let''s assign a nice value to x (a value that will work well with all of the numbers 3, 4 and 6. Let''s say x = 24 GIVEN: 4 machines make x units in 6 days This means 4 machines make 24 units in 6 days So, 4 machines make 4 units in 1 day So, 1 machine makes 1 unit in 1 day From here, ...”

“5-member committees Since the order in which we select the committee members does not matter, we can use COMBINATIONS We can select 5 people from 20 people in 20C5 ways 20C5 = (20)(19)(18)(17)(16)/(5)(4)(3)(2)(1) 4-member committees Since the order in which we select the committee members ...”

“This is a SHRINKING GAP question. Train A traveled at 35 miles per hour and Train B traveled at 25 miles per hour, 35 mph + 25 mph = 60 mph So, the gap CLOSES at a rate of 60 mph Train A and Train B began traveling towards each other from opposite ends of a 500-mile long track at 1:00 PM ...”

“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 ...”

“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.”

“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 ...”

“One approach is to treat this is a rate question. In 1990 the GAP BETWEEN V''s budget and Q''s budget was $120,000 ($780,000 - $660,000 = $120,000) Each year, the budget for Q increased by $30,000 and the budget for V decreased by $10,000. In other words, the GAP BETWEEN the budgets ...”

“(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: ...”

“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 ...”

“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 = ...”

“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 ...”

“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.”

“Hi Zaidf1997, It sounds like you''re just beginning your studies. Have you done any studying so far or are you just beginning? If you are just starting out, then it would be a good idea to take a FULL-LENGTH practice CAT Test; you can take 2 for free at www.mba.com (and they come with some ...”

“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 ...”

“Target question: Is xy + zt + yz + tx positive? Statement 1: |x| = |y| = |z| = t Let''s TEST some values. There are several values of x, y, z and t that satisfy statement 1. Here are two: Case a: x = y = z = t = 1. In this case, xy + zt + yz + tx = (1)(1) + (1)(1) + (1)(1) + (1)(1) = 4. ...”

“This is a tough one to use the INPUT-OUTPUT approach, but here is goes: Let c = $2 (it cost $2 to make each umbrella) Let x = 10 (we make 10 umbrellas) Let r = $5 (the retail price is $5 per umbrella) Let b = $0 (the below-cost sale price is $0 per umbrella) So, the manufacturer made 10 ...”

“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. ...”

“(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.”

“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 ...”

“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 ...”

“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 ...”

“After about 30 seconds, I recognized that I couldn''t see a nice straightforward solution (one that doesn''t involve considering multiple cases), so I had 3 options: 1) Keep searching for a nice straightforward solution 2) Guess and move on 3) List the possible outcomes Since the answer ...”

“ODDS: 1, 3, 5, 7, 9 EVENS: 2, 4, 6, 8 Take the task of removing the 9 chips and break it into stages. Stage 1: Select an ODD number to be the 1st selection There are 5 ODDs to choose from. So, we can complete stage 1 in 5 ways Stage 2: Select an EVEN number to be the 2nd selection ...”

“Let''s say Karina''s entire portfolio is worth $100 altogether. So, we want to divide this $100 into four integer amounts: w, x, y, z, where w < x < y < z, and we want to minimize the value of z In order to MINIMIZE the value of the z, we must MAXIMIZE the values of w, x, and y. Now ...”

“One approach is to assign a "nice" value (one that works well with 50 mph and 70 mph) to the distance her sister''s house. So, let''s say the distance is 350 miles Average speed = (total distance traveled)/(total travel time) TOTAL distance = 350 miles + 350 miles = 700 miles ...”

“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. ...”

“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 ...”

“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 ...”

“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 ...”

“Hi All, We''re told that 10 theater students are to begin work on a set for a musical. Working at a constant rate, they will finish the set in 60 days, but the director of the musical decides they need to finish in 50 days. We''re asked for the number of ADDITIONAL theater students we would ...”

“Hi All, We''re told that a circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide. We''re asked for the area of the walkway. This is an example of a ''punch out'' question - we need to find the area of the ENTIRE shape and then ''punch out'' the part ...”

“Hi All, We''re told that Kim has 40 percent MORE money than Sal, Sal has 20 percent LESS money than Phil and Sal and Phil have a combined total of $1.80. We''re asked for the amount of money that Kim has. This question can be approached in a couple of different ways, including some brute-force ...”

“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 ...”

“ Given: In a certain class, the ratio of girls to boys is 5:4. Let G = number of girls in the class Let B = number of boys in the class We can write: G/B = 5/4 Cross multiply to get: 4G = 5B Rearrange to get: 4G - 5B = 0 Target question: What is the value of G Statement 1: If four ...”

“Let x = Phil''s money Sal has 20 percent LESS money than Phil So, Sal''s money = (Phil''s money) - (20% Phil''s money) = x - (20% of x) = x - 0.2x = 0.8x Kim has 40 percent more money than Sal So, Kim''s money = (Sal''s money) + (40% Sal''s money) = (0.8x) + (40% of 0.8x) = ...”

“The question conveniently gives us the information to write the equation of the line in slope y-intercept form, y = mx + b, where m = slope and b = the y-intercept. Line in the xy-plane has a slope of 2 and a y-intercept of 2 So, the equation of the line is: y = 2x + 2 On this line, what is ...”

“Target question: What is the value of x? Given: y ≥ 0 Statement 1: |x - 3| ≥ y Let''s TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 10 and y = 2. We get |10 - 3| ≥ 2, which evaluates to be 7 ≥ 2, which satisfies ...”

“The total of company C''s assets in 1992 was N dollars Company C''s assets in 1993 was 400% greater than the total in 1992 So, 1993 assets = (1992 assets) + (400% of 1992 assets) = (N) + (400% of N) = (N) + (400/100 x N) = N + 4N = 5N Company C''s assets in 1994 was 300% greater than the ...”

“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 ...”

“The least expensive price for a bagel is $0.65 If a customer purchases 12 bagels (at $0.65 each), then he/she receives 13 bagels. So, the minimum amount that a customer could pay to receive 13 bagels = 12 x $0.65 = $7.80 Answer: B Cheers, Brent”

“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.”

“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 = ...”

“(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.”

“ Given: a, b, and c are positive integers. Target question: Is a + b + c an odd number? Statement 1: ab is an odd number No information about c. NOT SUFFICIENT Statement 2: c is an odd number No information about a or b. NOT SUFFICIENT Statements 1 and 2 combined If ab ...”

“Take the task of creating a cricket team and break it into stages. Stage 1: Select 5 batsmen Since the order in which we select the batsmen does not matter, we can use combinations. We can select 5 batsmen from 7 batsmen in 7C5 ways (21 ways) So, we can complete stage 1 in 21 ways ...”

“We can also solve the question algebraically. GIVEN: 1/x - 1/y = 1/z Multiply both sides by x to get: 1 - x/y = x/z Multiply both sides by y to get: y - x = xy/z Multiply both sides by z to get: yz - xz = yx Rearrange to get y terms on one side: yz - yx = xz Factor left side: y(z - x) = ...”

“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 ...”

“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.”

“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 ...”

“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 ...”

“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 ...”

“A quick solution is to assign some values to the highest paid and lowest paid workers Let $10,000 = the lowest salary LAST YEAR Let $40,000 = the highest salary LAST YEAR This satisfies the condition that the range LAST YEAR = $30,000 If the annual salary of each of the 100 employees this ...”

“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 ...”

“Let x = the smaller integer So, 1.25x = the larger integer (since the larger integer is 25% greater than the smaller integer) The sum of two integers is 27. We can write: x + 1.25x = 27 Simplify: 2.25x = 27 Solve: x = 27/2.25 IMPORTANT: What''s a nice fast way to evaluate 27/2.25? An easy ...”

“One approach is to check each answer choice, beginning with the largest answer choice E. 840 840 is divisible by 2, 3, 4, 5, 6 and 7 Answer: E Cheers, Brent”

“RULE: if the SUM of the digits of a number is divisible by 3, then that number is divisible by 3 Take, for example, the number 1,001,226 1 + 0 + 0 + 1 + 2 + 2 + 6 = 12 Since 12 is divisible by 3, we know that 1,001,226 is divisible by 3 If 123,45n is divisible by 3, then 1 + 2 + 3 + 4 + 5 + n ...”

“Target question: What is the sum of a, b, and c? This is a good candidate for rephrasing the target question. Since angles on a line add to 180°, we already know that b + c = 180 We get: a + b + c = a + 180 So, in order to find the sum of a, b and c, we need only find the value of a ...”

“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.”

“Notice that the question asks us to find that TOTAL number of people present. In other words, it the question does NOT ask us to find the number of associate professors or assistant professors present. Since each person brings THREE items, and since total of 21 items were brought (10 pencils ...”

“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.”

“The average (arithmetic mean) number of book borrowed per student was 2. Since there are 30 students altogether, the total number of borrowed books = (2)(30) = 60 2 students borrowed 0 books: total of 0 books 12 students borrowed 1 book each: total of 12 books 10 students borrowed 2 books ...”

“Target question: Is each of the numbers n the list equal to zero? Given: There are more than 2 numbers in the list Statement 1: The product of any 2 numbers in the list is ZERO There are several possible sets that satisfy this condition. Here are two: Case a: the set is {0, 0, 0} in ...”

“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.”

“Target question: Is mn < 10? Statement 1: m < 5 and n < 2 Let''s TEST some values. There are several values of m and n that satisfy statement 1. Here are two: Case a: m = 0 and n = 0. In this case mn = (0)(0) = 0. So, the answer to the target question is YES, mn IS less than 10 ...”

“Data Sufficiency lesson #4: GMAT Data Sufficiency Strategies - Part I Video : https://www.youtube.com/watch?v=Ep09hi1OJpI Cheers, Brent”

“Let''s first see what happens if Steven works as fast as possible. Since Bill can complete the job in 6 hours, Steven must complete the job in a little more than 6 hours. For example, we COULD see what happens if Steven takes 6.000000000000001 hours to complete the job. Unfortunately, ...”

“Target question: Is the hundreds digit of x equal to the sum of the hundreds digits of y and z ? Notice that there are essentially 3 ways for the hundreds digit of x to be different from the sum of the hundreds digits of y and z Scenario #1: the hundreds digits of y and z add to more than 9. ...”

“Hi All, We''re asked which of the following points is the intersection between the lines y = 3x + 6 and y = -2x - 4. This question can be solved in a number of different ways, including by TESTing THE ANSWERS. Since we''re dealing with two lines - and we now that the two lines intersect - ...”

“Hi All, We''re told that a certain taxi company charges $3.10 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. We''re asked for the total charge for a taxi ride that was 8 miles long? The prompt gives us the price per 1/5 of a mile for a taxi ride. It''s worth noting ...”

“Hi All, We''re told that George bought a large electronic item with a 15% off coupon and paid a total bill. When he got outside, he studied the receipt and realize that he mistakenly had been given DOUBLE the discount of the coupon, even though there was no double-coupon offer in effect that ...”

“George was SUPPOSED to receive a 15% discount, but he received a 30% discount. So, he should have returned 15% of the original cost. However, the manager asked for half that amount (i.e., 7.5% of the original cost) In other words, 7.5% of the original cost = $40.50 IMPORTANT: at this point, ...”

“Target question: Is x - y + 1 > x + y - 1 ? This is a good candidate for rephrasing the target question. Take: x - y + 1 > x + y - 1 Subtract x from both sides to get: -y + 1 > y - 1 Add y to both sides to get: 1 > 2y - 1 Add 1 to both sides to get: 2 > 2y Divide both ...”

“We need to consider 3 different cases: i) Anna visits 2 cities ii) Anna visits 3 cities iii) Anna visits 4 cities i) Anna visits 2 cities There are 4 options for the FIRST city and 3 options for the SECOND city So, the total number of 2-city itineraries = (4)(3) = 12 ii) Anna visits 3 ...”

“KEY CONCEPT: The point of intersection (call P) of the lines y = 3x + 6 and y = -2x - 4 will be such that the x- and y-coordinates of P will satisfy BOTH equations. Since both equations are set equal to y, we can write: 3x + 6 = -2x - 4 Add 2x to both sides: 5x + 6 = - 4 Subtract 6 from both ...”

“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 ...”

“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 ...”

“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 ...”

“4⁶ = (2²)⁶ = 2¹² Since 2¹² = (2³)(2⁹), we know 2³ is a divisor of 2¹² Since 2¹² = (2⁶)(2⁶), we know 2⁶ is a divisor of 2¹² Since 2¹² = (2⁹)(2³), we know 2⁹ is a divisor of 2¹² Since 2¹² = (2¹²)(2⁰), we know 2¹² is a divisor of 2¹² Since 2¹² = ...”

“Let x = the smaller integer So, x+1 = the larger integer (since the numbers are CONSECUTIVE) The squares of two consecutive positive integers differ by 55. We can write: (x + 1)² - x² = 55 Expand: x² + 2x + 1 - x² = 55 Simplify: 2x + 1 = 55 So: 2x = 54 Solve: x = 54/2 = 27 Answer: ...”

“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.”

“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, ...”

“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, ...”

“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 ...”

“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.”

“We can solve this question with the weighted averages formula: Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ... Let x = the number of units of 12% phosphoric acid solution needed ...”

“Here''s a similar question to practice with: https://www.beatthegmat.com/divisibility-t111432.html Cheers, Brent”

“Phone plan A charges $1.25 for the first minute and $0.15 for every minute thereafter. Let x = total duration of phone call (in minutes) So, the cost of an x-minute call = $1.25 + ($0.15)(x - 1) ASIDE: I created the expression ($0.15)(x - 1) because we pay $1.25 for the FIRST minute. So, if x = ...”

“Let''s apply probability rules First notice that, to get a matched pair, we can select 2 doves or 2 rabbits. So, P(matched pair) = P(1st pick is rabbit AND 2nd pick is rabbit OR 1st pick is dove AND 2nd pick is dove) We can now apply our AND and OR rules to get: P(matched pair) = x P(2nd ...”

“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 ...”

“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.”

“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 ...”

“Hi All, We''re told that while working at their individual same constant rate, 24 machines can complete a certain production job in 10 hours when they all work together. However, on a certain day, due to minor malfunction, 8 of those machines were not operating for the first 2 hours. We''re ...”

“Hi All, We''re told that Q is a positive integer that is divisible by BOTH 3 and 11. We''re asked which of the following MUST also divisible evenly into Q. This question can be approached in a couple of different ways, including by TESTing VALUES. With these types of prompts, it often helps ...”

“I. 14 14 is NOT divisible by 3 or 11 So, statement I is NOT true. ELIMINATE A and D III. 66 Integer q COULD equal 33 (which is divisible by 3 and 11) Since 33 is NOT divisible by 66, statement III is NOT true. ELIMINATE C and E By the process of elimination, the correct answer is B ...”

“Target question: How many bottles of beer did Kevin buy? Given: Kevin pays $1.00 for each can of beer and $1.50 for each bottle of beer. Kevin buys a total of 15 bottles and cans of beer Let C = the NUMBER of Cans that Kevin bought Let B = the NUMBER of Bottles that Kevin bought So, we can ...”

“(2²⁰²⁰ + 2²⁰¹⁸)/(2²⁰²⁰ - 2²⁰¹⁸) = (2²⁰¹⁸)(2² + 1) / (2²⁰¹⁸)(2² - 1) = 5/3. The correct answer is B.”