royrijit1

“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.”

“In deference to your mother, the offensive second "c" has been removed from my solution.”

“Statement 1: X = 20 miles per gallon. Y = 40 miles per gallon. Since the mixture of X and Y in the tank allows 200 miles to be covered using 8 gallons, we get: X+Y = 200/8 = 25 miles per gallon. To determine how X and Y must be combined to yield a rate of 25 miles per gallon, use ALLIGATION. ...”

“To make the math easier, we can replace the given values with rounder numbers, as follows: Since Rebeca arrives 1 hour late when traveling at the lower speed and 1 hour early when traveling at the higher speed, the time at the lower speed must be 2 hours greater than the time at the higher ...”

“100(11 - √119)(11 + √119) = 100(11² - √119²) = 100(121-119) = 100*2 = 200. When the correct answer is multiplied by 11+√119, the result must be as close as possible to 200. 11+√119 = 11 + (a bit less than 11) = a bit less than 22. Since 9*22 = 198, multiplying 9.2 by a bit less than ...”

“Statement 1: Case 1: a=0 and b=1, with the result that a+b = 0+1 = 1 In this case, a³+b³ = 0³ + 1³ = 1 Case 2: a=2 and b=-1, with the result that a+b = 2-1 = 1 In this case, a³+b³ = 2³ + (-1)³ = 7 Since a³+b³ can be different values, INSUFFICIENT. Statement 2: Case 3: a=1 and b=1, ...”

“Let x=12. Since 1/4 of the people rise up, the number who rise up = (1/4)(12) = 3. Since 3 people come back down, EVERYONE who rises up comes back down, with the result that all 12 people are practicing yoga on the ground. How many people are now practicing yoga on the ground? The correct ...”

“ One-fourth of the people rise up in the air If 1/4 of the x people are in the AIR, the remaining 3/4 of the x people are on the GROUND So, (3/4)x = number of people on the GROUND After a while, 3 of them come back down. So, the number of people on the GROUND is increased by 3 So, now ...”

“Target question: How many sides does N have? Statement 1: x + y = 45 Since all angles in a triangle add to 180°, we know that the missing angle is 135° https://i.imgur.com/oUCDRTN.png There are plenty of polygons that have at least one angle measuring 135°. Here are two: Case a: ...”

“2^32 - 2^31 - 2^30 = (2^30)(2^2 - 2^1 - 1) = (2^30)(4 - 2 - 1) = (2^30)(1) = 2^30 Answer: C Cheers, Brent”

“Target question: What is the value of k? Statement 1: The area of the garden is 189 square feet. Let''s drawn an auxiliary line that divides the shape into two rectangular regions A and B. https://i.imgur.com/hJBOxsO.png Regions A and B have the following measurements. ...”

“Let''s list the multiples of 17 that are between 18 and 3399 : 34 = 2(17) 51 = 3(17) 68 = 4(17) 85 = 5(17) . . . 3383 = 199(17) So, the number of multiples of 17 is EQUAL to the number of integers from 2 to 199 inclusive ASIDE: A nice rule says: the number of integers from x to y ...”

“GIVEN: P(snow) = 0.7, so P(no snow) = 0.3 Let''s use the complement to solve this. That is, P(event is held) = 1 - P(event is NOT held) P(event is NOT held) = P(no snow on Saturday AND no snow on Sunday) = P(no snow on Saturday) x P(no snow on Sunday) = 0.3 x 0.3 = 0.09 So, P(event is ...”

“Statement combined: Case 1: X = 53*2 = 106, with the result that X is divisible by 1, 2, 53, and 106 In this case, X has TWO prime factors: 2 and 53 Case 2: X = 53³, with the result that X is divisible by 1, 53, 53², and 53³ In this case, X has only ONE prime factor: 53 Since the number of ...”

“Prime numbers that are greater than 2 but less than 6: 3, 5 Prime numbers that are greater than 13 but less than 25: 17, 19, 23 Scan the answer choices . . . E) 51 = 3 x 17 PERFECT! Answer: E Cheers, Brent”

“A fraction will yield a terminating decimal if -- when the fraction is fully reduced -- the prime-factorization of its denominator includes only 2''s and or 5''s. Statement 1: Let x = an odd multiple of 5. Since the next largest odd multiples of 5 will be x+10 and x+20, we get: p = x + (x+10) ...”

“A radius drawn to a tangent point yields a RIGHT ANGLE: https://i.postimg.cc/Wq6BDNH7/two-triangles-and-semicircle-1.png In the figure above: Radius OT forms a right angle at tangent point T. OA and OT are radii and thus are equal. Since OA=OT, opposite angles OAT and ATO are equal. We can ...”

“P(select pair) = P(1st card is ANY card AND 2nd card matches 1st card) = P(1st card is ANY card) x P(2nd card matches 1st card) = 1 x 3/51 = 3/51 = 1/17 = C Aside: P(2nd card matches 1st card) = 3/51, because once 1 card is selected, there are 51 cards remaining in the deck. Among those 51 ...”

“One approach here is to apply the COMPOUND INTEREST formula. However, if you didn''t see that the question is analogous to a COMPOUND INTEREST question, we can also solve the question by looking for a pattern. Let''s try that: Time elapsed (in years) | salary 0 | s 0.5 | (1.015)(s) 1 | ...”

“Target question: Of the 3,000 cars manufactured in Factory Q LAST YEAR, how many were still in operation at the end of the year? Neither statement provides any information about the cars manufactured LAST YEAR. Instead, we''re told about ALL of the cars ever manufactured . As such, the ...”

“Total number of friendly numbers = total number of ways to arrange the 5 digits = 5! = 120. There are 5 options for the first digit: 1, 2, 3, 4, or 5. 120/5 = 24. Thus, the 120 friendly numbers are composed of five 24-number ranges, as follows: The integers beginning with 1 constitute friendly ...”

“Since angles on a LINE add to 180°, . . . https://i.imgur.com/kAdhC7N.png . . . we know that x + z = 180 Subtract x from both sides to get: z = 180 - x Since angles in a CIRCLE add to 360°. . . https://i.imgur.com/l1SKqw5.png . . . we know that 60 + (180 - x) + y = 360 Simplify left ...”

“KEY CONCEPT: In order for a point to be ON a line, the x- and y-coordinates of the point must satisfy the equation of that line So, for example, the point (3,7) lies ON the line defined by the equation y = 2x + 1, because x = 3 and y = 7 satisfy the equation y = 2x + 1 That is, 7 = 2(3) + 1 ...”

“ Given: Set S consists of n consecutive integers, where n > 1. Target question: What is the value of n? IMPORTANT: Notice that the two statements are VERY SIMILAR. That is, if the sum of the values is 14 (statement 2), then it is guaranteed that the sum is divisible by 7 (statement 1). ...”

“An integer is divisible by 4 if its last two digits form a multiple of 4. Two-digit multiples of 4 with a units digit of 2: 12, 32, 52, 72, 92 Since the last two digits must be one of the options above, between 1 and 200 there are 10 integers that have a units digit of 2 and are divisible by 4: ...”

“Statement 1: Case 1: AC = 10 and CE = 15, with the result that AE = 10+15 = 25 In this case, ABC + CDE = (10+10+10) + (15+15+15) = 75. Case 2: AC= 5 and CD = 20, with the result that AE = 5+20 = 25 In this case, ABC + CDE = (5+5+5) + (20+20+20) = 75. Since the sum of the perimeters is the same ...”

“For any EVENLY SPACED SET: average = median Statement 1: Here, the set consists of consecutive multiples of 3 and thus is evenly spaced. Case 1: 3, 6, 9 Average = median = 6. Case 2: 6, 9, 12 Average = median = 9. Since different averages are possible, INSUFFICIENT. Statement 2: Case ...”

“Options D and E should appear as shown below: P(exactly n times) = P(one way) * all possible ways. Let R = rain and N = no rain. Since P(R) = 20% = 2/10, P(N) = 80% = 8/10 = 2³/10. P(one way): One way to get exactly 2 days of rain is to have rain on the first 2 days but not on the ...”

“Let''s find some TOTALS for all 4 shipments combined. There are 51,000 chips altogether There are 17 defective chips altogether. So, 17/51000 of the chips are defective. (notice that 17 divides nicely into 51000!) SIMPLIFY: 1/3000 of the chips are defective So, if we have a shipment of ...”

“Since angles in a triangle add to 180°, we know that the missing angle = (90 - 2x)° https://i.imgur.com/FcSiZi2.png Aside: Notice that (90 - 2x)° + 90° + 2x° =180° Since angles on a line add to 180°, we know that the missing angle = (90 + 2x)° https://i.imgur.com/9Z5ULFo.png ...”

“Target question: What is the length of side BC? Statement 1: Line segment AD has length 6. BEFORE we deal with statement 1, let''s see what information we can add to the diagram. For example, since ∆BDC has 2 equal angles (of 2x°), we know that side BD = side BC: ...”

“Target question: What is the area of a right triangle? Statement 1: The length of one side is 3 Knowing the length of only 1 side will not help us answer the target question with certainty. Statement 1 is NOT SUFFICIENT Statement 2: The length of one side is 4 NOT SUFFICIENT (same ...”

“Some spaces and/or brackets would definitely help here. Do you mean x^3 - 1/x - 1 or x^3 - 1/(x - 1) or (x^3 - 1)/(x - 1)?? Cheers, Brent”

“ Given: n and p are integers Target question: Is p > 0? Statement 1: n + 1 > 0 No information about p. Statement 1 is NOT SUFFICIENT Statement 2: np > 0 There are several values of n and p that satisfy statement 2. Here are two: Case a: n = 1 and p = 1. In this case, ...”

“Hi All, We''re told that during the 4 years that Mrs. Lopez owned her car, she found that her total car expenses were $18,000. Fuel and maintenance costs accounted for 1/3 of the total and depreciation accounted for 3/5 of the REMAINDER. The cost of insurance was 3 times the cost of financing, ...”

“Hi All, We''re told that at Megalomania Industries, factory workers were paid $20 per hour in 1990 and $10 per hour in 2000 and the CEO of Megalomania Industries was paid $5 million per year in 1990 and $50 million per year in 2000. We''re asked for what percent greater was the percent increase ...”

“Hi All, We''re told that a company’s 4 cars running 10 hrs a day consume 1200 liters of fuel in 10 days. In the next 6 days, the company will need to run 9 cars for 12 hrs each so it rents 5 more cars which consume 20% less fuel than the company’s four cars. We''re asked for the number of ...”

“Some important rules: #1. ODD +/- ODD = EVEN #2. ODD +/- EVEN = ODD #3. EVEN +/- EVEN = EVEN #4. (ODD)(ODD) = ODD #5. (ODD)(EVEN) = EVEN #6. (EVEN)(EVEN) = EVEN Target question: Is x² - y² odd? IMPORTANT: Notice that we can factor x² - y² to get: x² - y² = (x + y)(x - y) ...”

“GIVEN: 75% women are LEFT handed This also tells us that 25% women are RIGHT handed GIVEN: There are 12 right-handed women Let W = total number of women in the group So, 25% of W = 12 Rewrite as: 0.25W = 12 Solve: W = 12/0.25 = 48 So, there are 48 women So, the number of men in the ...”

“Since A+B take 4 hours to produce 200 widgets, the combined rate for A+B = w/t = 200/4 = 50 widgets per hour. To determine A''s time to produce 200 widgets, we need to know A''s rate. Question stem, rephrased: What is A''s rate? Statement 1: Since B takes 5 hours to produce 50 widgets, ...”

“Triangle XYZ is an isosceles right triangle. Let''s sketch an isosceles right triangle: https://i.imgur.com/N3UOppf.png Side XY is longer than side YZ Since the hypotenuse is the longest side of a right triangle, side XY must be the hypotenuse. Add this to our diagram: ...”

“The sides of an isosceles right triangle are in the following ratio: x - x - x√2, where x and x constitute the base and height and x√2 is the hypotenuse. Since the triangle has a base of x, a height of x, and an area of 16, we get: (1/2)(x)(x) = 16 x² = 32 x = √32 Since XY is longer ...”

“Statement 1: Time and rate are RECIPROCALS. Since X and Y together take 2/3 as long as X alone, X and Y together work 3/2 as fast as X alone. Thus, if X''s rate alone = 2 units per hour, then X and Y''s combined rate = (3/2)(2) = 3 units per hour, implying that Y''s rate alone = 3-2 = 1 unit ...”

“Since A and B must occupy adjacent positions, consider AB a single element in the arrangement. The number of ways to arrange the 6 elements AB, C, D, E, F and G = 6! = 720. In 1/2 of these arrangements, C will be to the LEFT of AB. In the remaining 1/2 of these arrangements,C will be to the ...”

“Nice problem, Fabio! Statement 1: Case 1: a=4, b=1 and c=1, with the result that b+c≥2 In this case, abc = 4, so the answer to the question stem is YES. Case 2: a=0, b=1 and c=1, with the result that b+c≥2 In this case, abc = 0, so the answer to the question stem is NO. Since the answer ...”

“Hi mgec0424, To start, a 520 is a decent initial CAT Score (the average Score on the Official GMAT hovers around 550 most years). Scoring 530 on your second CAT isn''t necessary a ''bad'' thing either - since it takes time to properly use what you''ve learn and adapt your approach to the overall ...”

“Statement 1: If n=5, then the remainder when n is divided by 6 = 5/6 = 0 R5. If n=10, then the remainder when n is divided by 6 = 10/6 = 1 R4. Since different remainders are possible, INSUFFICIENT. Statement 2: Since n is a multiple of 12, n must also be a multiple of 6, with the result that ...”

“Since at least $5600 in profit must be earned by 140 units, the minimum required markup per unit = 5600/140 = $40. Thus, the minimum selling price = (cost per unit) + (minimum required markup per unit) = 16+40 = 56. The correct answer is D.”

“There are 8 TV''s in total 2 are broken 6 are fixed We want to find P(at least one TV is broken) When it comes to probability questions involving at least, it''s often best to try using the complement. That is, P(Event A happening) = 1 - P(Event A not happening) So, here we get: P(getting ...”

“Let x = the selling price per unit So, x - 16 = the PROFIT on ONE unit And 140(x - 16) = the PROFIT on the sale of 140 units (aka the weekly profit) What is the minimum selling price per unit that will ensure a weekly profit of at least $5600 from sales of power stabilizers? In other words, ...”

“Target question: What is the remainder when the positive integer n is divided by 6? Statement 1: n is multiple of 5 Let''s TEST some values. There are several values of n that satisfy statement 1. Here are two: Case a: n = 10. In this case, the answer to the target question is the ...”

“Statement 1: The product of the x-intercepts of line L and K is positive. K has a negative x-intercept, L has a negative x-intercept, the product of the slopes is positive: http://s4.postimage.org/ie5nbe78/lines_l_and_k_1.jpg K has a positive x-intercept, L has a positive x-intercept, the ...”

“Statements combined: Case 1: x=1 and y=1, with the result that x(y+5) = 6 and 6y²+41y+25 = 72 In this case, x is ODD, so the answer to the question stem is NO. Case 2: x=2 and y=1, with the result that x(y+5) = 12 and 6y²+41y+25 = 72 In this case, x is EVEN, so the answer to the question ...”

“SUM = (COUNT)(AVERAGE). Statement 1: x+y+k = (count)(average) = 3*7 = 21. No way to determine the value of x+y. INSUFFICIENT. Statement 2: x+y+3k = (count)(average) = 3*13 = 39. No way to determine the value of x+y. INSUFFICIENT. Statements combined: Subtracting x+y+k=21 from ...”

“a+b+3 = ODD only if a and b are both odd or both even. Question stem, rephrased: Are a and b both odd or both even? Statement 1: ab = ODD implies that a and b are both odd. Thus, the answer to the question stem is YES. SUFFICIENT. Statement 2: a-b = EVEN implies that a and b are either ...”

“Useful rule: (x^k)(y^k) = (xy)^k Example: (3^4)(7^4) = 21^4 (2^2018)(5^2019)(3^2) = (2^2018)((5^2018)(5^1))(3^2) = (2^2018)(5^2018)(5^1))(3^2) = (10^2018)(5^1))(3^2) = (10^2018)(5)(9) = (10^2018)(45) We know that (10^2018) = 1 followed by 2018 zeros So, (10^2018)(45) = 45 followed by ...”

“Target question: Is a + b + 3 an odd integer? Given: a and b are integers Statement 1: ab is an odd integer. Some useful rules: 1. ODD - ODD = EVEN 2. ODD - EVEN = ODD 3. EVEN - ODD = ODD 4. EVEN - EVEN = EVEN 5. (ODD)(ODD) = ODD 6. (ODD)(EVEN) = EVEN 7. (EVEN)(EVEN) = EVEN ...”

“GIVEN: p = length of the longest side Since the side lengths are consecutive even integers, we can say: p - 2 = length of the 2nd longest side p - 4 = length of the shortest side NOTE: The longest side is the HYPOTENUSE. So, p = length of the HYPOTENUSE And p - 2 = length of one leg of ...”

“Target question: What is the length of chord AC? Given: O is the center of the circle If O is the center of the circle, then AB is the circle''s DIAMETER If AB is the DIAMETER, then ∠C = 90°, because ∠C is an inscribed angle containing ("holding") the diameter. So, let''s ...”

“Hi All, For Test Takers who know the Combination Formula, this question is a fairly straight-forward prompt. If you DON''T know the Combination Formula though, then here''s what it is and how to use it. Any time a prompt asks for "groups" or "combinations" of things, then the ...”

“Hi All, We''re told that the sides of a right triangle are CONSECUTIVE EVEN INTEGERS, and the length of the LONGEST side is P. We''re asked which of the following equations could be used to find P. This question can be solved in a couple of different ways, including by TESTing VALUES. To ...”

“Hi All, The probability of pulling a heart out of a full deck of cards is 13/52 = 1/4, so the probability of NOT pulling a heart out of a full deck = 1 - 1/4 = 3/4. The probability of pulling a heart on the THIRD try, and NOT pulling a heart on the first two tries is: (3/4)(3/4)(1/4) = ...”

“Let''s take the task of creating the teams and break it into stages. Stage 1: Select two 5 contestants to be in tribe A Since the order in which we select the contestants does not matter, we can use combinations. We can select 5 contestants from 10 contestants in 10C5 ways 10C5 = ...”

“Hi All, We''re told that starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. We''re asked for the label on an integer that ...”

“What is the harmonic mean of 20 and 30? NOTE: 20 = 20/1 So, the reciprocal of 20 = 1/20 And the reciprocal of 30 = 1/30 The average of 1/20 and 1/30 = (1/20 + 1/30 )/2 = (3/60 + 2/60 )/2 = (5/60 )/2 = (5/60 )/(2/1) = (5/60 )(1/2) = 5/120 The reciprocal of 5/120 = 120/5 = 24 Answer: ...”

“ Given: A certain bag contains red, blue, and green marbles. Let R = # number red marbles in the bag Let B = # number blue marbles in the bag Let G = # number green marbles in the bag Target question: What is the value of G/R? Statement 1: The number of blue marbles in the bag is two ...”

“ Given: x is a nonzero number Target question: Which of the three numbers x, 1/x and x² is greatest? Statement 1: -1 < x < 1 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 = ...”

“Line A includes points (1, 0) and (a, b) and has a slope of -1. Thus: (b - 0)/(a-1) = -1 b = -a + 1 a+b = 1. The correct answer is B. The information about Line B is irrelevant.”

“Alternate approach: Case 1: VVCC, where the first two letters are vowels and the last 2 letters are consonants Number of options for the first vowel = 4. (Any of the 4 vowels) Number of options for the second vowel = 3. (Any of the 3 remaining vowels) Number of options for the first consonant ...”

“Hi All, We''re told that three digits have been removed from each of the following numbers and n = 25. We''re asked which of the numbers is equal to 3*2^(n-1). To start, the fact that three digits have been removed from each answer is irrelevant. When a GMAT question presents information ...”

“Hi All, We''re told that the organizers of a conference offered a certain number of simultaneous seminars with the intention that each seminar would be attended by 18 conference attendees. However, space limitations allowed only up to 15 conference attendees to participate in each of a number of ...”

“Hi All, We''re told that at a school-wide athletic fair, five students won a combined total of 20 ribbons, each of the five students won AT LEAST one ribbon and NO two students won the SAME number of ribbons. We''re asked for the greatest number of ribbons that the student with the ...”

“Hi regor60, I agree that this prompt is poorly-worded. The "intent" is to ask for every 4-letter arrangement that fits the given restrictions, INCLUDING "words" that do not appear in the dictionary (re: arrangements that are not actually words). GMAT question-writers are far ...”

“Hi All, We''re told that in the coordinate plane, Line A has a slope of -1 and an x-intercept of 1 and Line B has a slope of 2 and a y-intercept of -2. The two lines intersect at the point (a,b). We''re asked for the sum a and b. When dealing with lines, it often helps to write the given ...”

“If the average age is 25, we can write: (sum of all 3 ages)/3 = 25 This means, the sum of all 3 ages = 75 If the median is 24, then we can express the ages in ascending order as follows: __ , 24, __ Since the sum of the ages is 75, we can MINIMIZE the age of the oldest girl by MAXIMIZING the ...”

“Let''s use some weighted averages to solve this question Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ... Target question: What is the value of x ? Given: A contractor combined x ...”

“x = 10% gravel y = 2% gravel. z = the MIXTURE of x and y = 5% gravel. To determine the required ratio of x to y, use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS. Step 1: Plot the 3 percentages on a number line, with the percentages for x and y on the ends and the ...”

“Hi benjemin28, It''s worth noting that he Quant section of the GMAT is NOT a ''math test'' - it''s a ''critical thinking test'' that requires lots of little calculations as you work through it. Most GMAT questions are designed so that they can be solved in more than one way (and certain Tactics ...”

“Hi All, The concept in these types of questions is based on the ''worst case scenario'' - to guarantee that something will happen, you have to focus on the ''extreme/longest'' way that it could happen. Here, we have 4 black socks, 3 gray socks and 2 orange socks. The question asks for the ...”

“Hi All, We''re told that the original price of a certain TV set is discounted by X percent, the reduced price is then discounted by 2X percent and P is the original price of the TV set. We''re asked which of the following represents the price of the television set after the two successive ...”

“Since the committee must have 6 people, there are two cases that meet the given restrictions: 1) The committee has 2 men and 4 women 2) The committee has 3 men and 3 women 1) The committee has 2 men and 4 women Since the order in which we select the men and women does not matter, we can use ...”

“When solving mixture questions, I find it useful to sketch the solutions with the ingredients SEPARATED. Since we''re asked to find a PERCENTAGE, we can assign a "nice" value to the original volume. So, let''s say we start with 100 liters https://i.imgur.com/yt2KAw7.png As you can ...”

“ Given: Mr. Jones spends $25 on movie tickets for a party of adults and children. Target question: How many children''s tickets did he buy? Statement 1: Adult movie tickets cost $3 each and children''s tickets cost $2 each. There are several scenarios that satisfy statement 1. Here are ...”

“If we remove 1 black sock, 1 gray sock, and 1 orange sock, then we still don''t have a matching sock. So, we can select 3 socks WITHOUT having a matching pair. However, if we pick ANY sock for our fourth sock, that sock MUST match one of the first 3 socks selected. Answer: A Cheers, Brent”

“IMPORTANT: Notice that statements 1 and 2 provide the EXACT SAME INFORMATION. When this occurs, the correct answer is either D or E Since the information is so sparse, I have a feeling that the correct answer is E. So, I''m going to try to find two possible cases that satisfy both statements, yet ...”

“I thought I''d point out that Mitch''s Double Matrix Method approach 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 students, and the two characteristics are: - male or female - younger than 25 ...”

“Data Sufficiency lesson #3: Avoiding Common Mistakes - Part I Video : https://www.youtube.com/watch?v=iACq36scVYQ Cheers, Brent”

“I received a PM requesting that I respond. Premise: Insurance removes from depositors any financial incentive to find out whether the bank that holds their money is secure against failure. Conclusion: The insurance is partly responsible for the high rate of bank failures. To determine the ...”

“Every student is EITHER male OR female. Every student is EITER older OR younger. For an EITHER/OR problem, use a DOUBLE MATRIX to organize the data: _______________M______F_______Total older: younger: total: Let total students = 100: _______________M______F_______Total ...”

“For every tails, Kate gets $1; for every heads, she loses $1. 0 tails, 5 heads: Kate has 10+0-5 = $5 1 tails, 4 heads: Kate has 10+1-4 = $7 2 tails, 3 heads: Kate has 10+2-3 = $9 3 tails, 2 heads: Kate has 10+3-2 = $11 4 tails, 1 heads: Kate has 10+4-1 = $13 5 tails, 0 heads: Kate has ...”

“Hi All, We''re asked to choose the answer that is CLOSEST in value to (10^8-10^2)/(10^7-10^3). While you might be tempted to try lots of ''math steps'', if you consider how the answer choices are written, you can use a bit of estimation and logic to get to the correct answer without doing too ...”

“Hi All, We''re told that a company produces baseball cards in EQUAL numbers of regular packs of 16 and deluxe packs of 30. On a certain day, the company produces 241 cards. We''re asked for the SMALLEST number of additional cards the company needs to produce in order to maintain its regular ...”

“Hi All, We''re told that the probability of rain on any given day is 50%. We''re asked for the probability that it will rain on AT LEAST three days in a ROW during a five-day period. This question can be approached in a number of different ways; you might find it easiest to do a little math and ...”

“Hi All, We''re told that Father John forms a choir from the church attendants. 30 people attend John''s church and the choir has 28 spots available, with one person as the lead singer. We''re asked for the number of different combinations for the choir. This question involves the Combination ...”

“Hi All, We''re told that a scriptwriter has a particular series of fees for a script (based on the length of the script). The scriptwriter charges.... 1) $4 for every standard script, which is 4 pages or shorter in length 2) 50 cents for every additional page 3) NO CHARGE for every 11th ...”

“One box contains 12 items of clothing Let t, u, v, w, x, y, z = the number of items in each of the other 7 boxes Beth has a collection of 8 boxes of clothing for a charity, and the average (arithmetic mean) number of pieces of clothing per box is c. We can write: (t + u + v + w + x + y + z + ...”

“Hi All, We''re told that a paint crew gets a rush order to paint 80 houses in a new development. They paint the first Y houses at a rate of X houses per week. Realizing that they''ll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25X ...”

“Hi All, We''re told that 2/3 of the roads from A to B are at least 5 miles long, and 1/4 of the roads from B to C are at least 5 miles long. We''re asked to randomly pick a road from A to B and then randomly pick a road from B to C and determine the probability that AT LEAST ONE of the roads you ...”

“Hi kyuhunl, The degree to which you might find tutoring useful will depend greatly on the study materials that you''re currently using and how quickly you can learn (and properly practice) certain concepts and Tactics. Before I can offer you the specific advice that you’re looking for, it ...”

“ Given: Perpendicular lines m and n intersect at (0,b) Target question: What is the value of b? Statement 1: The slope of the line m is -1/2 Since line n is PERPENDICULAR to line m, we know that line n has slope 2 However, we can raise and lower the two lines so that the value of b is ...”

“Let y=0, implying that NONE of the 80 houses are painted at the original rate of x houses per week, with the result that ALL 80 houses are painted at the greater rate of (5/4)x houses per week. The total time it takes them to paint all the houses under this scenario is what fraction of the time ...”

“Let the tank = 60 liters. Since P takes 3 hours to fill the 60-liter tank, P''s rate = 60/3 = 20 liters per hour. Since Q takes 4 hours to fill the 60-liter tank, Q''s rate = 60/4 = 15 liters per hour. Since R takes 5 hours to empty the 60-liter tank, R''s rate = -(60/5) = −12 liters per ...”

“Let x=0. Plugging x=0 into (x-y-2)² + (x+z+3)² = 0, we get: (-y-2)² + (z+3)² = 0 Since neither (-y-2)² nor (z+3)² can be negative, the resulting equation is valid only if -y-2=0 and z+3=0, with the result that y=-2 and z=-3. Thus, y+z = -2 + (-3) = -5 The correct answer is E.”

“Hi All, We''re told that we have six marbles: 3 blue marbles, 2 red marbles, and one green marble - and that we are going to put them into three cups: a black cup, a white cup, and a purple cup. The only restriction is that the two red marbles CANNOT be in the same cup, meaning that we could put ...”

“Hi All, We''re told that during a two-week period, the price of an ounce of silver INCREASED by 25 percent by the end of the first week and then DECREASED by 20 percent of this new price by the end of the second week. We''re asked, if the price of silver was X dollars per ounce at the beginning ...”

“Since J catches up to K, J and K travel the same distance. Let t = J''s time. Since K leaves 15 minutes earlier than J, K''s time = t+15. Rate and time have a RECIPROCAL RELATIONSHIP. Since K''s rate is 80% of J''s rate, the ratio of K''s rate to J''s rate = 8/10 = 4/5. Thus, the ratio of ...”

“Let x=1. Plugging x=1 into f(2x-1) = ( x + 2 ) / ( x – 2 ), we get: f(2*1 - 1) = (1+2)/(1-2) f(1) = -3. When x=1, the question stem becomes: What is f(1)? Since f(1) = -3, the correct answer must yield -3 when x=1. Only A works: f(1) = (1+5)/(1-3) = 6/-2 = -3. The correct answer is A.”

“Hi All, This question is essentially about working through the necessary arithmetic. Thankfully, the math itself isn''t that tough, but you do have to stay organized to make sure that you''re setting up the proper calculations. We''re told that a typical dose of a drug is 2 cm^3 per 15 ...”

“Hi All, The answer choices to this question provide a fantastic shortcut. With the two machines that we''re given, we know that... Old Machine = 100 bolts/hour New Machine = 150 bolts/hour If they start at the same time, the two machines will create 250 bolts/hour The question asks ...”

“Hi All, We''re told that a lecture course consists of 595 students and that the students are to be divided into discussion sections, each with an EQUAL number of students. We''re asked which of the following CANNOT be the number of students in a discussion section. This question is really just ...”

“Hi All, A number of the posts have provided elegant solutions to this question. The basic math behind this prompt is Arithmetic and Prime Factorization though, so if you don''t immediately "see" the elegant approach, you can still get to the answer.... We''re asked to find the ...”

“(students per section)(number of sections) = 595 students number of sections = 595/(students per section). The equation in blue indicates that 595 must be divisible by the number of students per section. An integer is divisible by 3 only if its digit sum is a multiple of 3. The digit sum of ...”

“Correct: The contractors demolished the building to keep it from falling. Here, to keep is not an adjective modifying contractors but an ADVERB modifying demolished, expressing WHY the contractors DEMOLISHED the building. Question: WHY did the contractors demolish the building? Answer: TO KEEP it ...”

“Target question: What percent of the students in the class were females? Let''s 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 ...”

“Statement 1: Case 1: Job = 12 units Since A and B together take 4 hours to complete the 12-unit job, the combined rate for A+B = 12/4 = 3 units per hour. Since A alone takes 6 hours to complete the 12-unit job, A''s rate alone = 12/6 = 2 units per hour. B''s rate = (combined rate for A+B) - ...”

“An alternate approach is to BALLPARK. √2 ≈ 1.4 √3 ≈ 1.7 (1+√3) * √(2 + √3) ≈ (2.7)(√3.7) = (2.7)(a bit less than 2) = a bit less than 5.4. When we evaluate the answer choices, only C is a bit less than 5.4: √2(2 + √3) ≈ (1.4)(3.7) = 5.18. The correct answer is C.”

“We can use equivalent ratios to determine what the dosage SHOULD have been. We''ll use the ratio of drug dosage (in cubic centimeters)/body weight (in pounds) Let x = the dosage (in cubic centimeters) the patient SHOULD have received We get: 2/15 = x/120 Cross multiply to get: 15x = ...”

“Statement 1: The inequality implies that a is POSITIVE, allowing us to cross-multiply: 1*2 > a*1 2 > a Since 2>a and a>b>0, we get: 2>a>b>0 Thus, b<2. SUFFICIENT. Statement 2: If b=2, we get: 1/a + 1/2 = 1 1/a = 1/2 a=2 Not possible, since the prompt ...”

“Statement 1: Since the numbers are EVENLY SPACED, median = sum/count: 64/4 = 16. Since the median = 16, the 4 odd integers must be as follows: 13, 15, 17, 19. Thus, the greatest of the 4 odd integers = 19. SUFFICENT. Statement 2: The 4 odd integers yielded by Statement 1 -- 13, 15, ...”

“Let t = the time (in HOURS) that it takes Marla to complete 4 more laps than Nick. So, after t hours, we can write: (Marla''s lap count) = (Nick''s lap count) + 4 Now that we have a "word equation" we need only fill in the missing information Marla completes 32 laps per hour We can ...”

“The four 18-degree shaded regions = 4*18 = 72 degrees. The entire circle = 360 degrees. (shaded regions)/(entire circle) = 72/360 = 1/5. Thus: (unshaded regions)/(entire circle) = 1 - 1/5 = 4/5 = 80%. The correct answer is E.”

“I thought I''d point out that the approach demonstrated by Fabio and Jay is 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 paintings, and the ...”

“Given: f(x+y) = x + f(y) What is the value of f(100)? We need to somehow use the fact that f(0) = 5 to help us determine the value of f(100). Notice that we can rewrite 100 as 100 + 0 According to our the function f, we know that: f(100 + 0) = 100 + f(0) = 100 + 5 = 105 Answer: C ...”

“Given: P(succeeds on 1 throw) = 1/5 P(succeeds at least 3 times) = P(succeeds 4 times OR succeeds 3 times) = P(succeeds 4 times) + P(succeeds 3 times) P(succeeds 4 times) P(succeeds 4 times) = P(succeeds 1st time AND succeeds 2nd time AND succeeds 3rd time AND succeeds 4th time) = ...”

“APPROACH #1 - start with a convenient value of the server''s salary Let''s say her salary is $4 GIVEN: her tips were 5/4 of her salary 5/4 of $4 = $5 So, her tip total was $5 What fraction of her income for the week came from tips? Income = salary + tips = $4 + $5 = $9 Fraction = $5 /$9 ...”

“IMPORTANT: the diagrams in GMAT problem solving questions are DRAWN TO SCALE unless stated otherwise. We can use this fact to solve the question by simply "eyeballing" the diagram. The question is basically asking us to determine what percent of the circle is NOT shaded. Well, ...”

“Target question: Is x positive? Given: (x + y)/z = -2 Since the question asks about the variable x, let''s solve this equation for x. (x + y)/z = -2 So, x + y = -2z And, x = -2z - y This allows us to REPHRASE the target question.... REPHRASED target question: Is -2z - y positive? ...”

“Hi j_shreyans, I''m a big fan of TESTing Values (Mitch''s explanation), but this question can also be solved with algebra…. We''re told that adding a new tower to an existing hospital allows fore 3 times the number of available beds that were there before the tower was built: Just the ...”

“Hi All, We''re told that a certain company has 18 equally qualified applicants for 4 open positions. We''re asked for the number of different groups of 4 applicants that can be chosen by the company to fill the positions if the order of selection does not matter. This question is a fairly ...”

“Hi All, We''re told that when 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. We''re asked how many marbles must be added to the aquarium in total to raise the water 2 3/4 inches. This question is ultimately about ratios, so you can approach the math ...”

“---------------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 ...”

“The desired height increase = 11/4 inches. 12 marbles yield a height increase of 3/2 inches. Thus: (desired height increase of 11/4 inches) * (12 marbles)/(height increase of 3/2 inches) = (11/4 * 12)/(3/2) = 33/(3/2) = (33*2)/3 = 11*2 = 22 marbles. The correct answer is D.”

“From 18 applicants, the number of ways to choose 4 = 18C4 = (18*17*16*15)/(4*3*2*1) = (3*17*4*15) = 51*60 = 3060. The correct answer is E.”

“Let the PRE-TOWER number of beds = the LCM of the denominators in the problem = 3*5 = 15. Then the CURRENT number of beds = 3*15 = 45, implying that the number of beds in the NEW tower = 45-15 = 30. Occupied beds = (1/3)15 + (1/5)30 = 11. Non-occupied beds in the new tower = 30-11 = 19. ...”

“ Given: A dental licensure exam requires a 75% minimum score in order to pass each section Target question: Did Jennifer pass the 30-question third section? 75% of 30 = 22.5 So, in order to get at least 75% in the 3rd section, Jennifer must correctly answer 23 or more questions in the 3rd ...”

“Hi ALL, This question includes a ''conditional statement'' that effects how you''re supposed to handle each "step" in the math: "for each additional day....., the total fine is EITHER increased by 30 cents OR doubled, whichever results in the LESSER AMOUNT." Since ...”

“Hi All, We''re told that Machines A and B, working together, take T minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than T to complete the same work. Machine B, working alone, takes 25 minutes more than T to complete the same work. We''re asked for the ...”

“One more approach: Since A+B together complete the job in t minutes: Job = (A''s output in t minutes) + (B''s output in t minutes) If A works alone for t minutes, A can then complete the rest of the job in 64 minutes. In this case, the rest of the job = B''s output in t minutes. Thus, A''s ...”

“Barbara invests $2400 in the National Bank at 5%. So, her annual income for this investment = 5% of $2400 = $120 Let x = the additional money Barbara must invest at 8% So, her annual income for this investment = 8% of x = 0.08x So, Barbara''s TOTAL annual income = $120 + 0.08x We want the ...”

“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”

“A present perfect verb (has + VERBed or have + VERBed) expresses a PAST ACTION that affects the present. Generally, the usage of a present perfect verb implies that the subject of the verb still exists. Incorrect: The dinosaurs have evolved over time. The sentence above is illogical because the ...”

“Always keep your eye on the answer choices. Since A''s time alone (t+64) is greater than B''s time alone (t+25), the ratio of A''s time alone to B''s time alone must be GREATER THAN 1. Eliminate A, C and D. Since the ratio of A''s time to B''s time = (t+64)/(t+25), option E implies the ...”

“First day: Total fine = 10. For each additional day, the total fine either increases by 30 or doubles -- whichever results in a lesser amount. Second day: Adding 30 cents to the 1-day fine, we get 10+30 = 40. Doubling the 1-day fine, we get 2*10 = 20. Total fine = lesser amount = 20. ...”

“Hi All, We''re told that when 12 marbles are added to a rectangular aquarium, the water in the aquarium rises 1 1/2 inches. We''re asked how many marbles must be added to the aquarium in total to raise the water 2 3/4 inches. This question is ultimately about ratios, so you can approach the math ...”

“Hi All, We''re told that Barbara invests $2400 in the National Bank at 5%. We''re asked how much additional money she must invest at 8% so that the TOTAL annual income will be equal to 6% of her entire investment. This question can be approached in a number of different ways, including by ...”

“P(Tamara and Inga are BOTH chosen for the jury) = (# of ways to choose 7 people that include Tamara and Inga)/(TOTAL # of ways to choose 7 people) # of ways to choose 7 people that include Tamara and Inga Stage 1: place Tamara and Inga on the jury. This can be accomplished in 1 way Stage 2: ...”

“Clearly, neither statement alone is sufficient. Statements combined: Case 1: No one is a member of both clubs Total males = 15+10 = 25. Total members = 16+20 = 36. Resulting fraction: (total males)/(total members) = 25/36. Case 2: Every male in the music club is also in the drama ...”

“Let d = the number of miles between A and B. Since Georgia travels the entire d miles between A and B and then an additional 60 miles back toward A, Georgia''s distance = d+60. Since Frank travels all but 60 of the d miles between A and B, Frank''s distance = d-60. Since Georgia''s travels 3/2 ...”

“Target question: Did this team win at least half of the games it played last season? Rephrased target question: Did this team win more than 49 games? Statement 1: The team won 60% of its first 65 games In other words, the team won 39 of its first 65 games Since we don''t know the results ...”

“Hi All, We''re told that a in the first M games of a team´s season, the ratio of the team´s wins to its losses was 1:2 and in the subsequent N games, the ratio of the team´s wins to losses was 1:3. If M:N = 4:5, we''re asked for the ratio of the team´s wins to its losses for all M+N games. ...”

“Hi All, We''re told that a major airplane manufacturer announced the sale of 150 small airliners at $125 million each, 75 medium sized airliners at $175 million each, and 60 large airliners at $220 million each. We''re asked for the percentage of the company''s income that came from large and ...”

“Let S = the entire season (in other words, the mixture of M and N). Alligation can be performed only with percentages or fractions. Step 1: Convert the ratios to FRACTIONS. M: Since win:losses = 1:2, and 1+2=3, wins/total = 1/3. N: Since wins:losses = 1:3, and 1+3=4, wins/total = 1/4. ...”

“GIVEN: the roots/solutions are x = -3 and x = 2 Notice that x = -3 and x = 2 are solutions to the equation (x + 3)(x - 2) = 0 If we expand and simplify the left side of the equation, we get: x² + x - 6 = 0 So, the equation x² + x - 6 = 0 has roots -3 and 2 Compare this to x² + px + q = 0 to ...”

“Different approach: The question asks "which of the following must also be a positive integer factor of K?" So, if we can find an answer choice that is NOT a factor of K we can ELIMINATE that answer choice. A. m + n If K = 12, then if COULD be the case that m = 4 and n = 6 In ...”

“GIVEN: m is a factor of K This means that we can write: K = md for some integer d If m and d are both integers, then m and d are both factors of K Notice that, if K = md, then d = K/m, which means K/m is a factor of K Answer: D Cheers, Brent”

“ Given: J, K, L, M, and N are positive integers in ascending order Target question: What is the value of L? Statement 1: The value of K is 3. There are many scenarios that satisfy statement 1. Here are two: Case a: J = 1, K = 3, L = 4, M = 7, N = 8. In this case, the answer to the ...”

“120 = 30*4 210 = 30*7 270 = 30*9 The GCF = the value in blue = 30. Factors of 30 greater than 1: 2, 3, 5, 6, 10, 15, 30 --> 7 factors Thus, 120, 210, and 270 have 7 common factors greater than 1. The correct answer is D.”

“Since Stacy and Katie travel toward each other, they WORK TOGETHER to cover the 27 miles between them. Since Stacy is 1/4 faster than Katie, for every 4 miles that Katie travels, the distance traveled by Stacy = 4 + (1/4)(4) = 5 miles. Thus, of every 9 miles traveled when Stacy and Katie work ...”

“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. ...”

“Hi All, We''re told that a miniature roulette wheel is divided into 10 equal sectors, each bearing a distinct integer from 1 to 10, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector and the wheel is spun three times. We''re asked for ...”

“Hi All, We''re told that the total cost of a vacation was divided equally among 3 people and that if the total cost of the vacation had been divided equally among 4 people, then the cost per person would have been $50 LESS. We''re asked for the total cost of the vacation. This question can be ...”

“Hi All, We''re told that the price of a shirt that costs K dollars is increased by 30%, then that price is increased by an additional 50%. We''re asked for the final price of the shirt in dollars, in terms of K. This question can be solved in a number of different ways - including Algebraically ...”

“Let''s draw a rectangle around the triangle (as shown below) and then subtract from the rectangle''s area (28) the areas of the 3 right triangles that surround the triangle in question. We get the following: http://s13.postimage.org/a47qx0j8j/triangle_in_coordinate_plane_2.jpg So, the area ...”

“A shirt that costs k dollars is increased by 30%, So, the new coast = k + (30% of k) = k + 0.3k = 1.3k ASIDE So, increasing a value by 30% is the same as multiplying that value by 1.3 Similarly, increasing a value by 20% is the same as multiplying that value by 1.2 And increasing a value by ...”

“Let T = total cost of vacation So, T/3 = cost per person with THREE people And T/4 = cost per person with FOUR people If the total cost of the vacation had been divided equally among 4 people, the cost per person would have been $50 less. In other words (cost per person with FOUR people) = ...”

“Hi markymarc89, That''s OUTSTANDING news! With a 740/Q50, you can comfortably apply to ANY Business Schools that interest you. Since you''ve already taken care of your applications, there''s not much else to do at this point (unless you want to consider applying to any additional Schools). We''re ...”

“Let''s first see what happens when the tip is 10% 10% of $35.50 = $3.55 So, the total cost (WITH a 10% tip) = $35.50 + $3.55 = $39.05 So, the total cost must be GREATER THAN $39.05 This means the TOTAL cost could be $39.06 Check the answer choices.... A, D and E do not allow for the total cost ...”

“Target question: Is 4(3b + 2) = 5a? Statement 1: If i is divided by 5 the quotient is a and the remainder is 3 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 ...”

“ Given: The average of four numbers is 35 Target question: How many of the numbers are less than 35? If we''re able to see that the statements FEEL insufficient, and we''re able to come up with some counter-examples in our head, then we can head straight to... . . . Statements 1 and 2 ...”

“Target question: Is x < 16? Statement 1: x is less than the average (arithmetic mean) of the first ten positive integers Since the first ten positive integers are EQUALLY SPACED, the average = (smallest number + biggest number)/2 = (1 + 10)/2 = 5.5 So, x < 5.5 Since 5.5 < 16, we ...”

“Useful rule: the sum of the angles in an n-sided polygon = (n - 2)(180º) So, for example, the sum of the angles in an 11-sided polygon = (11 - 2)(180º) = (9)(180º) = 1620º What is the measure of each interior angle of a regular decagon? A decagon has 10 sides. The sum of the angles in ...”

“Target question: What is the value of x? Statement 1: x³ - x = 0 Factor to get: x(x² - 1) = 0 Factor again to get: x(x + 1)(x - 1) = 0 So, it could be the case that x = 0, x = -1 or x = 1 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT ...”

“I thought I''d point out that Jay''s approach is 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 MP3 players, and the two characteristics are: ...”

“Here''s another (longer) approach: When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k ...”

“Target question: How many sides does Polygon X have? Given: Polygon X has fewer than 9 sides Useful rule: The sum of the angles in an n-sided polygon = (n - 2)(180º) Since the polygon has FEWER than 9 sides, there are are exactly SIX possible cases: case a: There are 8 sides, in ...”

“Since dividing x by 5 yields a remainder, x is not a multiple of 5 and thus not a multiple of 10. Since x is not a multiple of 10, x/10 cannot yield an integer value. The correct answer is B.”

“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: ...”

“Hi All, We''re told that of the votes cast on a certain proposal, 80 MORE were in favor of the proposal than were against it and the number of votes against the proposal was 40 percent of the TOTAL vote. We''re asked for the total number of votes cast? (Each vote cast was either in favor of the ...”

“Hi All, We''re asked which of the following is closest to the value of (2^23)(5^26). If you don''t immediately see the ''Exponent'' rules that apply to this question, then you can still solve it with some basic Arithmetic and logic. To start, when you multiply a bunch of numbers together, the ...”

“Hi All, This question can be solved with a bit of ''brute force'' arithmetic, but the speed with which you solve it will likely depend on how quickly you can write everything down and how you do the work. We''re asked to find the three positive integers, whose squares add up to 75. To start, ...”

“We''re looking for 3 DIFFERENT squares that add to 75 Here are the only squares we need to consider: 1, 4, 9, 16, 25, 36, 49, 64 Can you find 3 that add to 75? After some fiddling, we may notice that 1 + 25 + 49 In other words, 1² + 5² + 7² = 75 We want the SUM of 1 + 5 + 7, which is ...”

“Data Sufficiency Video #2: The Elimination Method Video: https://www.youtube.com/watch?v=amhxP9My_pU Cheers, Brent”

“|x-1| = the distance between x and 1. |x+1| = the distance between x and -1. -1<--|x+1|-->x<--|x-1|-->1 Here, since the total distance between the two endpoints is 2, the sum of the 2 distances in red is 2. If x is any value between the two endpoints, then the sum of the two ...”

“A = (2-3+4)¹¹ = 3¹¹ B = (-2+3-4)¹¹ = (-3)¹¹ = -3¹¹ Thus: A+B = 3¹¹ - 3¹¹ = 0 2^(A+B) = 2⁰ = 1. The correct answer is C.”

“were + VERBing is the plural form of the PAST PROGRESSIVE tense (also known as the past continuous tense). The past progressive tenses serve to express actions that happen CONTINUOUSLY FOR A LIMITED DURATION OF TIME. OA: While businesses were expanding their production, unsold goods were piling ...”

“To minimize B''s time, we must maximize A''s time. Since each machine can work for at most 8 hours, let A''s time = 8 hours. Since A''s rate = 9000 pencils per hour, the number of pencils produced by A in 8 hours = rt = 9000*8 = 72,000. Remaining pencils = 100,000 - 72,000, = 28,000. Since ...”

“]The average salary of 15 people in the shipping department at a certain firm is $20,000 So, (sum of all 15 salaries)/15 = $20,000 Multiply both sides by 15 to get: sum of all 15 salaries = $300,000 The salary of 5 of the employees is $25,000 each and the salary of 4 of the employees is $16,000 ...”

“Original ratio values: P.................................................C...............................................A 6x<---distance of 4x--->10x<---distance of 5x--->15x Options for the new ratio: I) 1 : 2 : 3 I) 2 : 3 : 4 III) 4 : 7 : 10 The ratio values in each ...”

“Target question: Does each angle in the triangle measure less than 90 degrees? Given: A triangle has side lengths of a, b, and c centimeters Statement 1: The 3 semicircles whose diameters are the sides of the triangle have areas that are equal to 3 cm², 4 cm², and 6 cm², respectively. ...”

“GIVEN: x - 2y = 4 We want to find the value of x² - 4xy + 4y² - x + 2y We should notice that x² - 4xy + 4y² is equal to (x - 2y)² We should notice that - x + 2y is equal to -(x - 2y) We get: x² - 4xy + 4y² - x + 2y = (x - 2y)² - (x - 2y) Now replace x - 2y with 4 to get: = (x - ...”

“Target question: What is the value of z in the triangle above? IMPORTANT: Since angles in a triangle must add to 180 degrees, we can write: x + y + z = 180 Statement 1: x + y = 139 Take: x + y + z = 180 and replace (x + y) with 139 to get: 139 + z = 180 Solve equation for z to get: z = 41 ...”

“Take the task of selecting 4 books and break it into stages. Stage 1: Select two biology books Since the order in which we select the books does not matter, we can use combinations. We can select 2 books from 10 books in 10C2 ways (45 ways) So, we can complete stage 1 in 45 ways If ...”

“Target question: What was the number of defective batteries in a shipment of 4000 batteries? Statement 1: In a particular sample of 10 batteries selected from the shipment, 1 was defective. Don''t make the mistake of assuming that this means 1/10 of ALL batteries are defective. There''s no ...”

“Let x=4 and y=0, with the result that x-2y = 4. Plugging x=4 and y=0 into x² - 4xy + 4y² - x + 2y, we get: 4² - 0 + 0 - 4 + 0 = 12. The correct answer is A.”

“Hi All, We''re told that if Sam were TWICE as old as he is, then he would be 40 years older than Jim and that Jim is currently 10 years YOUNGER than Sam. We''re asked for Sam''s current age. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS. Since the ...”

“Hi All, This is an example of a ''Symbolism'' question - the prompt ''makes up'' a math symbol, tells you what it means, then asks you to perform a calculation using it. When dealing with these types of symbols, it often helps to jot down a few examples, so that you understand the work that will ...”

“Hi All, We''re told that on a game show, a contestant is given three keys, each which opens exactly one of three identical boxes. The first box contains $1, the second $100, and the third $1000. The contestant assigns each key to one of the boxes and wins the amount of money contained in any box ...”

“There aren''t many possible outcomes, so let''s start by listing all possibilities. Let A, B and C represent the 3 boxes, and let a, b, c, be the keys for those boxes (in that same order). A = $1 prize, B = $100 prize and C = $1000 prize If the boxes are arranged as A-B-C, then these are ...”

“http://s27.postimg.cc/531tmnqpr/circ_int.jpg Answer: E The important takeaway here is that "intersect" does not necessarily mean "pass through" So, a line that is tangent to a circle (touching the circle but not passing through it) can be said to intersect the circle. To ...”

“First, let''s take a moment to get a good idea of what this strange notation means. A few examples: -1 < x/2 ≤ 0 Multiply all sides of the inequality by 2 to get: -2 < x ≤ 0 Check the answer choices.... Only -3/2 falls inside that range. Answer: B Cheers, Brent”

“Hi Aliya, I have a feeling that your email system is treating the emails as spam. Have you checked your spam/junk folders? You might to sign up for the emails again, but this time, be sure to add guide@beatthegmat.com as a contact in your e-mail system. This will help ensure that the daily ...”

“This is a Variables in the Answer Choices question (VIAC). This question type can be answered algebraically or using the INPUT-OUTPUT approach. Mitch has demonstrated the INPUT-OUTPUT approach, so let''s solve the question algebraically. The average American spends y dollars on food per month, ...”

“Test the THRESHOLD. In the question stem, the threshold is 40 CHAIRS. The total cost of 40 chairs = 40*50 = 2000. Statement 1: The total price of the desks and chairs is 5,000. It is possible that 40 chairs are purchased (at a total cost of $2000) or that MORE CHAIRS are purchased. ...”

“Statement 1: To have exactly 3 positive factors, x must be the square of a prime number. Factors of x=2²=4: 1, 2, 4 Factors of x=3²=9: 1, 3, 9 Factors of x=5²=25: 1, 5, 25. Since x can be different values, INSUFFICIENT. Statement 2: Clearly INSUFFICIENT. Statements combined: x ...”

“Monthly food expense except in January: Let y=$2. Discount in January: Let x=100%. Since $2 is spent each month for 8 of the first 9 months, the total spent during these 8 months = 8*2 = 16. Since food purchases are 100% lower in January -- implying that they are FREE in January -- the amount ...”

“Target question: What is the value of a? Given: 81 divided by a results in a remainder of 1 In other words, 81 is 1 greater than some multiple of a This means that 80 is some multiple of a Another way to say this is: a is a divisor of 80 The divisors of 80 are: 1, 2, 4, 5, 8, 10, 16, ...”

“Let''s list and count all possible outcomes. Possible products when 2 is selected from set A: 8, 10, 12, 14, 16 Possible products when 3 is selected from set A: 12, 15, 18, 21, 24 Possible products when 4 is selected from set A: 16, 20, 24, 28, 32 Possible products when 5 is selected from set ...”

“Jim is 10 years younger than Sam Let x = Sam''s PRESENT age So, x - 10 = Jim''s PRESENT age If Sam were twice as old as he is, he would be 40 years older than Jim. TWICE Sam''s age = 2x So, we can write: 2x = (x - 10) + 40 Simplify: 2x = x + 30 Solve: x = 30 Answer: B Cheers, Brent”

“This question is a great candidate for the Double Matrix method, whichcan be used for most questions featuring a population in which each member has two characteristics associated with it. Here, we have a population of motel rooms, and the two characteristics are: - air conditioning or no air ...”

“Alternate approach: To determine the ratio of birds to dogs, plug in a TEST VALUE for the total number of pets. Let b = the number of birds and d = the number of dogs. Let the test value for the total number of pets = the LCM of 3 and 5 = 15. Since 1/5 are birds, b = 1/5 * 15 = 3. Since 1/3 ...”

“Target question: How many of the pets are dogs? Given: 1/3 of pets are dogs & 1/5 of pets are birds Let T = TOTAL number of pets. So, T/3 = number of dogs And T/5 = number of birds Statement 1: There are 30 birds at the pet shop So, T/5 = 30 This means that T = 150, which ...”

“Target question: Is x > y? Statement 1: -4x + 2y < y - 3x Add 4x to both sides to get: 2y < y + x Subtract y from both sides to get: y < x Perfect, the answer to the target question is YES, x IS greater than y Since we can answer the target question with certainty, statement 1 ...”

“It turns out that the cost per apple is irrelevant. Here''s why: The average (arithmetic mean) price of the 10 pieces of fruit is 56 cents So, (total value of all 10 pieces of fruit)/10 = 56 cents This means, total value of all 10 pieces of fruit = 560 cents How many oranges must Mary put ...”

“The mean of all 5 numbers is 8.8 (a + b + c + d + e)/5 = 8.8 Multiply both sides by 5 to get: a + b + c + d + e = 44 The sum of a, c and e is 24 (a + c + e) = 24 So, take a + b + c + d + e = 44 and rewrite as: (a + c + e) + b + d = 44 We get: (24) + b + d = 44 So, b + d = 20 b is the ...”

“Oops - pressed the wrong button. As you were! Brent”

“Target question: How old is Carmen now? Given: 3 years ago Jennifer was 22 years old So, Jennifer''s PRESENT age is 25 Statement 1: 10 years ago, Carmen was twice as old as Jennifer. If Jennifer''s PRESENT age is 25, then Jennifer''s age 10 YEARS AGO was 15 This means Carmen''s age 10 ...”

“No takers? Let''s say there are 100 apples in the barrel. 45% of the apples weigh MORE THAN 81 grams This means 55% of the apples weigh LESS THAN OR EQUAL to 81 grams In other words, 55 apples weigh LESS THAN OR EQUAL to 81 grams 81% of the apples weigh LESS THAN 145 grams This means 19% ...”

“Hi All, This question is essentially a "Work Formula" question, since it has 2 people working on a task together. You have to be really careful with the details though, since the two given rates are NOT for the same task.... We''re told that Danny can finish off the jar of candies in ...”

“Hi All, We''re told that a bus completed first 50 miles of a 120-mile trip at an average speed of 20 mph. Then it took a halt of 30 minutes and completed half of the remaining journey at an average speed of 35 mph. We''re asked for the average speed it should complete the REMAINING part of the ...”

“Statement 1: If d=72, then t = d/r = 72/72 = 1 hour. If d=144, then t = 144/72 = 2 hours. Since the time can be different values, INSUFFICIENT. Statement 2: Time and rate have a RECIPROCAL RELATIONSHIP: If the time is cut in HALF, then the rate DOUBLES. If the time DOUBLES, then the ...”

“ Given: A dental licensure exam requires a 75% minimum score in order to pass each section Target question: Did Jennifer pass the 30-question third section? 75% of 30 = 22.5 So, in order to get at least 75% in the 3rd section, Jennifer must correctly answer 23 or more questions in the 3rd ...”

“Perfect approach! ASIDE: We have 4 teams, and 2 teams play a game. So, the number of games played = the number of different ways to select 2 of the 4 teams = 4C2 = 6 Cheers, Brent”

“Target question: Does (a – 2)(b + 4) = 8? This is a good candidate for rephrasing the target question. When I SCAN the statements, I see that statement 1 has the term ab. This suggests to me that we might benefit from EXPANDING the expression, since that will result in an ab term. Take: (a ...”

“We want P(select at least one 6) When it comes to probability questions involving "at least," it''s best to try using the complement. That is, P(Event A happening) = 1 - P(Event A not happening) So, here we get: P(getting at least one 6) = 1 - P(not getting at least one 6) What does ...”

“GIVEN: x and y are consecutive integers such that x < y So, if x is ODD, then y is EVEN One option here is to replace the x''s and y''s with ODD and EVEN and apply the rules for ODDs and EVENs. Or we can just replace x and y with odd and even numbers. Let''s do that. Replace x with 1 ...”

“Target question: Is x > 0 ? Statement 1: x – y > –8 This statement doesn''t feel sufficient, so I''ll TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 1 and y = 0. In this case, the answer to the target question is YES, x ...”

“The key here is that f(51) is EQUAL to f(50) Here''s why: According to the definition of the function f, f(51) = (2)(4)(6). . . (48)(50), and f(50) = (2)(4)(6). . . (48)(50) So, f(51) - f(50) = (2)(4)(6). . . (48)(50) - (2)(4)(6). . . (48)(50) = 0 Answer: E Cheers, Brent”

“Let G = the gas in the tank and C = the capacity of the tank. Statement 1: G - (1/2)G = (1/3)C No way to solve for G. INSUFFICENT. Statement 2: G + 0.75 = C No way to solve for G. INSUFFICIENT. Statements combined: Since we have two variables (G and C) and two distinct linear ...”

“Hi All, We''re told that three children - John, Paul, and Ringo, are playing a game. Each child will choose either the number 1 or the number 2. When one child chooses a number DIFFERENT from those of the other two children, he is declared the winner. If all of the children choose the SAME ...”

“Hi All, We''re told that a will was written such that an estate would be divided among FIVE beneficiaries with the remainder donated to charity, with one stipulation in the will is that no one beneficiary can receive an amount within 20% of another''s amount. One of the beneficiaries received ...”

“Hi All, This question can be solved with fairly straight-forward Algebra (as some of the other solutions have proven). It can also be solved by TESTing THE ANSWERS and a bit of logic. We''re told that the total weight of Jake and his sister is 278 pounds. We''re also told that if Jake lost 8 ...”

“Hi JOHNMC, Raising a 430 to the point that you could consistently score 700+ will likely require at least another 3 months of consistent, guided study - and you''ll have to make significant improvements to how you handle BOTH the Quant and Verbal sections. Thankfully, the GMAT is a consistent, ...”

“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 ...”

“If the area of the square is 4, then each side has length 2 https://i.imgur.com/Ul16WsZ.png At this point, we have a special 30-60-90 right triangle. When we compare this blue triangle to the BASE 30-60-90 right triangle . . . https://i.imgur.com/vrYSacE.png . . . we see that the blue ...”

“Here, the value in red is the sum of Jake''s weight and TWICE the sister''s weight: 187 + 2(89.5) = 366. But the prompt gives an integer value for the sum of Jake''s weight and the sister''s ACTUAL weight -- a constraint that forces Jake''s weight to be an even integer.”

“The sum of Jake''s weight and his sister''s weight is an INTEGER VALUE. The answer choices indicate that Jake''s weight is an INTEGER VALUE. Implication: The sister''s weight must also be an integer value. Thus, the value in red -- 89.5 -- is not a valid option for the sister''s weight. Given ...”

“Set A = {2, 3, 4, 5}, and set B = {4, 5, 6, 7, 8}. If P = the product of one number chosen from set A and one number chosen from set B, how many DIFFERENT values of P are possible? A) 14 B) 15 C) 16 D) 18 E) 20 Answer: C Difficulty level: 600 - 650 Source: www.gmatprepnow.com”

“Target question: Is 40 Swiss Francs enough to buy 12 notebooks and 12 pencils? This is a great candidate for rephrasing the target question. Let N = the cost of 1 notebook (in Swiss francs) Let P = the cost of 1 pencil (in Swiss francs) So, 12 notebooks cost 12N and 12 pencils cost 12P ...”

“Let the river''s rate = 1 mph and the boat''s rate = 5 mph. When the boat travels DOWNRIVER, the boat and the river WORK TOGETHER, so we ADD their rates: 5+1 = 6 mph. When the boat travels UPRIVER, the boat and the river COMPETE, so we SUBTRACT their rates: 5-1 = 4 mph. Rate and time have ...”

“ALWAYS KEEP YOUR EYE ON THE ANSWER CHOICES. If Jake loses 8 pounds, he will weigh twice as much as his sister. j-8 = 2s j = 2s + 8 = even + even = even. Since Jake''s weight must be an EVEN VALUE, the correct answer is E.”

“Let x = the speed of the river (in miles per hour) So, 5x = the speed of the boat in (miles per hour) Let d = distance traveled (in miles) This means the boat''s speed going UPriver = 5x - x = 4x And the boat''s speed going DOWNriver = x + 5x = 6x time = distance/speed So, travel time ...”

“Here''s a solution that uses one variable. Let x = Jake''s present weight in pounds So, x - 8 = Jake''s hypothetical weight IF he were to lose 8 pounds If Jake loses 8 pounds, he will weigh twice as much as his sister. In other words, the sister weighs HALF as much as Jake''s hypothetical ...”

“The main concept here is that all 3 children are equally likely to win this game (unless one of them possesses supernatural powers that allow him to know what numbers the other two boys will choose :-)) Also note that, if everything is random, the probability of winning by choosing the number 2 ...”

“In a barrel full of apples, 45% of the apples weigh more than 81 grams, and 81% of the apples weigh less than 145 grams. What percent of the apples in the barrel weigh more than 81 grams but less than 145 grams? A) 16 B) 18 C) 26 D) 32 E) 36 Answer: C Difficulty level: 600 - 650 Source: ...”

“Given: radius = 3 Height = 10 Surface area of cylinder = 2πr² + 2πrh = 2π(3²) + 2π(3)(10) = 18π + 60π = 78π Answer: D Cheers, Brent”

“This is one of my all-time favorite questions!! The main concept here is that all 3 children are equally likely to win this game (unless one of them possesses supernatural powers that allow him to know what numbers the other two boys will choose :-)) Also note that, if everything is random, ...”

“Hi All, We''re told that Mixture A is 15 percent alcohol and mixture B is 50 percent alcohol and when a certain amount of each is poured together to create a 4-gallon mixture, the result contains 30 percent alcohol. We''re asked approximately how many gallons of mixture A are in the mixture. ...”

“Hi All, We''re asked which of the 5 answers is the equation for a line that is perpendicular to line K in the figure above. This question is based on line/graphing rules. To start, a PERPENDICULAR line is one that has an "opposite inverse" slope (sometime called a "negative ...”

“Hi All, We''re told that a certain concrete mixture contains gravel, water, and sand in a ratio of 1 to 3 to 5 by weight. We''re asked for the number of pounds of gravel that would be needed to produce 72 pounds of the mixture. This math behind this question can be approached in a number of ...”

“Hi JOHNMC, Since it sounds like you''re just beginning your studies, 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 additional practice materials). If you want to do a little studying first, so that you can ...”

“Let S = Sara''s age. Sum of the ages = 2+4+5+8+10+13+S = 42+S. Statement 1: Since the average age is equal to an INTEGER -- the fourth largest age -- we get: Sum of the ages = (number of ages)(average age) = (7)(INTEGER) = multiple of 7. The blue expression and the red expression each ...”

“From 2000 to 2003, the number of employees at a certain company increased by a factor of 1/4 Let x = the number of employees in 2000 So, the number of employees in 2003 = x + (1/4)x = (5/4)x From 2003 to 2006, the number of employees at this company decreased by a factor of 1/3 (5/4)x = the ...”

“Target question: How much money could be saved by purchasing 10 bagels at the sale price rather than at the usual price? Statement 1: The usual price for a bagel is $0.50 per bagel. Since there''s no information about the SALE price, there''s no way to calculate the amount saved. Since we ...”

“We can PLUG IN THE ANSWERS, which represent the value of m. When the correct answer is plugged in, the median will be equal to the range. Note: When the prompt includes the phrase which of the following, the correct answer is likely to be D or E. E: m=3 Resulting set: 1, 1, 2, 2, m=3, 3, 3, ...”

“Hi All, We''re told that in a 200 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. We''re asked for the LEAST number of members who are homeowners. This question is built around a couple of Number Properties - and to MINIMIZE the number of ...”

“Hi All, We''re told that Roger wants to arrange three of his five books on his bookshelf, but two of the five books are duplicates and cannot both be selected. We''re asked for the number different ways that Roger can arrange his books. The wording of this question is a bit ''quirky'', but the ...”

“Let X=8 and Y=4. Henry eats X scones in X percent of the time it takes Rachel to eat Y scones. Since Henry eats X=8 scones in 8% of the time it takes Rachel to eat Y=4 scones -- 10 minutes, according to the prompt -- the time for Henry to eat 8 scones = 8% of 10 minutes = (8/100)(10) = 4/5 ...”

“Let''s use the INPUT-OUTPUT approach. Let''s assign some values of X and Y so that they satisfy the information in the question. Let X = 25. This means Henry eats 25 scones in 25 percent of the time it takes Rachel to eat Y scones Let Y = 100. This means Henry eats 25 scones in 25 percent of ...”

“I''m not crazy about this question. The official answer suggests that, although 2 books are DUPLICATES, they''re still considered DIFFERENT. Here''s what I mean: Let''s let D and d represent the two duplicate books. Let, A, B and C represent the other three books. The official answer ...”

“IMPORTANT point: The VALUE of a 3-digit integer xyz is 100x + 10y + z Example: 723 = (7)(100) + (2)(10) + 3 Target question: What is the remainder when n is divided by 37? Statement 1: A + B/10 + C/100 = B + C/10 + A/100 Multiply both sides by 100 to get: 100A + 10B + C = 100B + 10C + ...”

“ Given: x and y are integers Target question: Is x² + x + y an odd integer? This is a good candidate for rephrasing the target question. Take x² + x + y and factor the first two terms to get: x(x + 1) + y Notice that x and x+1 are CONSECUTIVE INTEGERS, which means one value is ODD and ...”

“number of tiles = (wall area)/(tile area) = (800*300)/(25*12) = 32*25 = 800. The correct answer is E.”

“Consider the following equation: 7x + 5y = 70. If x and y are nonnegative integers, the following solutions are possible: x=10, y=0 x=5, y=7 x=0, y=14. Notice the following: The value of x changes in increments of 5 (the coefficient for y). The value of y changes in increments of ...”

“In order to minimize the number of homeowners, we must MAXIMIZE the number of men in the group, since the proportion of male homeowners (20%) is less than the proportion of female homeowners (25%) So, let''s see what happens if there are 199 men and 1 woman. If 20% (aka 1/5) of the men are ...”

“x is directly proportional to y implies the following: x/y = k. x = ky. In each case, k is a CONSTANT. The cost of a square slab is proportional to its thickness and also proportional to the square of its length. Thus: c = k * T * L². What is the cost of a square slab that is 3 meters ...”

“species may be singular or plural. Passage: Planting trees primarily from the species that turns out to have the best record of survival will assure downtown Thomasville of an abundant tree population 20 years from now. Here, the verb attributed to species is turns. Since turns is singular, ...”

“Hi yenngoc2409, I''m going to give you a hint so that you can adjust your calculation. Your result is too high because you have not accounted for the ''duplicate'' entries. For example, if the 4 cards were 2233, then you have an option that has two pair... but you also have two of the options ...”

“ It takes h + 3 hours to produce 360 toys when 2 machines work together So, during those h + 3 hours, EACH machine makes 180 toys So, ONE machine can produce 180 toys in h + 3 hours rate = output/time So, we can write: rate of ONE machine = 180/(h + 3) It takes h hours to produce 360 toys ...”

“(number of machines)(number of hours) = number of toys that are produced. In the prompt above, the blue values are THE SAME. Implication: 2 machines take h+3 hours to produce the same number of toys as 3 machines in 2 hours: 2(h+3) = 3h 2h + 6 = 3h 6 = h. Since 3 machines produce 360 toys ...”

“Rule: nCr = nC(n-r) Examples: 5C2 = 5C(5-2) = 5C3. 10C3 = 10C(10-3) = 10C7. 99C5 = 99C(99-5) = 99C94. Statement 2: Jay can select k-1 of his problems in 4851 different ways. Since 4851 is relatively small, test small values for k-1. Case 1: k-1 = 2 From 99 problems, the number of ...”

“Hi All, We''re told that the number of defects in the first five cars to come through a new production line are 9, 7, 10, 4, and 6, respectively and that the sixth car through the production line has either 3, 7, or 12 defects. We''re asked which of the following three values does the MEAN ...”

“Hi amg0410, To start, a 540 is a solid initial CAT Score (the average Score on the Official GMAT hovers around 550 most years). 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 your timeline and your goals: ...”

“Let x = 2 hours, y = 3 hours and z = 4 hours. Let the tank = 12 gallons. Since Alpha takes 2 hours to fill the 12-gallon tank, Alpha''s rate = w/t = 12/2 = 6 gallons per hour. Since Beta takes 3 hours to fill the 12-gallon tank, Beta''s rate = w/t = 12/3 = 4 gallons per hour. Since Gamma takes ...”

“Hi All, We''re told that Carlos runs a lap around the track in X SECONDS. His second lap is five SECONDS SLOWER than the first lap, but the third lap is two SECONDS FASTER than the first lap. We''re asked for Carlos’s average (arithmetic mean) number of MINUTES per LAP, in terms of X. This ...”

“Hi All, We''re told that Patricia builds two triangles, EACH with 30 feet of wood. The first triangle ABC is built to maximize the LENGTH of the BASE side. The second triangle DEF is built to maximize the AREA of the triangle. In addition, the lengths of all line segments are INTEGERS. We''re ...”

“Hi mbaorbust3, I''m sorry to hear that Test Day did not go as well as hoped. Business Schools generally don''t care if you retake the GMAT though, so you have little to worry about in that regard. Before we can discuss how you might improve this next phase of your studies, it would help if you ...”

“...the probability that it So, 1/4 of the 120 marbles are white. In other words, there are 30 white marbles. ...the probability that it So, 1/3 of the 120 marbles are green . In other words, there are 40 green marbles. Altogether, there are 70 marbles that are EITHER white or green. ...”

“Total # of combinations = (# of ways to select 2 chairs)(# of ways to select 2 tables) So, 150 = (# of ways to select 2 chairs)(# of ways to select 2 tables) # of ways to select 2 chairs 5 tables, choose 2 of them. Since the order of the selected chairs does not matter, we can use ...”

“Since 150 combinations are possible, we get: (number of ways to choose 2 chairs)(number of ways to choose 2 tables) = 150. From 5 chairs, the number of ways to choose 2 = 5C2 = (5*4)/(2*1) = 10. Thus: (10)(number of ways to choose 2 tables) = 150 number of ways to choose 2 tables = 150/10 = ...”

“Let x = 5 seconds for the first lap, implying 10 seconds for the second lap, 3 seconds for the third lap, and a total of 18 seconds for all 3 laps. (18 seconds)/(3 laps) = (6 seconds)/(1 lap) = 1/10 minute per lap. The correct answer must yield a value of 1/10 when x=5. Only D works: (x+1)/60 ...”

“The information in red is irrelevant. Only the following facts matter: Ross travels onward at a rate of 1 mile every 12 minutes. He travels home for twice the onward distance at half the onward speed. Onward speed = 1 mile per 12 minutes = 5 miles per 60 minutes = 5 mph. Let the onward ...”

“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 ...”

“Hi All, We''re told that Profit = Revenue - Costs and that costs will remain constant from 2007 to 2008, while revenues INCREASE by 10% in that same period. We''re asked for the percent increase in PROFITS from 2007 to 2008. This question comes down to some Arithmetic and the Percentage Change ...”

“Hi All, We''re told that a class consists of 12 girls and 20 boys. One-quarter of the girls in the class have blue eyes. We''re asked for the probability that a randomly selected child is a girl who does NOT have blue eyes. This question comes down to some basic organization and Arithmetic. ...”

“Hi szhao, To start, a 730 initial Score is an outstanding performance (the average Score on the Official GMAT hovers around 550 most years), so you''re clearly a strong critical thinker. Focusing on the GMAT now - years before you will actually need your Score - is also a smart choice. Since ...”

“The original total cost of the 10 pieces of fruit = 10*56 = 560. According to the answers, after 1, 2, 3, 4, or 5 oranges are removed -- so that 9, 8, 7, 6, or 5 pieces of fruit remain -- the average cost per piece decreases to 52. Since the original total cost is a multiple of 10, and the price ...”

“It turns out that the cost per apple is irrelevant. Here''s why: The average (arithmetic mean) price of the 10 pieces of fruit is 56 cents So, (total value of all 10 pieces of fruit)/10 = 56 cents This means, total value of all 10 pieces of fruit = 560 cents How many oranges must Mary put ...”

“Take the task of arranging the 10 books and break it into stages. Stage 1: Arrange the 4 books about Abe Lincoln in a row We can arrange n objects in n! ways. So, we can arrange the 4 books in 4! ways IMPORTANT: Now we''ll "glue" the 4 Abe Lincoln books together to form 1 SUPER ...”

“An alternative approach is to test the answer choices First, however, we can eliminate some answer choices by first testing an easy value: 50% Is 25 50% greater than 15? Well, 50% of 15 = 7.5 So, 50% greater than 15 = 15 + 7.5 = 22.5 22.5 is too small (we need to get 25), so we need a ...”

“Hi All, We''re told that the price of a phone call consists of a standard connection fee, which is constant, plus a per minute charge, a 10-minute call costs $2.90 and a 16-minute call costs $4.40. We''re asked for the cost of a 13-minute call. This question can be solved in a couple of ...”

“Hi All, This question can be solved by TESTing VALUES (and taking a few notes). 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. The common denominator ...”

“Let x = the product of the two denominators in the prompt = 3*4 = 12. Since 1/3 won a medal for swimming, the number who won a medal for swimming = (1/3)(12) = 4. Since 1/4 of the medal winners for swimming also won a medal for diving, the number who won both a medal for swimming and a medal for ...”

“Let C = price of connection fee Let M = the price PER MINUTE A 10-minute call costs $2.90 We can write: C + 10M = 2.90 A 16-minute call costs $4.40. We can write: C + 16M = 4.40 How much does a 13-minute call cost? So far, we have: C + 10M = 2.90 C + 16M = 4.40 ONE (slower) ...”

“Let $100 = share price at the beginning of the year At the end of the first quarter, the share price of a certain mutual fund was 20 percent higher than it was at the beginning of the year. So, $120 = share price at the end of the first quarter At the end of the second quarter, the share ...”

“Data Sufficiency Video #1: Introduction to GMAT Data Sufficiency Video: https://www.youtube.com/watch?v=3MaEqnSnK-s Cheers, Brent”

“Look for a pattern 17^1 = 17 17^2 = (17)(17) = ---9 17^3 = (17)(17^2) = (17)(---9) = ----3 17^4 = (17)(17^3) = (17)(---3) = ----1 17^5 = (17)(17^4) = (17)(---1) = ----7 NOTICE that we''re back to where we started. 17^5 has units digit 7, and 17^1 has units digit 7 So, at this point, ...”

“√3 ≈ 1.7. 7 + 4√3 ≈ 7 + (4)(1.7) = 13.8. 7 - 4√3 ≈ 7 - (4)(1.7) = 0.2. Thus, the given expression can be approximated as follows: (√13.8 + √0.2)² = a little more than 13.8. Only D is viable. The correct answer is D.”

“Offhand, I cannot cite an official SC that violates the rule discussed above.”

“Hi All, This question is essentially about arithmetic and taking the proper notes. You can go about the math steps in a couple of different ways though - depending on how you ''see'' this information. From the prompt, we know that the farmer spent $35 on feed.... 40% of his money on chicken ...”

“Hi All, "Range" questions come from the broader category of statistics, which will show up a couple of times on the GMAT. The range of a group of numbers is the difference between the largest number and the smallest number. Based on the original number of shares, the range would ...”

“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 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 ...”

“Given two sides of a triangle, the greatest possible area will be achieved if the two sides form a RIGHT ANGLE and serve as the triangle''s base and height. For the problem above, I posted an illustrated solution here: ...”

“One approach is to assign a NICE NUMBER to the volume of the swimming pool. This number will work well with the two pieces of information (fill pool in 9 hours and fill pool in 5 hours). So, let''s say that the volume of the pool is 45 gallons. The water from one outlet, flowing at a constant ...”

“Target question: Is x > y? This is a good candidate for rephrasing the target question. Since y is POSITIVE, we can safely take the inequality x > y and divide both sides by y to get: x/y > 1 REPHRASED target question: Is x/y > 1? Aside: Here’s a video with tips on rephrasing ...”

“P(dog selects matching pair) = P(dog chooses ANY sock 1st AND 2nd sock matches the 1st sock) = P(dog chooses ANY sock 1st) x P(2nd sock matches the 1st sock) = 24/24 x 1/23 = 1/23 Answer: C Cheers, Brent”

“Original range = (greatest number of shares) - (smallest number of shares) = 112-45 = 67. After 24 shares of Y are purchased, new Y = 94+24 = 118. After 20 shares of X are sold, new X = 56-20 = 36. New range = (new greatest number of shares) - (new smallest number of shares) = 118-36 = 82. ...”

“When the SAME DISTANCE is traveled at two different speeds, the average speed for the entire trip will be CLOSER TO THE LOWER SPEED than to the higher speed. The reason: The portion traveled at the lower speed takes LONGER. Since more time is spent at the lower speed than at the higher speed, the ...”

“Average speed = (TOTAL distance)/TOTAL travel time)Carlos drove to work at an average speed of 50 miles per hour Time = distance/speed So, travel time TO work = d/50 hours Carlos drove home from work at an average speed of 70 miles per hour So, travel time FROM work = d/70 hours So, TOTAL ...”

“He spent 40% (of the $35) on chicken feed. 40% of $35 = $14. So, he spent $14 on chicken feed. He got a 20% discount on the chicken feed. In other words, he paid 80% of the original price. So, let C = original price of chicken feed. We can write 80% of C = $14 Or we can write 0.8C = $14 ...”

“On Monday, the opening price of a certain stock was $100 per share and its closing price was $110 per share. On Tuesday the closing price of the stock was 10 percent less than its closing price on Monday, We can say that the stock LOST 10% of its value. OR we can say that the stock RETAINED 90% ...”

“Hi All, This question can be solved by TESTing THE ANSWERS. This is essentially a rate question, but the rate (and the time spent at that rate) changes depending on what time Rachel begins typing. Based on the information in the prompt, we know that if Rachel begins typing at 3pm, then she ...”

“Hi All, We''re told that in the first round of the elections, the only two candidates got exactly the SAME number of votes and during the second round, 15,000 votes switched from the first candidate to the second one. We''re also told that the total number of votes remained the same in both ...”

“Statement 1: The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively. Since 2+3+4 = 9, the total number of pens + pencils + pads must be a multiple of 9. No way to determine the exact number of staff members. INSUFFICIENT. Statement 2: ...”

“Jay''s solution is great. I just wanted to mention that this question hinges largely on the fact that the number of pens, pencils, and pads that each staff member receives MUST HAVE INTEGER VALUES. So, for example, if statement 1 were different and statement 2 read "The manager ...”

“The profit in 1982 = 15.6 - 12.0 = $3.6 million The profit in 1983 = 18.8 - 14.0 = $4.8 million Percent change = (100)(new - old)/old = (100)(4.8 - 3.6)/3.6 = (100)(1.2)/(3.6) = (100)(1/3) = 33 1/3% Answer: D Cheers, Brent”

“Another approach is to test the answer choices A. If the units digit of x is 1, is it the case that units digits of both (x+2)² and (x-2)² is 9? Well, (x+2)² = (1+2)² = 9. Works! To test (x-2)², let''s let x = 11. We get: (11-2)² = 9² = 81. NO GOOD ELIMINATE A B. If the units digit ...”

“Both of the following are viable: Vehicles powered by natural gas emit less of certain pollutants than those burning gasoline or diesel fuel. Vehicles powered by ndatural gas emit less of certain pollutants than do those burning gasoline or diesel fuel. The inclusion of do is optional. With or ...”

“What is the value of n-m? (m,0) and (n,0) are the two points where y=0 and the graph intersects the x-axis. Thus, m and n are the x-intercepts of the graph. Since m < n, n-m > 0. Question rephrased: What is the positive difference between the x-intercepts? Statement 1: 4b = a²-4 Test ...”

“3|x| < 4-x Case 1: Signs unchanged 3x < -x 4x < 4 x < 1 Case 2: Signs changed in the absolute value 3(-x) < 4-x -2x < 4 x > -2 Question stem, rephrased: If x is an integer such that -2 < x < 1, what is the value of x? Statement 1: x < 0 Here, x must ...”

“Hi All, We''re asked for the value of 25*8÷50÷2. This question involves rules called "Order of Operations", but as long as you know those rules, the work here isn''t too difficult. In Order of Operations, both multiplication and division are on the same ''level'' (meaning that you ...”

“Hi Linda, Training to score at a high level on the GMAT often requires more than just ''weekend study'', so if you can put in a little study time during the week (even if it''s just an hour a day), then that would likely help you a great deal. As it stands, with a 580, you''re actually closer to ...”

“Hi All, We''re told that the main ingredient in a certain prescription drug capsule cost $500 per kilogram. If each capsule contains 600 milligrams of ingredient, what is the cost of the ingredient in a capsule? (1 kilogram = 10^6 milligrams). This is a ''unit conversion'' question and comes ...”

“I''d typically assign a "nice" value to the original price, and then follow the steps that Mitch demonstrated. Alternatively, we can solve the question algebraically In 1991, the price of a house was 80% of its original price. Let x = the original price So, 0.8x = the 1991 price ...”

“Target question: What is ∠ABC? Given: Triangle ABC is an isosceles triangle So, ∆ABC has 2 equal angles Statement 1: ∠CAB = 45 degrees Since ∆ABC has 2 equal angles, there are two possible triangles that satisfy statement 1: Case a: ∠CAB = 45, ∠BCA = 45 and ∠ABC = 90. ...”

“To generalize Mitch''s and Fabio''s solutions, notice that, as long as we can get f(1) involved in the process, we''ll arrive at answer choice C every time. Notice that k = 1*k Since f(a*b) = f(a) + f(b), we can write: f(1*k) = f(1) + f(k) Simplify: f(k) = f(1) + f(k) Subtract f(k) from both ...”

“Let the original price = 100. 1991 price = 80% of 100 = 80. 1992 price = 60% of 100 = 60. Percent decrease from 80 to 60 = (Difference/Larger) * 100 = (20/80) * 100 = 25. The correct answer is B.”

“Each capsule contains 600 milligrams of ingredient. 10⁶ milligrams = 1 kilogram. 1 kilogram of ingredient = 500 dollars. To determine the cost per capsule, we must use the relationships above to convert 600 milligrams into dollars: (600 milligrams) * (1 kilogram)/(10⁶ milligrams) * ...”

“percent may serve as a NOUN. Of the students in the class, eighty percent passed the test. Here, eighty percent is a NOUN serving as the subject of passed. twice is a MODIFIER. It cannot serve as the subject of a sentence. Of the students in the class, twice passed the test. The sentence ...”

“Let a=1 and b=2. Plugging a=1 and b=2 into f(ab) = f(a) + f(b), we get: f(1*2) = f(1) + f(2) f(2) = f(1) + f(2) 0 = f(1). The correct answer is C.”

“Hi VJesus12, We''re told that after her birthday, Fiona had D dollars in gift money. She spent 3/5 of this on an electric skateboard, then she spent 1/3 of what WAS LEFT on a movie passcard, and then finally put the last $80 in the bank. Assuming she made no other purchases with that money, ...”

“Hi VJesus12, This question can be solved with a bit of general graphing (you do not need to be hyper-accurate with your drawing to get the correct answer). To start, we''re told that in the coordinate geometry plane, Point A is the midpoint between points (5,8) and (-3, -2). Draw those two ...”

“Hi VJesus12, We''re told that in the figure above, an EQUILATERAL triangle is inscribed in a circle and the arc bounded by adjacent corners of the triangle is between 4π and 6π long. We''re asked which of the following COULD be the diameter of the circle. As scary as this question might look, ...”

“Another approach is to use algebra. After her birthday, Fiona had D dollars in gift money. She spent 3/5 of this on an electric skateboard. If Fiona SPENT 3/5 of D dollars, then 2/5 of D dollars REMAINED In other words, the amount remaining at the end of the day = 2D/5 dollars The next day, ...”

“One option is to WORK BACKWARDS The next day, she spent 1/3 of what was left on a movie passcard, and then finally put the last $80 in the bank. If she spent 1/3 of her money on a movie passcard, then 2/3 of her money remained (which she put in the bank). This means 2/3 of her money = $80 We ...”

“ Given: A retailer sells only radios and clocks, and she currently has 44 total items in inventory. Target question: How many radios are there in the inventory Statement 1: The retailer has more than 28 radios in inventory There are several scenarios that satisfy statement 1. Here are ...”

“The error is highlighted above in blue. if a>0 we will have the answer as YES is ALMOST true. The only time it''s not true is when a = 1 If a = 1, then the answer is NO. We can verify this using either the original inequality or the rephrased inequality. Take "Is a + 1/a > ...”

“Consider the following equation: 5x + 7y = 70. If x and y are nonnegative integers, the following solutions are possible: x=0, y=10 x=7, y=5 x=14, y=0. Notice the following: The value of x changes in increments of 7 (the coefficient for y). The value of y changes in increments of 5 (the ...”

“The ratio of milk and water in a mixture is 2:1, Let milk = 2 liters and water = 1 liter. Some quantity of water is added to the mixture to make the ratio of milk and water in the new mixture 1:2. Since the resulting amount of water must be double the original 2 liters of milk, the resulting ...”

“Given the answer choices, the prompt should read as follows: A''s rate = (1 barrel)/(2 minutes) * (60 minutes)/(1 hour) = 30 barrels per hour. B''s rate = (1 barrel)/(3 minutes) * (60 minutes)/(1 hour) = 20 barrels per hour. C''s rate = (1 barrel)/(15 minutes) * (60 minutes)/(1 hour) = 15 ...”

“|a-b| = the distance between a and b |a+b| = |a-(-b)| = the distance between a and -b y = |2 + x| - |2 – x| y = |x+2| - |x-2| y = |x-(-2)| - |x-2| y = the subtraction of two distances: (distance between x and -2) - (distance between x and 2) On the number line: ...”

“Let the 7 cars be A, B, C, D, P, Q and S. Since P and Q must occupy adjacent positions, consider PQ a single element in the arrangement. The number of ways to arrange the 6 elements A, B, C, D, PQ and S = 6! = 720. In 1/2 of these arrangements, S will be to the LEFT of PQ. In the ...”

“This question illustrates a common trap on the GMAT. As Jay has shown, with statement 2, we''re able to write the equation 23x + 11y = 170 , and in high school we learned that, if we''re given 1 equation with 2 variables, we cannot find the value of either variable. However, if we restrict the ...”

“This Date Sufficiency question is almost identical to the following Problem Solving question, which requires us to find the actual area: http://www.beatthegmat.com/plz-explain-t270003.html Cheers, Brent”

“Let''s draw a rectangle around the triangle (as shown below) and then subtract from the rectangle''s area (28) the areas of the 3 right triangles that surround the triangle in question. We get the following: http://s13.postimage.org/a47qx0j8j/triangle_in_coordinate_plane_2.jpg So, the area ...”

“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 ...”

“Let $100 be the original price The price of a consumer good increased by p% during 2012 p% = p/100, so a p% INCREASE is the same a multiplying the original price by 1 + p/100 So, the new price = ($100)(1 + p/100) The price then decreased by 12% during 2013 A 12% DECREASE is the same a ...”

“The number of students who attend a school could be divided among 10, 12, or 16 buses, such that each bus transports an equal number of students. This tells us that the TOTAL number of students is a multiple of 10, 12 and 16 What is the minimum number of students that could attend the school? ...”

“Target question: What is the value of y - x? Given: Set K consists of a finite number of consecutive odd integers Statement 1: The average (arithmetic mean) of set K is –36 There''s a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the ...”

“Since the answer choices are so spread out, we can be quite aggressive with out estimation. First, 10⁸ - 10² can be rounded to 10⁸ Is this reasonable? Well, 10⁸ equals 100,000,000, so subtracting 10² (aka 100) from 100,000,000 still leaves us with approximately 100,000,000 ...”

“D: (a-0.9)(a-0.9) = (a-0.9)². The square of a value cannot be negative. The correct answer is D.”

“Statement 1: Case 1: N = 4000 nails per hour, M = 2000 nails per hour Since N''s rate = 4000 nails per hour, the time for N to produce 8000 nails = 8000/4000 = 2 hours. Since M''s rate = 2000 nails per hour, the time for M to produce 6000 nails = 6000/2000 = 3 hours. In this case, M works longer ...”

“Target question: What is the value of P(white or even)? To solve this, we need P(A or B) = P(A) + P(B) - P(A & B) So, P(white or even) = P(white) + P(even) - P(white & even) Statement 1: P(white & even) = 0 We can add this to our probability equation to get: P(white or even) = ...”

“Let: W = the total number of white marbles. E = the total number of even marbles. WE = the total number of white even marbles. Statement 1: Thus, WE = 0. No way to determine the value of W or E. INSUFFICIENT. Statement 2: Implication: W-E = (0.2)(25) = 5. Case 1: W=10, E=5, WE=0 ...”

“Statement 2: Brittany always leaves the hotel at exactly 5.30pm. To see the situation more clearly, plug in a value for the distance between the hotel and the office. Let the distance = 6 miles. Since Allison takes 1 hour -- from 5 to 6pm -- to travel the entire distance, Alison''s rate = d/t = ...”

“Target question: Did the profit exceed $4 million on sales of 380,000 units? Given: The profit from the sale of a certain appliance increases, though not proportionally, with the number of units sold. IMPORTANT: This means that we CANNOT make any "good" assumptions about the ...”

“Hi jain2016, Since we have the probabilities of each person winning a game, we can ''map out'' the 3 situations in which 2 of them win and 1 of them loses: A wins, B wins, C loses = (1/5)(3/8)(5/7) = 15/240 A wins, B loses, C wins = (1/5)(5/8)(2/7) = 10/240 A loses, B wins, C wins = ...”

“Hi All, We''re told that Y = 2 + 2K and Y ≠ 0. We''re asked for the value of 1/Y + 1/Y + 1/Y + 1/Y. This question can be solved in a number of different ways, including by TESTing VALUES. Since we''re adding four fractions with the SAME denominator, we can just use some basic Arithmetic and ...”

“Let k=0, implying that y = 2 + 2*0 = 2. Plugging y=2 into 1/y + 1/y + 1/y + 1/y, we get: 1/2 + 1/2 + 1/2 + 1/2 = 2. The correct answer must yield a value of 2 when k=0. Only B works: 2/(1+k) = 2/(1+0) = 2. The correct answer is B.”

“Given: y = 2 + 2k Rewrite as: y/1 = (2 + 2k)/1 Flip both fractions to get: 1/y = 1/(2 + 2k) So, 1/y + 1/y + 1/y + 1/y = 1/(2 + 2k) + 1/(2 + 2k) + 1/(2 + 2k) + 1/(2 + 2k) = 4/(2 + 2k) = 4/(2)(1 + k) = 2/(1 + k) Answer: B Cheers, Brent”

“Target question: Is x/y < 0? Statement 1: (x^4)(y^5) < 0 There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 1 and y = -1. Notice that (x^4)(y^5) = (1^4)(-1^5) = (1)(-1) = -1, which is less than 0. In this case, x/y = 1/(-1) = -1. So, the answer to ...”

“In my previous response, I provided links to three official examples. This construction seems viable.”

“It is possible for back-to-back modifiers joined solely by a comma to have the same referent. Three examples: http://www.beatthegmat.com/the-hognose-snake-puts-on-an-impressive-bluff-t93558.html http://www.beatthegmat.com/parallelism-issue-t96011.html ...”

“The usage of the term arrangements is misleading. The prompt seems intended to ask the following: The first player selected can be paired with any of the 5 other players. Thus, the number of options for the first player selected = 5. At this point, 4 players remain. The next player ...”

“GIVEN: √(4 + 1/n) = 5√(5/n) Square both sides to get: (5)(5)√(5/n)√(5/n) Simplify right side again: 4 + 1/n = 25(5/n) Simplify right side: 4 + 1/n = 125/n Multiply both sides by n to get: 4n + 1 = 125 Subtract 1 from both sides to get: 4n = 124 Solve: n = 124/4 =31 Answer: A ...”

“I thought I''d point out that Jay''s approach is also 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 construction worker, and the two ...”

“Target question: How many of the numbers are less than 35? Given: The average of four numbers is 35 All this tells us is that the SUM of the 4 numbers is 140 (since 140/4 = 35) Given the limited amount of information, it''s likely that the correct answer is C or E Statement 1: None of ...”

“The determine the percent decrease, we need to know the RATIO between the remaining amount of sugar after cookie-making and the original amount of sugar. Statement 1: Case 1: Remaining sugar after cookie-making = 10 pounds Since the remaimning amount of sugar would need to increase by 30% to ...”

“Question stem, rephrased: Do x and y have different signs? Statement 1: |x+y| < |x|+|y| Since an absolute value cannot be negative, both sides here are NONNEGATIVE, enabling us to safely square the inequality: (|x+y|)²< (|x|+|y|)² x² + y² + 2xy < x² + y² + 2|x||y| xy < ...”

“Sum of the 4 numbers = (quantity)(average) = 4*35 = 140. Statement 1: None of the numbers are exactly 3 To save time, check whether it''s possible to get different answers to the question stem while also satisfying Statement 2. Case 1: 0, 33, 33, 74 --> sum = 0+33+33+74 = 140 In this ...”

“Statement 1: The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend. Case 1: Distance between Townsend and Smallville = 80 miles Time to travel from Townsend to Smallville at a speed of 40 mph = 80/40 = 2 hours. Time to travel from Smallville to Townsend = ...”

“Let x = the number of 100-point labs and y = the number of 85-point labs. Question stem, rephrased: What is the value of x? Statement 1: 100x + 85y = 1140 20x + 17y = 228 The value in blue implies the following: Since 20x will have a units digit of 0, 17y must have a UNITS DIGIT OF 8. ...”

“Alternate approach: Since an absolute value cannot be negative -- implying that the right side of the equation must be NONNEGATIVE -- we know that x≥0. If x²-6=x, we get: x²-x-6=0 (x-3)(x+2) = 0 Only the factor in green implies a nonnegative option for x: x-3=0 x=3. The correct ...”

“A quick approach is to simply test the answer choices A) -2 No good. The absolute value of something cannot be negative B) 0 Plug in to get |0² - 6| = 0. Doesn''t work. C) 1 Plug in to get |1² - 6| = 1. Doesn''t work. D) 3 Plug in to get |3² - 6| = 3. WORKS!!! Answer: D Cheers, ...”

“ Given: m and n are positive integers such that m > n Target question: What is the remainder when m² – n² is divided by 21? Statement 1: The remainder when (m + n) is divided by 21 is 1 There are several values of m and n that satisfy statement 1. Here are two: Case a: m = 12 and ...”

“Target question: What is the value of (ax + ay)/(x + y)? This is a good candidate for rephrasing the target question. Take the expression: (ax + ay)/(x + y) Factor the numerator to get: a(x + y)/(x + y) Simplify the fraction to get: a Since (ax + ay)/(x + y) = a, we can rephrase the target ...”

“Target question: Can n be expressed as the difference of 2 prime numbers? Statement 1: (n-17)(n-21) = 0 This tells us that EITHER n = 17 OR n = 21 IMPORTANT: Upon seeing that n can equal one of two values, some students will incorrectly conclude that statement 1 is not sufficient. However, ...”

“The usage of number implies that we should consider NON-INTEGER values. Both statements are satisfied by z=18.1 and z=19.1 Since the units digit of z can be different values, the two statements combinecd are INSUFFICIENT. The correct answer is E.”

“In order to minimize the number of homeowners, we must MAXIMIZE the number of men in the group, since the proportion of male homeowners (20%) is less than the proportion of female homeowners (25%) So, let''s see what happens if there are 199 men and 1 woman. If 20% (aka 1/5) of the men are ...”

“Hi All, Since the answers to the question are all numbers, we can use the answers ''against'' the prompt and TEST THE ANSWERS. Here''s how… Let''s start with Answer B. Answer B: 36 boards IF the number of boards was 36, then the 20th board from the top would be the 17th board from ...”

“Hi All, We''re told that in a 200 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. We''re asked for the LEAST number of members who are homeowners. This question is built around a couple of Number Properties - and to MINIMIZE the number of ...”

“Hi All, We''re told that a department store receives a shipment of 1,000 shirts, for which it pays $9,000. The store sells the shirts at a price 80 percent above cost for one month, after which it reduces the price of the shirts to 20 percent above cost. The store sells 75 percent of the shirts ...”

“Target question: What is the value of the integer n? Statement 1: n is a prime factor of 21 21 = (3)(7) So, EITHER n = 3 OR n = 7 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: n is a factor of 49 49 has three positive factors: 1, ...”

“This question becomes a lot easier if we recognize that (2x + y)² = 4x² + 4xy + y² (which is VERY similar to 4x² - 4xy + y²) Here''s what I mean: Take 2x + y = 3 and square both sides to get: (2x + y)² = 3² Simplify both sides to get: 4x² + 4xy + y²= 9 We now have two (quite ...”

“√(a²) = |a|. Question stem, rephrased: Is |x+1| = x+1? The answer will be YES if x+1 is NONNEGATIVE: x+1≥0 x≥-1. Question stem, rephrased again: Is x≥-1? Statement 1: x=0 or x=2. Since x≥-1 in both cases, the answer to the question stem is YES. SUFFICIENT. Statement 2: ...”

“Let x=2 and apply the function three times: f(2) = 1 - 1/2 = 1/2. f(1/2) = 1 - 1/(1/2) = -1. f(-1) = 1 - (1/-1) = 2. The correct answer must yield a value of 2 when x=2. Only A works. The correct answer is A.”

“Any BAG taken on the subway IS subject to search by the police. Any BAGS taken on the subway ARE subject to search by the police. In each of these sentences, any is a MODIFIER describing the subject in blue. In the first sentence, the verb (is) is SINGULAR to match the singular subject in blue. ...”

“Statement 1: No information about Charlie or Daryl. INSUFFICIENT. Statement 2: For every 2 home run hits made by Charlie and Daryl combined, Brady made 4 home run hits, implying that Brady made 4 of every 6 home run hits: 4/6 = 2/3. SUFFICIENT. The correct answer is B.”

“IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . . DIFFERENCE between A and B < length of third side < SUM of A and B Let''s focus on this part: length of third side < SUM of A and B We can also say that the length of LONGEST side must be less than the SUM of ...”

“ Given: Brady, Charlie, and Daryl play on the same baseball team. Target question: The number of home runs hit by Brady in a particular season is what fraction of the total home runs hit by the three players in that season? This is a good candidate for rephrasing the target question. Let ...”

“Target question: What is the 1st term in sequence S ? Statement 1: The 3rd term in S is 2 Since we''re not given any information about the NATURE of the sequence, there''s no way to answer the target question with certainty. So, statement 1 is NOT SUFFICIENT Statement 2: The 2nd term in ...”

“Here''s our video on Weighted Averages video: https://www.youtube.com/watch?v=B7J6lr_qBG4 Cheers, Brent”

“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 ...”

“Target question: Marcia''s bucket can hold a maximum of how many liters of water? In other words, what is the TOTAL CAPACITY of Marcia''s bucket? Statement 1: The bucket currently contains 9 liters of water. Not enough info to determine the TOTAL CAPACITY of Marcia''s bucket. Since we ...”

“Let''s start from the bottom and work our way up: We''ll start with the 16th board counting from the bottom of the stack Right BELOW that 16th board, we have a board that we''ll call Larry. So, Larry is the 15th board counting from the bottom of the stack. So, starting from the bottom and ...”

“We can PLUG IN THE ANSWERS, which represent B''s speed. When the correct answer is plugged in, B''s time - A''s time = 3 hours. For each team: Time = distance/speed = 300/speed. B: B''s speed = 15 mph, implying that A''s speed = 15+5 = 20 mph In this case, B''s time - A''s time = 300/15 - ...”

“1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 = 16 20 = 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 In the rendering above: The red values represent the number of boards when counting from the TOP. The blue values represent the number of boards when counting from the ...”

“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, ...”

“I thought I''d point out that Manasa3190''s approach is 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 people, and the two characteristics are: ...”

“Hi All, We''re told that it takes Jacob X hours to complete a project and it takes Mike Y hours to complete the same project. We''re asked for the number of hours it would take them to complete the project if they worked together. This is a great ''concept'' question; if you recognize the ...”

“Hi All, We''re told that the employees of Smith Enterprises received wage increases ranging from 30 cents to 87.5 cents per hour. We''re asked for the MAXIMUM wage increase for a 40-hour week. This question comes down to some basic arithmetic (but you might find it faster to do your math in a ...”

“Hi All, We''re told that of the paintings that a certain artist created last year, the number of paintings that were UNFRAMED was 5 times the number of paintings that were FRAMED and 48 percent of the UNFRAMED paintings and 30 percent of the FRAMED paintings were SOLD. We''re asked for the ...”

“Hi All, We''re told that BEFORE expansion, a zoo had 343 birds in 7 cages and AFTER the expansion was complete, there were 719 birds in 11 cages. We''re asked for the approximate percent increase in the average number of birds per cage. This question is based around a couple of standard math ...”

“Hi All, We''re told that Scott takes a trip and drives 6 hours from Town X to Town Z at a rate of 50 miles per hour. On his way back, Scott drives 75 miles per hour and stops in Town Y which is MIDWAY between Town X and Town Z. We''re asked for the number of HOURS Scott takes to drive from Town ...”

“Hi All, The information in the prompt include a variety of nice ''round'' numbers, so it''s likely that the number of calculators in the shipment is also a round number AND divides evenly into 300. Only two of the answers ''fit'' that idea - 25 and 30, so let''s TEST THE ANSWERS and see if ...”

“IMPORTANT: Let''s use HOURS throughout our solution, and then convert hours to minutes at the end. When car Y had traveled for z HOURS, car Y had traveled 23 miles more that car X had from the time that car X left Town T. z = car Y''s travel time in HOURS So, z + 3/10 = car X''s travel time in ...”

“Statement 1: To MINIMIZE the number of coins so that a sum of 170 cents is yielded by at most 8 coins, we must MAXIMIZE the number of quarters. Since 7*25 = 175 cents, the number of quarters must be less than 7. 170 cents will be yielded by 6 quarters (totaling 150 cents) and 2 dimes (totaling 20 ...”

“Hi All, We''re told that Fred has a jarful of nickels, dimes, and quarters, in the ratio of 2:5:10, respectively and the total value of these coins is $15.50. We''re asked for the number of DIMES in Fred’s jar. This question is based on ratio rules - and ratios are all about multiples - so you ...”

“Hi All, We''re asked for the mathematical equivalent of the following formula: $$R=\frac{\frac{24F}{N}}{P+\frac{A}{12}}$$ While the prompt (and the answers) might look ''complex'', the work involved is based on a simple math premise (common denominators), so as long as you are thorough ...”

“Hi All, We''re asked for the largest value of N for which 10^N is a factor of 50! This question comes down to ''prime factorization'' and requires a degree of thoroughness on your part (to make sure that you find all of the 10s in 50!) To start, 50! = (50)(49)(48)(47)(46)(45).....(3)(2)(1), ...”

“Hi All, We''re told that a retailer sells pashminas at a ten percent discount, a pashmina COST him $75 and he wants to make a profit of no less than twenty percent on the COST (after the discount). We''re asked for the minimum tag price he needs to put on a pashmina. To start, this question ...”

“Hi Linda, Many Test Takers spend 3 months (or more) of consistent study time before they hit their ''peak'' scores, so you shouldn''t feel too down about this performance if you studied for just 6 weeks (and primarily just on the weekends). Thankfully, the GMAT is a consistent, predictable Exam, ...”

“Let the tank = 36 gallons. Since the first pipe takes 3 hours to fill 1/2 the tank -- and (1/2)(36) = 18 gallons -- the rate for the first pipe = w/t =18/3 = 6 gallons per hour. Since the second pipe takes 6 hours to fill 2/3 of the tank -- and (2/3)(36) = 24 gallons -- the rate for the second ...”

“Since the desired salt percentage -- 50% -- is HALFWAY between the salt percentages for A and B (20% and 80%), the resulting solution must contain equal amounts of A and B. The correct answer is C.”

“What is the value of T-C? Statement 1: T:B = 4:5. To combine T:B = 4:5 and C:B = 5:8, the element common to both ratios -- B -- must be represented by the SAME VALUE in each: T:B = 4:5 = 32:40. C:B = 5:8 = 25:40. Combining the two ratios, we get: C:T:B = 25:32:40. Case 1: T=32 and C=25, ...”

“Hi All, When it comes to maximizing or minimizing a value in a group of numbers, you have to think about what the other numbers would need to be to accomplish your goal. Here, we have a group of 15 DISTINCT (meaning DIFFERENT) integers with a median of 25 and a RANGE of 25. That range will ...”

“Hi All, We''re told that a certain punch contains grape juice, orange juice, and pineapple juice and no other ingredients in a ratio of 2:3:7 respectively and a bowl contains 156 total ounces of this punch. We''re asked for the number of ounces of grape juice in the punch. This question can be ...”

“Let D = DVD owners, C = cellphone owners, and M = MP3 owners. T = D + C + M - (DC + DM + CM) - 2(DCM). The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS. When we add together everyone in D, everyone in C, and everyone in M: Those in exactly 2 of the groups (DC + DM + ...”

“The sum of the parts of the ratio = 2+3+7 = 12. Thus -- of every 12 ounces -- 2 ounces are grape juice, 3 ounces are orange juice, and 7 ounces are pineapple juice. Since grape juice constitutes 2 of every 12 ounces, the amount of grape juice is equal to 2/12 of the total: (2/12)(156) = 2*13 = ...”

“Strategy: Try to show that four of the answer choices do NOT have to be positive. Case 1: x=1 and y=1 In this case, A, B and D are not positive. Eliminate A, B and D. Case 2: x=1 and y=2 In this case, C is not positive. Eliminate C. The correct answer is E.”

“Statement 1: Since the numbers are EVENLY SPACED, median = sum/count: 64/4 = 16. Since the median = 16, the 4 odd integers must be as follows: 13, 15, 17, 19. Thus, the greatest of the 4 odd integers = 19. SUFFICENT. Statement 2: The 4 odd integers yielded by Statement 1 -- 13, 15, 17, 19 ...”

“Every test-taker should know the following quadratic identities: (x+y)² = x² + y² + 2xy (x-y)² = x² + y² - 2xy (x+y)(x-y)² = x² - y² Substituting x²+y²=28 and xy=11 into (x+y)² = x² + y² + 2xy, we get: (x+y)² = 28 + 2*11 = 50. The correct answer is C. An alternate ...”

“P(2 different languages) = 1 - P(2 of the same language). Case 1: P(2 English books are selected) P(1st book is English) = 5/10. (Of the 10 books, 5 are English.) P(2nd book is English) = 4/9. (Of the 9 remaining books, 4 are English.) To combine these probabilities, we multiply: 5/10 * 4/9 = ...”

“Hi All, We''re told that the SUM of the weekly salaries of 5 employees is $3,250 and that each of the 5 salaries is to increase by 10 percent. We''re asked for the AVERAGE increase in weekly salary per employee. This question ultimately comes down to working through some arithmetic, but ...”

“Hi LDCross, For free math practice and help, I recommend that you set up an account at Khan Academy (www.khanacademy.org). The site is completely free and makes the learning a bit more fun and ''game-like'' (as opposed to the dry academic approach taken by most books). While the site is vast, ...”

“Total amount of feed = (number of chickens)(number of days). The number of chickens is INVERSELY PROPORTIONAL to the number of days. If the number of chickens DOUBLES, then the feed will last for 1/2 the number of days. If the number of chickens TRIPLES, then the feed will last for 1/3 the ...”

“Take the task of shipping the 4 boxes and break it into stages. Let''s call the 4 boxes A, B, C and D Stage 1: Select a truck to ship box A in There are 4 trucks from which to choose, so we can complete stage 1 in 4 ways Stage 2: Select a truck to ship box B in There are 4 trucks ...”

“ Given: A quorum of at least half the 20 directors must pass the resolution by at least a two-thirds majority Target question: At a meeting of the board of directors, did resolution X pass or fail?  Statement 1: Ten directors voted for the resolution.  KEY: We don''t know how many ...”

“Hi All, We''re told that a plane traveled K miles in its first 96 minutes of flight time and it completed the remaining 300 miles of the trip in T minutes. We''re asked for the average speed of the plane, in miles per hour, for the entire trip. This question can be solved by TESTing VALUES. ...”

“ Given: Every student at the Performing Arts Academy must take at least one of the two drama courses offered, Classical Theater or Improvisation. 15% of the students who take Classical Theater also take Improvisation Let''s use the Every student at the Performing Arts Academy must take at least ...”

“ Given: At a certain department store present-wrapping counter, each clerk will wrap no fewer than twenty and no more than thirty presents per hour. Target question: If seventy people are standing in line, will all of their presents be wrapped after one hour? Statement 1: Each person in ...”

“9am-10am: Since Harry reaches checkpoint P at 9am -- and travels at rate of 30 mph -- from 9am to 10am Harry travels 30 miles beyond checkpoint P. Thus, when Ron reaches checkpoint P at 10am, he is 30 miles behind Harry. Checkpoint Q: When people compete, SUBTRACT THEIR RATES. Every hour Ron ...”

“Hi All, While an Algebra approach (using the "weighted average" formula) would work nicely on this prompt, you can also answer it rather quickly by TESTing THE ANSWERS and using a bit of logic. Here, we''re going to mix 400 ounces of a 6% acid solution with X ounces of a 12% acid ...”

“Let y = the height of the shorter tree The taller tree is x times the height of the shorter tree. Ho So, yx = the height of the taller tree The two trees have a combined height of 60 feet We can write: y + yx = 60 How tall is the shorter tree, in terms of x? We must solve the equation ...”

“Hi All, This is an example of a Work Formula question. Any time you have two entities (people, machines, water pumps, etc.) working on a job together, you can use the following formula: (AB)/(A+B) = Total time to do the job together Here, we''re told that the total time = 4 hours and ...”

“Hi All, We''re told that two trees have a combined height of 60 feet and the taller tree is X times the height of the shorter tree. We''re asked to find the height of the shorter tree in terms of X. This question can be approached in a couple of different ways, including by TESTing VALUES. IF ...”

“Let''s pick some nice numbers that adhere to the given information. ...the constant rate of one pump was 1.5 times the constant rate of the other So, the fast pump has a pumping rate that''s 1.5 faster then the slow pump. So, let''s say the SLOW pump pumps at 2 gallons per hour This means ...”

“ Given: There are two types of rolls on a counter, plain rolls and seeded rolls. Let P = # of plain rolls Let S = # of seeded rolls Target question: What is the value of P + S? Statement 1: The ratio of the number of seeded rolls on the counter to the number of plain rolls on the ...”

“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 J = the number of hours that John works. Since John assembles 3 chairs per hour, the number of chairs assembled by John = 3J. Let L = the number of hours that Larry works. Since Larry assembles 4 chairs per hour, the number of chairs assembled by Larry = 4L. Since John and Larry work a total ...”

“Number of options for Phoebe = 1. (Must be Margherita.) Number of options for Ross = 3. (Of the 4 remaining pizzas, any but Hawaiian.) Number of options for Chandler = 3. (Any of the 3 remaining pizzas.) Number of options for Joey = 2. (Either of the 2 remaining pizzas.) Number of options for ...”

“Target question: Does this month have 30 or 31 days? IMPORTANT: Notice that the question does not ask "How many days are in this month?" If that were the case, then we''d have to consider February. Instead, the question is ruling out February by basically telling us that the month in ...”

“One approach is to count all possible arrangements (that may or may not break the given rule) and then subtract all outcomes the break the rule. Here''s another approach. Take the task of arranging the 5 letters and break it into stages. Stage 1: Arrange the 3 CONSONANTS (D, G and T) in a ...”

“Target question: Is x² > y²? Statement 2: x > y There are several values of x and y that satisfy statement 2. Here are two: Case a: x = 2 and y = 1. In this case, x² = 4 and y² = 1. So, the answer to the target question is YES, x² IS greater than y² Case b: x = -2 and y = -3. ...”

“Hi All, We''re told that a certain company charges $6 per package to ship packages weighing less than 2 pounds each. However, for a package weighing 2 pounds or more, the company charges an initial fee of $6 plus $2 per pound. We''re told that a certain package cost $38 to ship. We''re asked for ...”

“Hi All, Each of the other explanations explains the ''math'' behind this prompt, so I won''t rehash any of that here. Instead, I want to talk about the ''patterns'' behind this question, and how you can answer it without doing much math at all. To start, we have to sort through a lot of ...”

“Hi All, This question can be solved by TESTing VALUES. I''m going to use the variable "J" instead of an "I" (since that might be mistaken for the number 1)... We''re told to add "2% of one''s income" to "the average of 100 and 1% of one''s income" ...”

“Hi All, We''re told that a two-bedroom apartment costs 50% more to rent than a one-bedroom apartment. If Alex were to rent a two-bedroom apartment for X months it would cost him the same amount as it would to rent a one-bedroom for 12 months. We''re asked for the value of X. This question can be ...”

“Hi LDCross, This 610 is a strong initial CAT Score (the average Score on the Official GMAT hovers around 550 most years) - and your Verbal Scaled Score is fantastic. As such, you might just need to put the proper focus/effort into building up your Quant knowledge and learning/practicing the ...”

“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 ...”

“P(both dice will come up with either a 1 or a 2) = P(1st die is 1 or 2 AND 2nd die is 1 or 2) = P(1st die is 1 or 2) x P(2nd die is 1 or 2) = 2/6 x 2/6 = 1/3 x 1/3 = 1/9 Answer: C Cheers, Brent”

“A fast and easy approach is to assign a "nice" value to the monthly rent of a ONE-bedroom apartment. Let''s say the rent on a ONE-bedroom apartment is $100 per month A two-bedroom apartment costs 50% more to rent than a one-bedroom apartment 50% of $100 = $50 So, the rent on a ...”

“Target question: What is the value of x? Given: If the remainder when positive integer x is divided by 7 is 4 When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For ...”

“Let the monthly rent for a one-bedroom apartment = $2, implying that the monthly rent for a two-bedroom apartment = 2 + (50% of 2) = 2 + 1 = $3. Since the monthly rent for a one-bedroom apartment = $2, the total amount required to rent a one-bedroom apartment for 12 months = 2*12 = 24. If Alex ...”

“Let''s assign a nice value to the share value in the 1st quarter. Let''s say the share value in the 1st quarter = $100 The value of a share was 25% less in the 2nd quarter over the 1st quarter . . . So, the share value in the 2nd quarter = $100 - (25% of $100) = $100 - $25 = $75 . . . ...”

“Target question: How much money could be saved by purchasing 10 bagels at the sale price rather than at the usual price? Statement 1: The usual price for a bagel is $0.50 per bagel. Since there''s no information about the SALE price, there''s no way to calculate the amount saved. Since we ...”

“The CRITICAL POINTS are where the expressions inside the absolute values are equal to 0. x+5 = 0 when x=-5. Substituting x=-5 into y = |x+5|-|x-5|, we get: y = |-5+5| - |-5-5| = 0-10 = -10. x-5 = 0 when x=5. Substituting x=5 into y = |x+5|-|x-5|, we get: y = |5+5| - |5-5| = 10-0 = ...”

“One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. Since replacing 1 man with 2 girls does not change the amount of time required to complete the job, 1 man is the equivalent of 2 ...”

“One approach is to determine the size of the job One woman and one man can build a wall together in two hours, but the woman would need the help of two girls in order to complete the same job in the same amount of time. The part in blue tells us that 2 girls have the same output as 1 man. ...”

“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 Target question: Is x > 0 ? Statement 1: |x+3| < ...”

“Target question: What is the y-intercept of line L? IMPORTANT: When I scan the two statements, I see that they are strongly related. If the x-intercept is -1/3 (as per statement 2), the slope of the line is GUARANTEED to be 3 times its y-intercept (as per statement 1). Here''s why... ...”