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Math Revolution GMAT Instructor
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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13 Sep 2019, 08:22
[GMAT math practice question] (number properties) N is a 2digit number. When N is divided by 2, the remainder is 1, when it is divided by 3 the remainder is 2, and when it is divided by 5 the remainder is 4. What is the sum of all possible values of N? A. 155 B. 166 C. 177 D. 188 E. 200 => Using the quotientremainder theorem, we may write n as 2a + 1, 3b + 2, and 5c + 4, where a, b and c are nonnegative integers. The possible values of 2a + 1 are 1, 3, 5, … . The possible values of 3b + 2 are 2, 5, 8, 11, … The possible values of 5c + 4 are 4, 9, 14, 19, 24, 29, … Since the first common value from these lists is 29 and the least common multiple of 2, 3 and 5 is 30, N is an integer of the form 30k + 29. The possible values of N with 2 digits are 29, 59 and 89. Thus, the sum of all possible values of N is 29 + 59 + 89 = 177. Therefore, C is the answer. Answer: C
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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15 Sep 2019, 19:13
[GMAT math practice question] (number properties) Let aob denote the greatest common divisor of a and b, and let a□b denote the least common multiple of a and b. What is (xoy)□(x□y)? 1) (63o99)x=540 2) 3y(18□45)=0 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2) The following reasoning shows that condition 1) implies that x = 60: (63o99)x=540 => (9*7o9*11)x=540 => 9x=540 => x=60 The following reasoning shows that condition 2) implies that y = 60: 3y(18□45)=0 => 3y(9*2□9*5)=0 => 3y9*2*5=0 => 3y90=0 => y30=0 => y=30 Thus, we may calculate (xoy)□(x□y) = (60o30)□(60□30) = 30□60=60 Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B. However, each of the conditions only gives us information about one of the variables, so neither is sufficient on its own. Therefore, C is the answer. Answer: C Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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16 Sep 2019, 18:15
[GMAT math practice question] (absolute values) What is the value of 2xy? 1) 3x2y+4 + x+2y2=0 2) x and y are rational numbers => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. Condition 1) is equivalent to two equations: 3x2y+4=0 and –x+2y2 = 0. When we solve this system of occasions, we obtain x = 1 and y = 1/2. Thus, condition 1) is sufficient on its own. Note the VA tells us this will be the case. The question has two variables, but condition 1) provides 2 equations. Condition 2) is clearly not sufficient on its own. Therefore, the answer is A. Answer: A
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19 Sep 2019, 18:04
[GMAT math practice question] (algebra) Using the formula a^2–b^2 =(a+b)(ab), find the value of (1+ 1/2 )(1+ 1/4)(1+1/16). A. 255/128 B. 255/256 C. 257/128 D. 127/128 E. 555/128 => Let X = (1+1/2)(1+1/4)(1+1/16). Then (11/2)X = (11/2)(1+1/2)(1+1/4)(1+1/16) =(11/4)(1+1/4)(1+1/16) =(11/16)(1+1/16) =11/256 =255/256. So, (1/2)X = 255/256, and X = 255/128 Therefore, A is the answer. Answer: A
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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22 Sep 2019, 18:59
[GMAT math practice question] (algebra) <x,y> denotes x + y/2. What is the value of x? 1) <x,y> = y + x/2 2) <2x,2y>+1=<y,x>  2 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. When we simply condition 2), we have <2x, 2y>+1=<y, x>2 => 2x + 2y/2 + 1 = y + x/2  2 => 2x + y + 1 = y + x/2 – 2 => (3/2)x = 3 => x = 2. Condition 2) is sufficient. Condition 1) Since we have <x,y> = y + x/2 = x + y/2, we have y/2 = x/2 or x = y. Condition 1) is not sufficient, since it does not yield a unique solution. Therefore, B is the answer. Answer: B
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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23 Sep 2019, 18:16
[GMAT math practice question] (ratio) There is a% of saline solution of 500g. Alice wants to have b% of saline solution by boiling saline solution where b > a. What is the lost weight of the saline solution by boiling? 1) a = 20 2) a/b = 2/5 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. Let x be the lost weight of b% saline solution by boiling. The question asks the value of x such that (a/100)500 = (b/100)(500x). (a/100)500 = (b/100)(500x) => 500a = b(500x) => 500a = 500b – bx => bx = 500(ba) => x = 500(ba)/b => x = (500)(1a/b) Thus, condition 2) is sufficient. When a question asks for a ratio, if one condition includes a ratio and the other condition just gives a number, the condition including the ratio is most likely to be sufficient. This tells us that B is most likely to be the answer to this question. Condition 1) is not sufficient obviously, since we don’t have any information about the variable a. Therefore, B is the answer. Answer: B
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25 Sep 2019, 18:25
[GMAT math practice question] (number Properties) A composite number n can be represented as a product of two different primes a and b (n=ab). If 100<nab<200, what is nab? A. 4 B. 5 C. 6 D. 7 E. 8 => Since we have n = ab, we have nab = n^2 and 100<n^2<200. Perfect squares between 100 and 200 are 11^2 = 121, 12^2 = 144, 13^2 = 169 and 14^2 = 196. n = 14 is the only one among those numbers, 11, 12, 13 and 14 which is a product of two different prime integers. Thus we have a=2, b=7 or a=7, b=2. Thus n – a – b = n – ( a + b ) = 14 – (2 + 7) = 14 – 9 = 5. Therefore, B is the answer. Answer: B
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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29 Sep 2019, 18:44
[GMAT math practice question] (number properties) What is the value of p*q? 1) p and q are prime numbers 2) qp=3 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. Since we have 2 variables (p and q) and 0 equations, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2) Since p and q are prime numbers and q – p = 3 which is an odd number, p and q have different parities. It means that either p or q is an even prime number. Then we have p = 2, since 2 is the smallest and unique even prime number. So q = 5. Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B. Condition 1) Since there many possibilities for (p, q), the condition is obviously not sufficient. Condition 2) If p = 2 and q = 5, then we have p*q = 10. If p = 1 and q = 4, then we have p*q = 4. Since condition 2) does not yield a unique solution, it is not sufficient. Therefore, C is the answer. Answer: C Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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01 Oct 2019, 18:36
[GMAT math practice question] (algebra) If 2x=3y(xy≠0), what is (5x^2+xy)/(3x^2 4xy)? A. 14 B. 16 C. 17 D. 19 E. 21 => Since 2x=3y, we have y = (2/3)x. (5x^2+xy)/(3x^2 4xy) = (5x^2+x*(2/3)x)/(3x^2 4x*(2/3)x) = (5x^2+(2/3)x^2)/(3x^2 4(2/3)x^2) = ((17/3)x^2)/((1/3)x^2) = 17. We can also substitute x = 3 and y = 2 for a shortcut and get 17. Therefore, C is the answer. Answer: C
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04 Oct 2019, 00:45
[GMAT math practice question] (number properties) For a positive integer n, P(n) is denoted as the product of each digit of n. For example, P(29)=2*9=18, P(457)=4*5*7=140. a, b and c are 2digit positive integers with P(a)P(b)P(c)=9. What is the maximum value of a+b+c? A. 91 B. 102 C. 113 D. 124 E. 135 => In order to have a maximum value of P(a)P(b)P(c), the possible cases of tuples (a,b,c) we should consider are (91,11,11) and (31,31,11). For (91,11,11), we have 91 + 11 + 11 = 113. For (31,31,11), we have 31 + 31 + 11 = 73. Thus, the maximum of a + b + c is 113. Therefore, C is the answer. Answer: C
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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06 Oct 2019, 19:26
[GMAT math practice question] (algebra) abc ≠ 0. What is the value of a(1/b + 1/c) +b(1/c + 1/a) + c(1/a + 1/b)? 1) a+b+c≤0 2) a+b+c = 0 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. So, we will first simply the original condition as follows: a(1/b + 1/c) +b(1/c + 1/a) + c(1/a + 1/b) = a/b + a/c + b/c + b/a + c/a + c/b = (b+c)/a + (a+c)/b + (a+b)/c = (a+b+ca)/a + (a+b+cb)/b + (a+b+cc)/c = (a+b+c)/a – a/a + (a+b+c)/b – b/b + (a+b+c)/c – c/c = (a+b+c)[(1/a)+(1/b)+(1/c)] – 3 If a+b+c= 0, then we have (a+b+c)[(1/a)+(1/b)+(1/c)] – 3 = 3. Condition 1) a+b+c≤0 means a+b+c=0 since a+b+c≥0 So, we have a(1/b + 1/c) +b(1/c + 1/a) + c(1/a + 1/b) = 3. Since condition 1) yields a unique solution, it is sufficient. Condition 2) Since we have a+b+c=0, we have a(1/b + 1/c) +b(1/c + 1/a) + c(1/a + 1/b) = 3. Since condition 2) yields a unique solution, it is also sufficient. Therefore, D is the answer. Answer: D Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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09 Oct 2019, 18:34
[GMAT math practice question] (number properties) f(x) denotes the maximum prime factor of x, where x is a positive integer. For example, f(30)=f(2*3*5)=5. What is the value of f(abc)? 1) f(a) = 2 2) f(b)+f(c)=14 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. Since we have 3 variables and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2) If a = 2, b = 7 and c = 7, then f(abc) = f(2*7^2) = 7. If a = 2, b = 3 and c = 11, then f(abc) = f(2*3*11) = 11. Both conditions together do not yield a unique solution, so they are not sufficient. Therefore, E is the answer. Answer: E In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions when the answer is A, B, C, or D.
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10 Oct 2019, 18:25
[GMAT math practice question] (arithmetic) What is the value of 1/(5*6) + 2/(6*8) + 3/(8*11) + 4/(11*15)? A. 1/10 B. 3/10 C. 3/14 D. 2/15 E. 3/16 => Remember the following properties. 1/n(n+1) = 1/n – 1/(n+1). 2/n(n+2) = 1/n – 1/(n+2). 3/n(n+3) = 1/n – 1/(n+3). 4/n(n+4) = 1/n – 1/(n+4). … Then we have 1/(5*6) + 2/(6*8) + 3/(8*11) + 4/(11*15) = (1/51/6)+(1/61/8)+(1/81/11)+(1/111/15) = 1/5 – 1/15 = 2/15 Therefore, D is the answer. Answer: D
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13 Oct 2019, 18:32
[GMAT math practice question] (function) f(x) is a function. What is the value of a? 1) f(a)+ 4f(1/a)=15a 2) f(a)=f(a) => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. Since we have many variables to determine a function and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2) When we substitute a by 1/a in condition 1), we have f(1/a) + 4f(a) = 15(1/a) or 4f(1/a)+16f(a) = 60(1/a). Then, since we have 4f(1/a) = 15a – f(a) from condition 1), we have 4f(1/a) + 16f(a) = (15a – f(a)) + 16f(a) = 15f(a) + 15a = 60/a or f(a) = a + 4/a. When we substitute a by –a, we have f(a) = a – 4/a and –a + 4/a = a – 4/a. Then, we have a = 4/a or a2 = 4 and we have solutions a = 2 or 2. Since both conditions do not yield a unique solution, they are not sufficient. Therefore, E is the answer. Answer: E In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions when the answer is A, B, C, or D.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT
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14 Oct 2019, 22:52
[GMAT math practice question] (geometry) AB is a straight line. What is the measure of the angle ∠AOD? 1) ∠EOB = (4/5)∠AOD 2) ∠DOE = ∠AOB/2 Attachment:
10.10.png [ 10.83 KiB  Viewed 18 times ]
=> Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. Assume <AOD = x, <DOE = y and <EOB = z. Then we have x + y + z = 180. Since we have 3 variables (x, y and z) and 1 equation (x + y + z = 180), C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2) We have z = (4/5)x from condition 1) and y = 90 from condition 2). Then we have x + z = 90 and x + (4/5)x = 90, or (9/5)x = 90. Then, x = 50. Therefore, C is the answer. Answer: C Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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