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Math Revolution GMAT Instructor
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10 Sep 2018, 18:39
[ Math Revolution GMAT math practice question] The numbers x, y and z are in the ratio 3 to 4 to 5. What is the value of x? 1) y = 16 2) The difference between y and z is 4 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method I s 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. The original condition gives the proportion x : y : z = 3 : 4 : 5, so we can write x = 3k, y = 4k and z = 5k. We have 4 variables and 3 equations. Therefore, D is most likely to be the answer. Condition 1) is sufficient since 16 = y = 4k, and so k = 4. Then x = 3k = 12. Condition 2) is also sufficient since 4 = z – y = 5k – 4k = k. So, x = 3k = 12. Tip 1) of VA method states that D is most likely to be the answer if conditions 1) and 2) give similar information. Therefore, D is the answer. Answer: D
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11 Sep 2018, 19:45
[ Math Revolution GMAT math practice question] What is the value of the 2digit positive integer n if its tens digit is four times its units digit? 1) n is an even number 2) The units digit of n is greater than 1 => 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. The only positive twodigit integers n satisfying the original condition are 82 and 41. Condition 1) is sufficient since 82 is the only one of these integers that is even. Condition 2) is also sufficient, since 82 the only one of these integers with a units digit that is greater than 1. Therefore, D is the answer. Answer: D
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12 Sep 2018, 18:06
[ Math Revolution GMAT math practice question] Which of the following lines is perpendicular to y=(1/2)x? A. y=2x B. y=x/2 C. y=2x D. y=x/2 E. y=x => Two lines are perpendicular if and only if the product of their slopes is 1. Since (1/2)*(2) = 1, the slope of the line perpendicular to y = (1/2)x is 2. The only answer choice with a slope of 2 is A. Therefore, A is the answer. Answer: A
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13 Sep 2018, 18:12
[ Math Revolution GMAT math practice question] If x and y are integers, what is the least possible positive value of 21x+35y? A. 1 B. 3 C. 5 D. 7 E. 9 => 21x + 35y = 7*3x + 7*5y = 7(3x+5y) is a multiple of 7. The smallest positive multiple of 7 is 7. So, we look for x and y such that 21x + 35y = 7. This will occur when 3x + 5y = 1. When x = 2 and y = 1, 3x + 5y = 3*2 + 5*(1) = 6 – 5 = 1, and 21x + 35y = 7(3x+5y) = 7(1) = 7. Thus, 7 is the answer. Therefore, the answer is D. Answer: D
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The Ultimate Q51 Guide [Expert Level]
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13 Sep 2018, 19:49
MathRevolution wrote: [ Math Revolution GMAT math practice question] If x and y are integers, what is the least possible positive value of 21x+35y? A. 1 B. 3 C. 5 D. 7 E. 9 => 21x + 35y = 7*3x + 7*5y = 7(3x+5y) is a multiple of 7. The smallest positive multiple of 7 is 7. So, we look for x and y such that 21x + 35y = 7. This will occur when 3x + 5y = 1. When x = 2 and y = 1, 3x + 5y = 3*2 + 5*(1) = 6 – 5 = 1, and 21x + 35y = 7(3x+5y) = 7(1) = 7. Thus, 7 is the answer. Therefore, the answer is D. Answer: D Hi MathRevolution, Given the answer choices, I understand how D would be the correct answer and chose the same but am trying to understand why aren't we considering the negative values or 0 in the question? The question doesn't ask for the least positive value.



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13 Sep 2018, 22:34
Shruti0805 wrote: MathRevolution wrote: [ Math Revolution GMAT math practice question] If x and y are integers, what is the least possible positive value of 21x+35y? A. 1 B. 3 C. 5 D. 7 E. 9 => 21x + 35y = 7*3x + 7*5y = 7(3x+5y) is a multiple of 7. The smallest positive multiple of 7 is 7. So, we look for x and y such that 21x + 35y = 7. This will occur when 3x + 5y = 1. When x = 2 and y = 1, 3x + 5y = 3*2 + 5*(1) = 6 – 5 = 1, and 21x + 35y = 7(3x+5y) = 7(1) = 7. Thus, 7 is the answer. Therefore, the answer is D. Answer: D Hi MathRevolution, Given the answer choices, I understand how D would be the correct answer and chose the same but am trying to understand why aren't we considering the negative values or 0 in the question? The question doesn't ask for the least positive value. The question asks: what is the least possible positive value. Thank you = Kudos
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16 Sep 2018, 18:36
[ Math Revolution GMAT math practice question] Is xy>0? 1) x^3y>0 2) x^2y>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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. Since even powers are always nonnegative, we can ignore the even exponents. Condition 1) x^3y > 0 is equivalent to xy > 0, which is the question itself. Therefore, condition 1) is sufficient. Condition 2) x^2y>0 is equivalent to y > 0. It is not sufficient Therefore, A is the answer. Answer: A
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17 Sep 2018, 18:24
[ Math Revolution GMAT math practice question] Does y=ax^2+bx+c intersect the xaxis? 1) a<0 2) 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. Since we are asked about a quadratic polynomial, the question asks if the discriminant b^24ac is positive. Neither condition 1) nor condition 2) on its own is sufficient to determine this. Considering both conditions 1) & 2) together yields b^24ac > 0 since b^2 ≥ 0 and ac < 0. Therefore, C is the answer. Answer: C
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[ Math Revolution GMAT math practice question] If n is an integer, is (n+1)^2 an even integer? 1) n1 is an even integer 2) (n1)^2 is an even integer => 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. (n+1)^2 is an even integer => n+1 is an even integer => n is an odd integer Condition 1) Since “n1 is an even integer” is equivalent to “n is an odd integer”, condition 1) is sufficient. Condition 2) “(n1)^2 is an even integer” is equivalent to “n1 is an even integer”, which is condition 1). Condition 2) 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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18 Sep 2018, 18:30
MathRevolution wrote: [ Math Revolution GMAT math practice question] If n is an integer, is (n+1)^2 an even integer? 1) n1 is an even integer 2) (n1)^2 is an even integer => 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. (n+1)^2 is an even integer => n+1 is an even integer => n is an odd integer Condition 1) Since “n1 is an even integer” is equivalent to “n is an odd integer”, condition 1) is sufficient. Condition 2) “(n1)^2 is an even integer” is equivalent to “n1 is an even integer”, which is condition 1). Condition 2) 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). What's the difficulty level of this question?
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19 Sep 2018, 18:52
[ Math Revolution GMAT math practice question] Is x<0? 1) x=x 2) x>x => 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. Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first. Condition 1) x = x => x ≤ 0 In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient. Since the solution set “x<0” of the question doesn’t include the solution set “x ≤ 0” of the condition 1), condition 1) is not sufficient. Condition 2) x>x => x < 0 Since condition 2) is equivalent to the question, condition 2) is sufficient. Therefore, B is the answer. Answer: B If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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19 Sep 2018, 20:57
MathRevolution wrote: [ Math Revolution GMAT math practice question] The numbers x, y and z are in the ratio 3 to 4 to 5. What is the value of x? 1) y = 16 2) The difference between y and z is 4 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method I s 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. The original condition gives the proportion x : y : z = 3 : 4 : 5, so we can write x = 3k, y = 4k and z = 5k. We have 4 variables and 3 equations. Therefore, D is most likely to be the answer. Condition 1) is sufficient since 16 = y = 4k, and so k = 4. Then x = 3k = 12. Condition 2) is also sufficient since 4 = z – y = 5k – 4k = k. So, x = 3k = 12. Tip 1) of VA method states that D is most likely to be the answer if conditions 1) and 2) give similar information. Therefore, D is the answer. Answer: D Is this really a tough question?? I don't think so.
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20 Sep 2018, 18:28
[ Math Revolution GMAT math practice question] If 5^{m2}2^{m+2} is an ndigit integer, where m is an integer greater than 2, what is the value of n, in terms of m? A. n=m4 B. n=m2 C. n=m1 D. n=m E. n=2m => 5^{m2}2^{m+2} = 5^{m2}2^{m2+4} = 5^{m2}2^{m2}*2^4 = (5*2)^{m2}*2^4= (10)^{m2}*2^4 = 16*(10)^{m2} = 16*(100…0)= 1600…0 with m2 0’s. 10^{m2} has m2 digits that are 0 and 16*(10)^{m2} has digits including 1, 6 and m2 digits that are 0. Thus, 16*(10)^{m2} has m – 2 + m = m digits. Therefore, D is the answer. Answer: D
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24 Sep 2018, 06:23
[ Math Revolution GMAT math practice question] 2^p/2^q=? 1) p = q + 2 2) pq=8 => 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. Modifying the question: What is the value of 2^p/2^q= 2^{pq}? So, we need to be able to find the value of pq. Thus, condition 1), which is equivalent to p – q = 2, is sufficient. Condition 2): If p =4 and q = 2, then 2^p/2^q= 2^{pq} = 2^2 = 4. If p =8 and q = 1, then 2^p/2^q= 2^{pq} = 2^7 = 128. Since we don’t have a unique solution, condition 2) is not sufficient. Therefore, A is the answer. Answer: A
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25 Sep 2018, 03:46
[ Math Revolution GMAT math practice question] If x, y, z are integers, is xyz a multiple of 6? 1) x+y+z is a multiple of 6 2) x, y, and z are consecutive integers => 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. Since we have 3 variables (x, y and z) 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) Since x and y are two consecutive integers, one of them, x or y is an even integer, and xy is a multiple of 2. Since x, y and z are three consecutive integers, one of them, x, y or z is a multiple of 3, and xyz is a multiple of 3. Therefore, xyz is a multiple of 6. Both conditions (together) are sufficient. 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. Condition 1) If x = 1, y = 2 and z = 3, then xyz = 6 is not a multiple of 6. If x = 2, y = 2 and z = 2, then xyz = 8 is a multiple of 8. Since we do not have a unique answer, condition 1) is not sufficient. Condition 2) Using the same argument as the one given for both conditions together, condition 2) is sufficient. Therefore, B is the answer. Answer: B 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 on which the answer is A, B, C or D.
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26 Sep 2018, 18:12
[ Math Revolution GMAT math practice question] What is the perimeter of a rectangle? 1) The square of the diagonal is 52. 2) The area of the rectangle is 24. => Forget conventional ways of solving math qAnswer: CAnswer: Cuestions. 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. When we apply VA method to geometry, we need to count the number of variables. For a rectangle, we have two variables for the length and the width of the rectangle. Let x and y be the length of the width of the rectangle, respectively. 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) We have x^2+y^2 = 52 by Pythagoras’ theorem, and Area = xy = 24. So, (x+y)^2 = x^2+2xy + y^2 = (x^2+y^2) +2xy = 52 + 48 = 100. Therefore, x+y = 10 and we can calculate the perimeter. Both conditions (together) are sufficient. Therefore, C is the answer. Answer: C
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27 Sep 2018, 18:47
[ Math Revolution GMAT math practice question] √32+3√2+5+√3+1√2=? A. 0 B. 2√2 C. 2√3 D. 9 E. 11 => A=A when A>0, 0=0, and A=A when A<0 Since √32 < 0, we have √32 = (√32). Since 3√2 > 0, we have 3√2 = 3√2. Since 5+√3 > 0, we have 5+√3 = 5+√3 Since 1√2 < 0, we have 1√2 = (1√2) So, √32+3√2+5+√3+1√2= (√32) +(3√2) + (5+√3) (1√2) = √3+2 + 3√2 + 5+√3 – 1 +√2 = 9. Therefore, the answer is D. Answer: D
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30 Sep 2018, 23:00
[ Math Revolution GMAT math practice question] For an integer n greater than 1, the set S n={ kn  k is an integer greater than or equal to 1} is defined. What is the value of n? 1) 2 is contained in the set S n. 2) 4 is contained in the set S n. => 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. Condition 1) Only S 2 = { 2, 4, 6, … } includes 2. Therefore, n = 2. Condition 1) is sufficient. Condition 2) Two sets, S 2 = { 2, 4, 6, … } S 4 = { 4, 8, 12, … } contain 4. So, n could be 2 or 4. Since we don’t have a unique solution, condition 2) is not sufficient. Therefore, A is the answer. Answer: A If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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01 Oct 2018, 18:00
[ Math Revolution GMAT math practice question] When f(x)=ax^2+bx+c (a≠0), is x+1 a factor of f(x)? 1) f(1)=0 2) f(1)=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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. x+1 is a factor of f(x) precisely when f(x) = (x+1)(ax+b) for some numbers a and b. This occurs when f(1) = 0, but not necessarily when f(1) = 0. Thus, only condition 2) is sufficient. Therefore, B is the answer. Answer: B If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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03 Oct 2018, 18:22
[ Math Revolution GMAT math practice question] What is the standard deviation of a, b and c? 1) a^2+b^2+c^2 = 77 2) a+b+c =15 => 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. The mean of a, b and c is m = ( a + b + c ) / 3. So, a + b + c = 3m. The variance of a, b and c, that is, the square of the standard deviation of a, b and c, is given by VAR = SD^2 = { ( a – m )^2 + ( b – m )^2 + ( c – m )^2 } / 3 = { a^2  2am + m^2 + b^2  2bm + b^2 + c^2  2cm + m^2 } / 3 = { a^2 + b^2 + c^2 – 2m(a+b+c) + 3m^2 } / 3 = { a^2 + b^2 + c^2 – 2m*3m + 3m^2 } / 3 = { a^2 + b^2 + c^2 – 3m^2 } / 3 = ( a^2 + b^2 + c^2 ) / 3 – m^2 = ( a^2 + b^2 + c^2 ) / 3 – { ( a + b + c ) / 3 }^2 This value can be calculated using the information given in conditions 1) and 2). Thus, both conditions together are sufficient. Therefore, C is the answer. Answer: C When we have a sum of data values and a sum of the squares of data values, we can always calculate the standard deviation.
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