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Math Revolution GMAT Instructor
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Re: Math Revolution Approach (DS) [#permalink]
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06 Feb 2018, 23:45
[GMAT math practice question] What is the value of (x+3y)/(3xy)? 1) x2y = 1 2) x2y = 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. When the question asks for a ratio, a fraction, a percent, a proportion or a rate, if one of conditions provides a ratio and the other condition provides a number, the condition with a ratio could be sufficient. This question asks for a ratio. Condition 1) provides a number and condition 2) provides the ratio, x/y = 2. Thus, condition 2) is likely to be sufficient. Condition 1) : If x = 3 and y = 1, then (x+3y)/(3xy) = 6/8 = 3/4 If x = 5 and y = 2, then (x+3y)/(3xy) = 16/13 Since we do not obtain a unique answer, condition 1) is not sufficient. Condition 2) : Since x = 2y, (x+3y)/(3xy) = 5y/5y = 1. Condition 2) is sufficient. Therefore, B is the answer. Answer: B
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Math Revolution GMAT Instructor
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Re: Math Revolution Approach (DS) [#permalink]
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08 Feb 2018, 00:10
[GMAT math practice question] If n is a positive integer, is 91 a factor of n? 1) 91 is a factor of n^2 2) 91 is a factor of 2n => 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 (n) 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) Since 91 = 7*13, n^2 is a multiple of both 7 and 13. Since 7 and 13 are prime numbers, n must be a multiple of both 7 and 13. Condition 1) is sufficient. Condition 2) If 91 is a factor of 2n, then 91k = 2n for some integer k. Since 91 is odd, k must be an even integer. Write k = 2a, for some integer a. Then 2n = 91*2a. It follows that n = 91*a. Thus, n is a multiple of 91. Condition 2) is sufficient. This is a CMT(Common Mistake Type) 4(B) question. Condition 2) is easy to understand and condition 1) is difficult to figure out. If you are unable to figure out condition 2), you should choose D as the answer. Therefore, the answer is D. 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. Answer: D
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Math Revolution GMAT Instructor
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Re: Math Revolution Approach (DS) [#permalink]
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09 Feb 2018, 00:40
[GMAT math practice question] If x and y are integers, is 4x^2y2 an odd number? 1) x is an odd number 2) y is an odd number => 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, and then recheck the question. Modifying the question: In order for 4x^2 – y^2 to be odd, y^2 must be odd since 4x^2 is always even. This is equivalent to y being odd. So, the question asks if y is odd. Thus, the answer is B. Condition 1) If y is an odd number, then both 2x + y and 2x – y are odd numbers and (2x+y)(2xy) is an odd number. If y is an even number, both 2x + y and 2x – y are even numbers and (2x+y)(2xy) is an even number. Since the question does not have a unique answer, condition 1) is not sufficient. Therefore, the answer is B. Answer: B
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Re: Math Revolution Approach (DS) [#permalink]
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11 Feb 2018, 16:55
[GMAT math practice question] If x and y are integers, is x^2+11x+13y an even number? 1) x=11 2) y=13 => 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, and then recheck the question. Now, x^2+11x+13y = x(x+11)+13y. As x(x+11) is always an even integer (one of x and x + 11 must be even), x^2+11x+13y is even precisely when 13y is even. This is equivalent to y being even, so the question can be restated as ‘Is y an even number?’. Condition 1) If x = 11 and y = 1, then x^2+11x+13y = 255 is an odd integer. If x = 11 and y = 2, then x^2+11x+13y = 268 is an even integer. Since the question does not have a unique answer, condition 1) is not sufficient. Condition 2) If y = 13, then y is odd, and the answer to the question is ‘no’. Condition 2) is sufficient. Therefore, B is the answer. Answer: B
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Math Revolution GMAT Instructor
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GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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11 Feb 2018, 16:57
[GMAT math practice question] If x, y and z are positive numbers, is xy+z > x+yz? 1) x>1 2) y>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. Since we have 3 variables (x and y) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. Conditions 1) & 2): xy + z > x + yz ⇔ xy – x – yz + z > 0 ⇔ x(y1)z(y1) > 0 ⇔ (xz)(y1) > 0 ⇔ x – z > 0 since y > 1. If x = 2, y = 2, and z = 1, then xy + z = 5, x + yz = 4 and xy + z > x + yz. So, the answer is ‘yes’. If x = 2, y = 2, and z = 3, then xy + z = 7, x + yz = 8 and xy + z < x + yz. So, the answer is ‘no’. Since the question does not have a unique answer, both conditions together are not sufficient. Therefore, E is the answer. 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. Answer: E
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Math Revolution GMAT Instructor
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Re: Math Revolution Approach (DS) [#permalink]
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14 Feb 2018, 00:21
[GMAT math practice question] Is xy<15? 1) x<3 2) y<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. 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. Conditions 1) & 2): Since x < 3 and y < 5, we have xy > 15, and the answer is ‘no’. Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, both conditions are sufficient, when used together. Since this is an inequality question (one of the key question areas), we should also consider choices A and B by CMT(Common Mistake Type) 4(A). Condition 1) This condition provides us with no information about the variable y, so it is not sufficient: If x = 4 and y = 1, then xy = 4 < 15, and the answer is ‘yes’. If x = 4 and y = 5, then xy = 20 > 15, and the answer is ‘no’. Since we do not obtain a unique answer, this condition is not sufficient. Condition 2) This condition provides us with no information about the variable x, so it is not sufficient: If x = 1 and y = 5, then xy = 5 < 15, and the answer is ‘yes’. If x = 4 and y = 5, then xy = 20 > 15, and the answer is ‘no’. Since we do not obtain a unique answer, this condition 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: Math Revolution Approach (DS) [#permalink]
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15 Feb 2018, 03:39
[GMAT math practice question] Events E and F are independent. Is the probability that both events E and F will occur less than 0.6? 1) The probability that event E will occur is 0.4. 2) The probability that event F will occur is 0.5. => 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question. The definition of independent events E and F is P(E∩F) = P(E)P(F). The question asks if P(E)P(F) < 0.5. Since we have 2 variables (P(E) and P(F)) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. Conditions 1) & 2): P(E ∩F) = P(E)P(F) = 0.4 * 0.5 = 0.2 < 0.6. Thus, both conditions together are sufficient. Since this is a probability question (one of the key question areas), we should also consider choices A and B by CMT(Common Mistake Type) 4(A). Condition 1): Since P(E) = 0.4 and P(F) ≤ 1, P(E ∩F) = P(E)P(F) ≤ 0.4 * 1 = 0.4 < 0.6. Condition 1) is sufficient on its own. Condition 2): Since P(E) ≤ 1 and P(F) = 0.5, P(E ∩F) = P(E)P(F) ≤ 1 * 0.5 = 0.5 < 0.6. Condition 2) is sufficient on its own. Therefore, the answer is D. Answer: D 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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Math Revolution GMAT Instructor
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Re: Math Revolution Approach (DS) [#permalink]
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16 Feb 2018, 04:04
[GMAT math practice question] If the average (arithmetic mean) of set A is 100 and the average (arithmetic mean) of set B is 100, what is the range of sets A and B combined? 1) The range of set A is 20. 2) The range of set B is 30. => 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. There is no relationship between the average of a set and its range. In addition, there is no way of determining the range of a set from the ranges of its subsets. Notice that “E” is in “no rElation”. Many questions about “relation” have the answer E. Thus, E is likely to be the answer. We can verify this by considering both conditions together: If A = { 90, 110 } and B = { 85, 115 }, then the range of A∪B={85,90,110,115} is 30. If A = { 90, 110 } and B = { 92, 93, 95, 98, 122 }, then the range of A∪B={ 90, 92, 93, 95, 98, 110, 122 } is 32. Since the range of A∪B is not uniquely determined, both conditions together are not sufficient. Therefore, the answer is E. Answer: E
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Re: Math Revolution Approach (DS) [#permalink]
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18 Feb 2018, 18:20
[GMAT math practice question] What is the value of the positive integer k? 1) When k is divided by 3, the remainder is 2. 2) When k is divided by 5, the remainder is 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. Since we have 1 variable (k) 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): Two possible values of k which satisfy condition 1) are 5 and 8. Since it does not give us a unique value of k, condition 1) is not sufficient. Condition 2): Two possible values of k which satisfy condition 2) are 1 and 6. Since it does not give us a unique value of k, condition 2) is not sufficient. Conditions 1) & 2): Two possible values of k which satisfy both conditions 1) & 2) are 11 and 26. Since they do not give us a unique value of k, conditions 1) & 2) together are not sufficient. Therefore, E is the answer. Answer: E
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Re: Math Revolution Approach (DS) [#permalink]
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18 Feb 2018, 18:21
[GMAT math practice question] Is n an even number? 1) n(n+1) is an even number 2) n(n+2) is an even number => 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 (n) 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): All integers satisfy condition 1) since n(n+1) is the product of two consecutive integers: If n = 1, n(n+1) = 1*2 = 2 is an even number, but n is odd, so the answer is ‘no’. If n = 2, n(n+2) = 2*3 = 6 is an even number and n is even, so the answer is ‘yes’. Since we do not have a unique answer, condition 1) is not sufficient. Condition 2) The product of two integers can only be even if at least one of them is even. Since n and n+2 must both be even, or both be odd, n must be even. Thus, 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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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Re: Math Revolution Approach (DS) [#permalink]
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21 Feb 2018, 00:03
[GMAT math practice question] The lengths of two sides of a certain triangle are 3 and 9. What is the length of the 3rd side of the triangle? 1) The perimeter of the triangle is 20 2) The length of the 3rd side of the triangle is a multiple of 4 => 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, and then recheck the question. Assume x is the length of the 3rd side of the triangle. 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. Note: Since (using the triangle inequality) x > 9 + 3 = 12 and x < 9 – 3 = 6, we have 6 < x < 12. Condition 1) x + 3 + 9 = 20 Thus x = 8. Condition 1) is sufficient. Condition 2) The only integer between 6 and 12 that is a multiple of 4 is 8. Thus, x = 8. Condition 2) is sufficient, too. In addition, since conditions 1) and 2) are similar, D is most likely to be the answer. Therefore, D is the answer. Answer: D 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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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Re: Math Revolution Approach (DS) [#permalink]
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22 Feb 2018, 01:08
[GMAT math practice question] If uv<0, is u^99v^100<0? 1) u<0 2) v>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, and then recheck the question. In an inequality that has the righthand side equal to 0, even exponents can be ignored. Asking if u^99v1^00<0 is equivalent to asking if u < 0: simply divide both sides by u^98v^100 (> 0). We only need to consider the variables with odd exponents. Since the exponent of u is 99, which is an odd number, we must have u < 0. In addition, since uv < 0 by the original condition, u < 0 implies that v > 0. Thus, condition 1) is equivalent to condition 2), and D is most likely to be the answer by Tip 1). Therefore, the answer is D. Answer: D 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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