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Math Revolution GMAT Instructor
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Re: Math Revolution Approach (DS) [#permalink]
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07 Mar 2018, 03:37
[GMAT math practice question] Is x^y <0? 1) x is positive 2) y is a prime 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. We then recheck the question. Question: x^y <0 ⇔ x < 0 and y is an odd integer. Condition 1) Since x > 0, x^y > 0, regardless of the value of y. Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient. Condition 2) If x = 1 and y = 3, x^y = (1)^3 = 1 < 0, and the answer is ‘yes’. If x = 1 and y = 2, x^y = (1)^2 = 1 > 0, and the answer is ‘no’. Condition 2) is not sufficient since the question does not have a unique answer. Therefore, A is the answer. Answer: A 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
Joined: 16 Aug 2015
Posts: 5034
GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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08 Mar 2018, 02:23
[GMAT math practice question] Is x/y^3>0? 1) xy>0 2) xy>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. The question can be modified as follows: x/y^3>0 ⇔ xy>0. This can be seen by multiplying both sides by y^4. It is same as condition 2). Condition 1) If x = 2 and y = 1, xy = 2 > 0, and the answer is ‘yes’. If x = 2 and y = 1, xy = 2 < 0, and the answer is ‘no’. Since we don’t have a unique answer, condition 1) is not sufficient. Therefore, the answer is B. 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.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5034
GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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09 Mar 2018, 00:20
[GMAT math practice question] If x and y are integers, is x a multiple of 5? 1) x+y is a multiple of 5 2) x+2y is a multiple of 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. After comparing the number of variables with the number of equations, we can save time by considering conditions 1) & 2) together first. Conditions 1) & 2): x = 2(x+y) – (x+2y) is a multiple of 5 since 2(x+y) and (x+2y) are multiples of 5. Thus, both conditions 1) & 2) 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 = 5 and y = 5, x is a multiple of 5, and the answer is ‘yes’. If x = 2 and y = 3, x is not a multiple of 5, and the answer is ‘no’. Thus condition 1) is not sufficient. Condition 2) If x = 5 and y = 5, x is a multiple of 5, and the answer is ‘yes’. If x = 1 and y = 2, x is not a multiple of 5, and the answer is ‘no’. Thus condition 2) is not sufficient. Therefore, the answer is C. 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.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5034
GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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11 Mar 2018, 18:29
[GMAT math practice question] Is at least one of 3 consecutive integers a multiple of 5? 1) The sum of the integers is divisible by 5 2) The product of the integers is divisible by 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. Write the 3 consecutive integers as n1, n, n+1. 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 ( n – 1 ) + n + ( n + 1 ) = 3n is divisible by 5, and 3 and 5 are prime numbers, n is a multiple of 5, since 3 is not divisible by 5. Condition 1) is sufficient. Condition 2) Since (n1)n(n+1) is divisible by 5 and 5 is a prime number, one of n1, n and n+1 is a multiple of 5. Condition 2) is sufficient. 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.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5034
GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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11 Mar 2018, 18:31
[GMAT math practice question] If x=yz, is x>y? 1) y<0 2) z<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. We can modify the question as follows: x>y ⇔ xy > 0 ⇔ z > 0 by the original condition ⇔ z < 0 This is the same as condition 2). Condition 1) If x = 1, y = 2, and z = 1, x > y, and the answer is ‘yes’. If x = 2, y = 1, and z = 1, x < y, and the answer is ‘no’. Condition 1) is not sufficient since the question does not have a unique answer. Therefore, B is the answer. Answer: B
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5034
GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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14 Mar 2018, 00:22
[GMAT math practice question] If x + y > 0, is xy^2 + x^2y > 0? 1) x > y 2) xy > 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. Question: xy^2 + x^2y > 0 => xy(x+y) > 0 => xy > 0, since x + y > 0 So, the question asks if xy > 0. Since xy > 1 > 0 can be derived from condition 2), it is sufficient. Condition 1) gives us no information about the sign of xy. Therefore, B is the answer. Answer: B
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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5034
GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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15 Mar 2018, 02:21
[GMAT math practice question] Is (x1)^3< (x1)? 1) x>1 2) x<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. The question can be modified as follows: (x1)^3< (x1) => (x1)^3 (x1) < 0 => (x1)((x1)^2 1) < 0 => (x1)((x1)+1)((x1)1) < 0 => x(x1)(x2) < 0 => x < 0 or 1 < x < 2 So, the question asks whether x < 0 or 1 < x < 2. Condition 1) Since the set of the question doesn’t include that of condition 1), it is not sufficient. Condition 2) Since the set of the question includes that of condition 2), it is sufficient. Therefore, the answer is B. Answer: B
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5034
GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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16 Mar 2018, 00:51
[GMAT math practice question] What is the median value of the data displayed in the following frequency table? Attachment:
a.png [ 2.35 KiB  Viewed 11 times ]
1) x=2 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. If y = 1, the median is x. If y = 2, the median is ( x + 3 ) / 2 If 3 ≤ y ≤ 9, the median is 3. If y = 10, the median is ( 3 + 4 ) / 2 = 3.5 If y ≥ 10, the median is 4. Thus, the condition 2) is sufficient. Therefore, the answer is B. Answer: B
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"




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