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Math Revolution GMAT Instructor
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Re: Math Revolution Approach (DS) [#permalink]
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10 Jun 2018, 18:31
=> 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. For y=ax^2+bx+c to have an xintercept, we must have b^24ac ≥ 0. Thus, condition 1) gives the answer of ‘no’. Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient. Condition 2) If a = 1, b = 0, c = 0, we have y = x, which has an xintercept of zero, so the answer is ‘yes’. If a = 1, b = 0, c = 1, we have y = x^2 – 1, which has no xintercept. The answer is ‘no’ in this case. Since we don’t have a unique solution, condition 2) is not sufficient. Therefore, A is the answer. Answer: A
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5585
GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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10 Jun 2018, 18:33
=> 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 have xyzx=0 or x(yz1)=0 from the original condition, either x = 0 or yz = 1. Since yz = 0 by condition 1), we must have x = 0. Thus, condition 1) is sufficient. Condition 2) tells us that xy = 0. This implies that xyz = 0. Since xyz= x, we must have x = 0. Thus, condition 2) is also sufficient. Therefore, D is the answer. Answer: D
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5585
GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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13 Jun 2018, 02:55
[GMAT math practice question] Is x<y? 1) 3^x<2^y 2) x>0 and y>0 => 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): Since 3^x < 2^y and x, y are positive, we have 2^x < 3^x < 2^y or 2^x < 2^y. It follows that x < y. Both conditions together are sufficient. Since this question is an inequality 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 and y = 2, then the answer is “yes”. If x = 1 and y = 1, then the answer is “no”. Thus, condition 1) is not sufficient on its own since it does not give a unique solution. Condition 2) If x = 1 and y = 2, then the answer is “yes”. If x = 2 and y = 1, then the answer is “no” Thus, condition 2) is not sufficient on its own since it does not give a unique solution. 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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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5585
GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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14 Jun 2018, 02:44
[GMAT math practice question] Is x+x <2? 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 definition of the absolute value gives us two cases to consider when examining the question. Case 1: x ≥ 0 x + x < 2 => x + x < 2 => 2x < 2 => x < 1 The question asks if 0 ≤ x < 1 in this case. Case 2: x < 0 x + x < 2 => (x) + x < 2 => 0 < 2 As this is always true, the answer is always “yes” if x < 0. Combining these two cases shows that the question asks if x < 1. 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 Thus condition 1) is not sufficient, but condition 2) is sufficient since the solution set of the question includes the solution set of condition 2), but it doesn’t include that of condition 1). Therefore, B is the answer. Answer: B
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5585
GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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15 Jun 2018, 02:03
[GMAT math practice question] If n is a positive integer, is 3^4+3^{n+4} divisible by 5? 1) n is an even integer. 2) 3^8 +3^{n+8} 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. 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) If n = 2, then 3^4 + 3^{n+4} = 3^4 + 3^6 = 3^4(1+3^2) = 81*10 = 810, and the answer is “yes”. If n = 0, then 3^4 + 3^{n+4} = 3^4 + 3^4 = 3^4(1+1) = 81*2 = 162, and the answer is “no”. Condition 1) is not sufficient. Condition 2) Now, 3^8 + 3^{n+8} = 3^8(1+3^n) is divisible by, but 3^8 is not divisible by 5. Since 5 is a prime number, 1+3^n must be divisible by 5. Thus, 3^4 + 3^{n+4} = 3^4(1+3^n) is also divisible by 5. 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
Posts: 5585
GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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17 Jun 2018, 18:25
[GMAT math practice question] If x and y are prime numbers, and n is a positive integer, what is the number of factors of xnyn? 1) xy=6 2) n=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. Since we have 3 variables (x, y and n) 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 prime numbers and xy = 6, we must have x = 2 and y = 3, or x = 3 and y = 2. If x = 2 and y = 3, then x^ny^n = 2^23^2 has (2+1)(2+1) = 9 factors, since x and y are different prime numbers and n = 2. If x = 3 and y = 2, then x^ny^n = 3^22^2 has (2+1)(2+1) = 9 factors, since x and y are different prime numbers and n = 2. Since we have a unique answer, 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) Since it doesn’t give us any information about the variable n, condition 1) is not sufficient. Condition 2) Since it doesn’t give us any information about the variables x and y, condition 2) is not sufficient. Therefore, C is the answer. Answer: C 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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Math Revolution GMAT Instructor
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GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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17 Jun 2018, 18:26
[GMAT math practice question] △ is one of operations addition, subtraction, multiplication and division. What is the value of 2△2? 1) 4△2=2 2) 3△1=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. The operation △ can be considered to be one variable. Since we have 1 variable 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 4△2=2, △ is subtraction or division. If △ is subtraction, then 2△2 = 0. If △ is division, then 2△2 = 1. Since we don’t have a unique solution, condition 1) is not sufficient. Condition 2) Since 3△1=3, △ is multiplication or division. If △ is multiplication, then 2△2 = 4. If △ is division, then 2△2 = 1. Since we don’t have a unique solution, condition 2) is not sufficient. Conditions 1) & 2) The two conditions show that △ must be division. Thus, 2△2 = 1. Since we have a unique solution, condition 2) is sufficient. Therefore, C is the answer. Answer: C 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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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 $99 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: 5585
GPA: 3.82

Re: Math Revolution Approach (DS) [#permalink]
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20 Jun 2018, 01:44
[GMAT math practice question] The total price of books A, B, and C is $306. What is the median price of books A, B, and C? 1) The price of book A is $102. 2) The price of book B is $20 more than that of book C. => Let a, b and c be the prices of books A, B and C, respectively. Since we have 3 variables (a, b and c) and 1 equation, 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. The equation given by the original condition is a + b + c = 306. Conditions 1) & 2): Since a = 102 and b = c+ 20, we have a + b + c = 102 + c + 20 + c = 2c + 122 = 306 or 2c = 184. So, c = 92, b = 112 and a = 102. Thus, the median is 102. 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) a = 102 is the average price of the books since the total price is 306. If b < 102, then c > 102, and the median is a = 102. If b = 102, then c = 102, and the median is 102. If b > 102, then c < 102, and the median is a = 102. Thus, the median is 102 in all cases. Condition 1) is sufficient. When we have 3 data values, if one value is equal to the average value, then it is the median. Condition 2) If a = 102, b = 92 and c = 112, then the median price is 102. If a = 86, b = 100 and c = 120, then the median price is 100. Since it doesn’t give us a unique solution, condition 2) is not sufficient. 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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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 $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"




Re: Math Revolution Approach (DS)
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