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N is a positive integer. What is the value of N?

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N is a positive integer. What is the value of N?

by Max@Math Revolution » Tue Aug 27, 2019 11:36 pm

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[GMAT math practice question]

N is a positive integer. What is the value of N?

1) N is divisible by 75
2) N has 75 positive factors, including 1 and N.
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Sep 01, 2019 9:05 pm

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C

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=>

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.
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Since we have 1 variable (N) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
The possible values of N are 75, 150, .... Since condition 1) does not yield a unique solution, it is not sufficient.

Condition 2)
2^{74} and 2^4*3^4*5^2 have 75 factors. Since condition 2) does not yield a unique solution, it is not sufficient.

Conditions 1) & 2)
N = 3^{24}*5^2 and N=2^4*3^4*5^2 have 75 factors. Since both conditions together do not yield a unique solution, they are not sufficient.

Therefore, E is the answer.
Answer: E


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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