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Is n an integer?

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by Max@Math Revolution » Thu May 17, 2018 12:25 am

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Answers

A

B

C

D

E

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Difficulty—

[GMAT math practice question]

Is n an integer?

1) 2n is an integer
2) 1/n is an integer
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu May 17, 2018 3:05 am
Max@Math Revolution wrote:[GMAT math practice question]

Is n an integer?

1) 2n is an integer
2) 1/n is an integer
Both statements are satisfied by the following cases:
Case 1: n = 1, with the result that 2n = 2 and 1/n = 1
In this case, n is an integer, so the answer to the question stem is YES.
Case 2: n = 1/2, with the result that 2n = 1 and 1/n = 2
In this case, n is NOT an integer, so the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by Max@Math Revolution » Sun May 20, 2018 5:03 pm
=>
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 2n = 2, then n = 1, which is an integer.
If 2n = 1, then n = 1/2, which is not an integer.
Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
If 1/n = 1, then n = 1, which is an integer.
If 1/n = 2, then n = 1/2, which is not an integer.
Since we don't have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
n = 1 satisfies both conditions, and n is an integer.
n = 1/2 satisfies both conditions, and n is not an integer.
Both conditions together 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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