Data Sufficiency

[Math Revolution GMAT math practice question]

If n is an integer greater than 1, what is the value of n?

1) n is a prime number
2) (n+2)/n is an integer

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If n is an integer greater than 1, what is the value of n?

1) n is a prime number
2) (n+2)/n is an integer

Statement 1:
Here, n can be any prime number.
INSUFFICIENT.

Statement 2:
(n+2)/n = n/n + 2/n = 1 + 2/n.
Given that n must be an integer, 1 + 2/n will yield an integer value only if n is a FACTOR OF 2.
Factors of 2: 1 and 2.
Since n must be greater than 1, n=2.
SUFFICIENT.

The correct answer is B.

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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.

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 there are many prime numbers, condition 1) is not sufficient.

Condition 2)
If n = 1, then (n+2)/n = 3 is an integer.
If n = 2, then (n+2)/n = 2 is an integer.
Since we don't have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
If n = 2, then (n+2)/n = 2 is an integer.
If n = 3, then (n+2)/n = 5/2 is not integer.
If n is a prime number bigger than 2, (n+2)/n is not an integer.
Thus n = 2 is the unique solution and both conditions together are 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.

Max@Math Revolution wrote:

If n is an integer greater than 1, what is the value of n?

1) n is a prime number
2) (n+2)/n is an integer

Condition 2)
If n = 1, then (n+2)/n = 3 is an integer.
If n = 2, then (n+2)/n = 2 is an integer.
Since we don't have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
If n = 2, then (n+2)/n = 2 is an integer.
If n = 3, then (n+2)/n = 5/2 is not integer.
If n is a prime number bigger than 2, (n+2)/n is not an integer.
Thus n = 2 is the unique solution and both conditions together are sufficient.

Therefore, C is the answer.
Answer: C

Since the prompt indicates that n is an integer greater than 1, the case in red is not possible.
The only value that satisfies Statement 2 is n=2, making Statement 2 SUFFICIENT.
The correct answer thus is not C but B.