What is the number of factors of a positive integer n?

[Max@Math Revolution]

[GMAT math practice question]

What is the number of factors of a positive integer n?

1) n is a multiple of 7
2) n is a prime number

[Brent@GMATPrepNow]

What is the number of factors of a positive integer n?

1) n is a multiple of 7
2) n is a prime number

Target question: What is the number of factors of a positive integer n?

Statement 1: n is a multiple of 7
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 7. In this case, n has TWO factors (1 and 7)
Case b: n = 7. In this case, n has FOUR factors (1, 2, 7 and 14)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n is a prime number
ALL prime numbers have exactly TWO factors.
So, if n is a prime number, then the TWO factors are 1 and n
In other words, n has exactly TWO factors
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

[Max@Math Revolution]

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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)
n = 7 : The number of factors of n is 2.
n = 14 : The number of factors of n is 4.
Since the answer is not unique, condition 1) is not sufficient.

Condition 2)
n = p^1, where p is a prime number.
The number of factors on n is 1 + 1 = 2.
Thus, condition 2) is 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.