Data Sufficiency

ardz24 wrote:Is 12 a factor of the positive integer n?

(1) n is a factor of 36.
(2) 3 is a factor of n.

Target question: Is 12 a factor of the positive integer n?

Statement 1: n is a factor of 36
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 12, in which case 12 IS a factor of n
Case b: n = 6, in which case 12 is NOT a factor of n
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3 is a factor of n
Once again, there are several values of n that satisfy statement 2. Here are two:
Case a: n = 12, in which case 12 IS a factor of n
Case b: n = 6, in which case 12 is NOT a factor of n
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: n = 12, in which case 12 IS a factor of n
Case b: n = 6, in which case 12 is NOT a factor of n
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

ardz24 wrote:Is 12 a factor of the positive integer n?

(1) n is a factor of 36.
(2) 3 is a factor of n.

We need to determine whether n/12 = integer.

Statement One Alone:

n is a factor of 36.

We do not have enough information to answer the question. If n is 1, then n/12 is not an integer; however, if n is 36, then n/12 is an integer. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

3 is a factor or n.

We do not have enough information to answer the question. If n is 3, then n/12 is not an integer; however, if n is 36, then n/12 is an integer. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

We still do not have enough information to answer the question. If n is 3, then n/12 is not an integer; however, if n is 36, then n/12 is an integer.

Answer: E