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
