Please note that I rewrote the target question to be more like an official GMAT question.sud21 wrote:Is integer N a multiple of 36?
1) N is a multiple of 12
2) N is a multiple of 20
First recognize that 36 = 2x2x3x3
From here, we should recognize that if a number, N, is a multiple of 36, then there must be two 2's and two 3's in the prime factorization of N.
Now let's rephrase the target question as "Does prime factorization of N have at least two 2's and two 3's in it?"
Aside: Many integer properties questions can be tackled by examining the prime factorizations of the given values.
Statement 1:
12=2x2x3
If N is a multiple of 12, then the prime factorization of N must have at least two 2's and one 3.
Since we cannot be certain that the prime factorization of N has at least two 2's and two 3's, statement 1 is NOT SUFFICIENT.
Statement 2:
22=2x2x5
If N is a multiple of 20, then the prime factorization of N must have at least two 2's and one 5.
Since we cannot be certain that the prime factorization of N has at least two 2's and two 3's, statement 2 is NOT SUFFICIENT.
Statements 1 & 2:
From the two statements, we know that the prime factorization of N must have at least two 2's, one 3 and one 5.
Since we cannot be certain that the prime factorization of N has at least two 2's and two 3's, the statements combined are NOT SUFFICIENT, and the answer is E
Cheers,
Brent
