number properties

[sud21]

Is a certain number the multiple of 36?
1) It is the multiple of 12
2) It is the multiple of 20

[Brent@GMATPrepNow]

Is integer N a multiple of 36?
1) N is a multiple of 12
2) N is a multiple of 20

Please note that I rewrote the target question to be more like an official GMAT question.

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

[Brent@GMATPrepNow]

Is integer N a multiple of 36?
1) N is a multiple of 12
2) N is a multiple of 20

We can also solve the question using counterexamples.

Statement 1:
If N is a multiple of 12, then there are various cases to consider. Here are two cases.
case a: N=360, in which case N is a multiple of 36
case b: N=240, in which case N is not a multiple of 36
INSUFFICIENT

Statement 2:
If N is a multiple of 20, then there are various cases to consider. Here are two cases.
case a: N=360, in which case N is a multiple of 36
case b: N=240, in which case N is not a multiple of 36
INSUFFICIENT

Aside: Notice that I used the same values of N for both statements. This speeds things up nicely.

Statements 1 & 2:
If N is a multiple of 12 and a multiple of 20, then there are various cases to consider. Here are two cases.
case a: N=360, in which case N is a multiple of 36
case b: N=240, in which case N is not a multiple of 36
INSUFFICIENT

Answer = E

Cheers,
Brent