If m is an integer greater than 1, is m an even integer?

1) as 32 is a factor of m so 32 multiplied by any number give even integer so m is even integer. SUFFICIENT

2) all the factors of 32 are even except 1. As m is greater than 1 so m is even. SUFFICIENT

Answer D

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Statement 1) 32 is a factor of m

means m/32 = integer

so m has to be 32 or a multiple of it. Sufficient

Statement 2)

m is a factor of 32 since 32 = 2^5 and we know that m is an integer > 1 then it must be even to be a factor of 32.

Sufficient.

answer choice D

If m is an integer greater than 1, is m an even integer?

(1) 32 is a factor of m.

This statement tells us m is a multiple of 32. Thus, m is an even integer as all multiples of 32 are even.

(2) m is a factor of 32.

Each factor of 32 greater than 1 is even. Thus, m is an even integer. SUFFICIENT.

(1) 32 is an even number and m is a multiple of 32, So m is Even. Sufficient.

(2) The factors of 32 are: 32, 16, 8, 4, 2, and 1; But m>1, So m is Even. Sufficient.

The answer is D.

Solution:

We need to determine whether m is an even integer given that m > 1.

Statement One Alone:

Since 32 is a factor of m, and m is a multiple of 32. Since 32 is an even integer and any multiple of an even integer is also even, we see that m must be even. Statement one alone is sufficient.

Statement Two Alone:

The factors of 32 are 1, 2, 4, 8, 16, and 32. Since m > 1, then m could be 2, 4, 8, 16, or 32. Regardless of which integer m is, we see that m is even. Statement two alone is sufficient.

Answer: D

(1) 32 is a factor of m. m is multiple of 32 i.e. 32x. Whatever the nature of x(odd integer or even integer) when multiplied with an even number(here 32) will be even. Hence sufficient.
(2) m is a factor of 32. 32 = 2^5 has only one odd factor, which is 1 and all the remaining factors are even. Since given that m > 1, then m must be even. Sufficient.

Thus D is the answer

The most crucial piece of information in this question – m is greater than 1!!!

Is m even? We can answer the question with a Yes and say it’s even; we can answer the question with a No and say it’s odd. These are the two unique answers expected in this question.

From statement I alone, 32 is a factor of m.

Note that an odd integer is never divisible by an even integer. Therefore, if 32 is a factor of m, m has to be even since 32 is even.
Statement I alone is sufficient to say that m is even. Answer options B, C and E can be eliminated.

From statement II alone, m is a factor of 32.

32 has a total of 5 factors of which four are even and only one is odd. The odd factor is 1. This is where the question data throws in its weight, telling us m cannot be 1.
Therefore, m has to be one of the even factors of 32.
Statement II alone is sufficient to say that m is even. Answer option A can be eliminated.

The correct answer option is D.

Hope that helps!
Aravind BT

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