Data Sufficiency

Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?

1. p is odd.
2. 41 < p < 49

OA: E

Anurag, since 45 can be expressed as the product of two integers greater than 1 (5 x 9), shouldn't the answer be C?

Troika wrote:Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?

1. p is odd.
2. 41 < p < 49

OA: E

Hi!

Like a lot of data sufficiency questions, investing a bit of time in the question stem to understand what the question is really about makes working with the statements much simpler.

Let's break down the stem:

Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?

What kind of positive numbers CANNOT be expressed as the product of two integers greater than 1? Primes! So, here's what the question is really asking:

Is the positive integer p non-prime?

and, of course, since a "yes" answer to that question is the same as a "no" answer to "Is the positive integer p prime?", we could just rephrase the question that way as well.

So, now we know what we're after: is the positive integer p prime?

(1) p is odd

Some primes are odd, some non-primes are odd (e.g. 13 and 15) - insufficient.

(2) p is between 41 and 49

41 is non-prime, 43 is prime - insufficient.

Together: 43, 45 and 47 all satisfy both statements. 43 is prime, 45 isn't: still insufficient, choose E!

Anurag & Stuart, thanks for the explanations!