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Primes

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by Troika » Thu Jun 07, 2012 5:41 pm
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
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by Anurag@Gurome » Thu Jun 07, 2012 7:46 pm
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
Both statements taken together, p can is either 43 or 45 or 47.
Now, 43 and 47 cannot be expressed as the product of two integers, each of which is greater than 1 but 45 can be.

Hence, both statements together is also not sufficient to answer the question.

The correct answer is E.
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by Troika » Thu Jun 07, 2012 7:59 pm
Anurag, since 45 can be expressed as the product of two integers greater than 1 (5 x 9), shouldn't the answer be C?
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by Anurag@Gurome » Thu Jun 07, 2012 8:02 pm
Troika wrote:Anurag, since 45 can be expressed as the product of two integers greater than 1 (5 x 9), shouldn't the answer be C?
The statements together do not point that p is equal to 45, they point that p can be either 43 or 45 or 47.

Now, for p = 43 and p = 47, the answer to the question is NO
And for p = 45, the answer to the question is YES

Hence, we cannot properly answer the question.
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by Stuart@KaplanGMAT » Thu Jun 07, 2012 9:56 pm
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!
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by Troika » Fri Jun 08, 2012 7:22 am
Anurag & Stuart, thanks for the explanations!
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