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Can the positive integer p be expressed as the product of

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by BTGmoderatorLU » Sat Nov 17, 2018 1:56 pm

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Source: GMAT Paper Tests

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

1) 31 < p < 37
2) p is odd.

The OA is A.
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Source: — Data Sufficiency |

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by [email protected] » Sat Nov 17, 2018 2:14 pm
Hi All,

We're told that P is a positive integer. We're asked if P can be expressed as the PRODUCT of two integers, each of which is greater than 1. This is a YES/NO question can be be solved by TESTing VALUES.

1) 31 < p < 37

With the range given in Fact 1, P can only be 5 different values...IF...
P = 32 = (2)(16) and the answer to the question is YES
P = 33 = (3)(11) and the answer to the question is YES
P = 34 = (2)(17) and the answer to the question is YES
P = 35 = (5)(7)) and the answer to the question is YES
P = 36 = (2)(18) and the answer to the question is YES
The answer is ALWAYS YES.
Fact 1 is SUFFICIENT

2) P is odd.
IF....
P = 1, then the answer to the question is NO.
P = 6 = (2)(3), then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Final Answer: A

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Rich
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Re: Can the positive integer p be expressed as the product of

by Scott@TargetTestPrep » Mon Jul 05, 2021 4:56 am
BTGmoderatorLU wrote: ↑
Sat Nov 17, 2018 1:56 pm
 Source: GMAT Paper Tests

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

1) 31 < p < 37
2) p is odd.

The OA is A.
Solution:

Question Stem Analysis:

We need to determine whether integer p can be expressed as the product of two integers, each of which is greater than 1. That is, we need to determine whether p is a composite number.

Statement One Alone:

We see that p can be 32, 33, 34, 35, or 36. Since each one of these numbers is a composite number, statement one alone is sufficient.

Statement Two Alone:

Statement two alone is not sufficient. For example, if p = 15, then p can be expressed as the product of two integers, each of which is greater than 1 (notice that 15 = 3 x 5). However,if p = 17, then p can’t be expressed as the product of two integers, each of which is greater than 1 (notice that 17 is a prime).

Answer: A

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[email protected]

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