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# Can the positive integer p be expressed as the product of

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Joined: 06 Jun 2007
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Can the positive integer p be expressed as the product of [#permalink]  14 Nov 2007, 04:05
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Can the positive integer p be expressed as the product of two integers,each of which is greater than I?

(1) 3I<p<37
(2) p is odd

Plz explain..

Cheers,
Circkit
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Joined: 06 Mar 2006
Posts: 497
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Statement 2 by itself is insufficient. You don't know what I is. The answer could be Yes or No.

Statement 1 by itself is also insufficient. If I is 1 and P is a prime number; the P cannot be expressed as the product of two integers greater than I.
If P is even number or other non prime odd number, then P might be able to be expressed as the product of two integers greater than I.

Together, still insufficient.

Therefore, I think the answer is E.
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Re: DS- positive integer [#permalink]  14 Nov 2007, 12:45
circkit wrote:
Can the positive integer p be expressed as the product of two integers,each of which is greater than I?

(1) 3I<p<37
(2) p is odd

Plz explain..

Cheers,
Circkit

It is either A or E.

I rephrase it to: Is integer p NOT prime?

(1) 31<p<37

p: 32, 33, 34, 35, 36

32 = 16 * 2
33 = 11 * 3
34 = 17 * 2
35 = 7 * 5
36 = 12 * 3

Although we don't know which of those numbers is p, but p can be any of those numbers and still satisfy the question as NONE OF THEM ARE PRIME. I am not sure if my reasoning is valid to make it SUFF on the GMAT.

(2) p is odd

p can be 3, 9, 11, 27

3=3 * 1 .......... NO
9=3 * 3 ...........YES
11=11 * 1 ........NO
27=9*3 ...........YES

Sometime NO, sometime YES, we don't know for sure, so INSUFF

----

If A is not the answer then it is E.
Director
Joined: 13 Dec 2006
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I will go with A

Question says that can the positive integer p be expressed and not will the positive integer p be expressed. It means we have to search for the solution, where our requirement should be one of the possible solution.

Case 1 - P lies between 3I and 37, in this case we dont know the value of I, which can be eithe positive or negative. The maximum value of I can be 11, making 3I = 33. In this case P can be 34, 35, or 36. In such situation two integers, whose product will give the value of P, will not be greater than I.

But if I is a negative integer, Z, or positive integer lesser than 4, its possible that the 2 integers, whose product = p, are greater than I.

Case 2 - Insufficient, as I is not defined.

Amar
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