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

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Can the positive integer 'p' be expressed as the product of [#permalink]

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12 Aug 2008, 06:32
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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

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Re: DS - Positive Integer [#permalink]

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12 Aug 2008, 06:45
klb15 wrote:
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

1) 31 < p < 37

p can be 32,33,35,36
-- All these numbers can be expresses as product of two integers. So no definite answer
Insufficient

2) p is add.. there are multiple solutions..
insufficient

combine both. : INSUFFICIENT

two possibilites 33 and 35

Ans E.
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Re: DS - Positive Integer [#permalink]

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12 Aug 2008, 06:52
1
KUDOS
Don't for get what the question asks: "Can the positive integer p be expressed..."

The answer for this is yes, it can be.
P = 32 = 8 * 4
p = 33 = 3*11
p = 34 = 2*17
p = 35 = 5 * 7
p = 36 = 3 * 12

ever integer that p could represent can be expressed as the product of two integers.

#1 is sufficient.

#2 is sufficient. If p is odd, then it can be 33 or 35 or 3 or 7 (remember take each statement alone, so 31 < p < 37 isn't relevant information with #2). Each of these can still be expressed as the product of two integers. So #2 is sufficient as well. Because at least 1 is sufficient alone, we don't have to try them together.

x2suresh wrote:
klb15 wrote:
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

1) 31 < p < 37

p can be 32,33,35,36
-- All these numbers can be expresses as product of two integers. So no definite answer
Insufficient

2) p is add.. there are multiple solutions..
insufficient

combine both. : INSUFFICIENT

two possibilites 33 and 35

Ans E.

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Re: DS - Positive Integer [#permalink]

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12 Aug 2008, 08:04
winnie wrote:
I think A

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Re: DS - Positive Integer [#permalink]

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12 Aug 2008, 08:58
jallenmorris wrote:
#2 is sufficient. If p is odd, then it can be 33 or 35 or 3 or 7 (remember take each statement alone, so 31 < p < 37 isn't relevant information with #2). Each of these can still be expressed as the product of two integers. So #2 is sufficient as well. Because at least 1 is sufficient alone, we don't have to try them together.

The question is really asking: is p a non-prime? Statement 1 is sufficient; there are no primes between 31 and 37. Statement 2 is not sufficient- all we know is that p is an odd positive integer. p could be equal to 7, in which case p cannot be expressed as a product of two positive integers larger than 1. p could just as well be equal to 15, and thus equal to 3*5. A.

edit- I think you missed the part in the question that says 'each of which is greater than one'. If that didn't appear in the stem, we wouldn't need the statements at all- every positive integer can be expressed as the product of two positive integers (itself and 1), of course.
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Re: DS - Positive Integer [#permalink]

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12 Aug 2008, 09:04
I didn't miss it, I remember reading it, but i didn't follow my own steps in answering DS questions:

2) Find key words, Not, Only, Except, Prime, Positive, Integer, etc
3) Find qualifiers, Less than, Greater than, etc
4) rephrase question into easier format. (I.e., is x positive? becomes Is x always positive or always negative?)
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Re: DS - Positive Integer [#permalink]

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12 Aug 2008, 09:11
jallenmorris wrote:
I didn't miss it, I remember reading it, but i didn't follow my own steps in answering DS questions:

2) Find key words, Not, Only, Except, Prime, Positive, Integer, etc
3) Find qualifiers, Less than, Greater than, etc
4) rephrase question into easier format. (I.e., is x positive? becomes Is x always positive or always negative?)

Agree with A.

you are right...
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Re: DS - Positive Integer [#permalink]

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12 Aug 2008, 19:40

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Re: DS - Positive Integer [#permalink]

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13 Aug 2008, 04:00
(1) 31 < p < 37
Sufficient. For all p, where 31 < p < 37, p is not a prime number.

(2) p is odd
Insufficient, because p can be a prime of not a prime

Ans: A

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Re: DS - Positive Integer [#permalink]

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14 Aug 2008, 10:10
jallenmorris wrote:
I didn't miss it, I remember reading it, but i didn't follow my own steps in answering DS questions:

2) Find key words, Not, Only, Except, Prime, Positive, Integer, etc
3) Find qualifiers, Less than, Greater than, etc
4) rephrase question into easier format. (I.e., is x positive? becomes Is x always positive or always negative?)

The answer is indeed A. Mr. Suresh has an excellent mathematical aptitude, must have did a silly mistake.

Jallen, you always help aspirants with good suggestions and explanations. I get to learn a lot from your posts. Thanks!!

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Re: DS - Positive Integer [#permalink]

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14 Aug 2008, 10:13
Thanks for the feedback/encouragement!

rahulgoyal1986 wrote:
jallenmorris wrote:
I didn't miss it, I remember reading it, but i didn't follow my own steps in answering DS questions:

2) Find key words, Not, Only, Except, Prime, Positive, Integer, etc
3) Find qualifiers, Less than, Greater than, etc
4) rephrase question into easier format. (I.e., is x positive? becomes Is x always positive or always negative?)

The answer is indeed A. Mr. Suresh has an excellent mathematical aptitude, must have did a silly mistake.

Jallen, you always help aspirants with good suggestions and explanations. I get to learn a lot from your posts. Thanks!!

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Re: DS - Positive Integer   [#permalink] 14 Aug 2008, 10:13
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