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

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30 Sep 2013, 20:36

Bunuel wrote:

abhisheksharma wrote:

What if i say that P = 33 x 1.

So it implies that surely one of the integer is greater than 1 but other one is 1 itself ?

Mental block..!!!

33 also can be expressed as 3*11, so the answer to the question "can the positive integer P be expressed as a product of two integers, each of which is greater than 1?" is still YES.

I agree, but then I came across this question.

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3. (2) n is odd.

and I am confused again.

In both questions we know that the number is an integer, let's suppose the number is 33 for both questions(for easier calculation) 33 can be 33 x 1 or 11 x 3. (can be true) & 33 can be 31 + 2 or 27 + 6 (can be true) than why is the answer E in this particular case ??

So it implies that surely one of the integer is greater than 1 but other one is 1 itself ?

Mental block..!!!

33 also can be expressed as 3*11, so the answer to the question "can the positive integer P be expressed as a product of two integers, each of which is greater than 1?" is still YES.

I agree, but then I came across this question.

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3. (2) n is odd.

and I am confused again.

In both questions we know that the number is an integer, let's suppose the number is 33 for both questions(for easier calculation) 33 can be 33 x 1 or 11 x 3. (can be true) & 33 can be 31 + 2 or 27 + 6 (can be true) than why is the answer E in this particular case ??

O_o confused. Please help.

For original question, EVERY possible value of p (32, 33, 34, 35, and 36) CAN be written as the product of two integers, each of which is greater than 1. Thus answer B.

For the other question, SOME possible values of n (for example n=5) CAN be written as the sum of two different positive prime numbers and others cannot (for example n=11). Thus answer E.

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

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29 Apr 2015, 18:58

Bunuel wrote:

abhisheksharma wrote:

What if i say that P = 33 x 1.

So it implies that surely one of the integer is greater than 1 but other one is 1 itself ?

Mental block..!!!

33 also can be expressed as 3*11, so the answer to the question "can the positive integer P be expressed as a product of two integers, each of which is greater than 1?" is still YES.

Hi Bunuel, Thanks for the explanation, but still there is some doubt I have: What if I change range in point (1) as to contain few prime numbers as well. So now will the answer change to E (Both insuff)? Lets say range is 40<p<49

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

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29 Apr 2015, 21:04

This cannot be 600-700 level question. It simply ask for factor of these numbers (a*b) where a and b are > 1. 1. there is no prime number between 31 and 37 so : Sufficient 2. there are so many prime numbers to take the value of P. : not sufficent

Ans: A
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Re: Can the positive integer p be expressed as the product of [#permalink]

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29 Apr 2015, 21:07

sandeep1756 wrote:

Hi Bunuel, Thanks for the explanation, but still there is some doubt I have: What if I change range in point (1) as to contain few prime numbers as well. So now will the answer change to E (Both insuff)? Lets say range is 40<p<49

Thanks in advance.

: To answer your question if you include any prime number between the range than yes ans will be E, as you won't be able to give specific values for a and b ; (P=a*b)
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Re: Can the positive integer p be expressed as the product of [#permalink]

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06 Jun 2016, 20:04

1

This post received KUDOS

Required: Can p be expressed as the product of two integers, each of which is greater than 1 Or is p = x*y, where x and y are greater than 1. This means p can have the numbers that are not prime, since a prime number has only 2 factors: 1 and the number itself.

Statement 1: 31 < p < 37 Values of p can be = 32, 33, 34, 35, 36 None of these is prime, hence p can be written as a product of x and y SUFFICIENT

Statement 2: p is odd. Odd numbers can both be prime and non prime INSUFFICIENT

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

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

This question is a great candidate for rephrasing the target question. If an integer p can be expressed as the product of two integers, each of which is greater than 1, then that integer is a composite number (as opposed to a prime number). So . . . .

REPHRASED target question: Is integer p a composite number?

Aside: We have a video with tips on rephrasing the target question (below)

Statement 1: 31 < p < 37 There are 5 several values of p that meet this condition. Let's check them all. p=32, which means p is a composite number p=33, which means p is a composite number p=34, which means p is a composite number p=35, which means p is a composite number p=36, which means p is a composite number Since the answer to the REPHRASED target question is the SAME ("yes, p IS a composite number") for every possible value of p, statement 1 is SUFFICIENT

Statement 2: p is odd There are several possible values of p that meet this condition. Here are two: Case a: p = 3 in which case p is not a composite number Case b: p = 9 in which case p is a composite number Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT