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Can the positive integer p be expressed as the product of

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

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New post 30 Sep 2013, 21:36
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 ??


O_o confused. Please help.
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Re: Can the positive integer p be expressed as the product of  [#permalink]

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New post 01 Oct 2013, 00:30
abhisheksharma wrote:
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 ??


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.

The second question is discussed here: can-the-positive-integer-n-be-written-as-the-sum-of-two-126725.html

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

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New post 29 Apr 2015, 19:58
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

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

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New post 29 Apr 2015, 22:04
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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New post 29 Apr 2015, 22:07
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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New post 20 Dec 2015, 10:30
The question means

Is p=ab where a and b>1

P, a, b are all integers

Statement 1:
31 < p <37 => p = 32, 33, 34, 35, 36

All of these can be. 1 is sufficient

Statement 2: P is odd. It could be an odd prime or a composite odd
Insuff.

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

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New post 06 Jun 2016, 21:04
1
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

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

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New post 18 Jan 2018, 10:43
Top Contributor
Minotaur 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


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

Answer : A

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

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New post 18 Jan 2018, 11:00
1
Need to find if p is prime or not.
As non prime numbers can be expressed as product of two factors.

Between 31 and 37 :
These are the numbers
32,33,34,35,36 : All of these numbers are not prime. So it can be expressed as product of two factors.

p is odd.
All odd numbers are not always prime.
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Re: Can the positive integer p be expressed as the product of &nbs [#permalink] 18 Jan 2018, 11:00

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