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Math Expert V
Joined: 02 Sep 2009
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What is the value of a positive integer x? (1) x has exactly two disti  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 37% (01:07) correct 63% (01:22) wrong based on 67 sessions

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What is the value of a positive integer x?

(1) x has exactly two distinct factors.
(2) The difference between any two distinct factors of x is odd.

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Re: What is the value of a positive integer x? (1) x has exactly two disti  [#permalink]

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Bunuel wrote:
What is the value of a positive integer x?

(1) x has exactly two distinct factors.
(2) The difference between any two distinct factors of x is odd.

Question: WHat is the value of Positive integer x?

Statement 1: x has exactly two distinct factors.

i.e. x is Prime Number
but x may be 2, 3, 5, 7, 11 etc hence
NOT SUFFICIENT

Statement 2: The difference between any two distinct factors of x is odd.
This is possible only if the number has exactly two factors (i.e.e x is Prime number) and one of them must be odd (i.e. 1) and other must be even
which is possible only if x is 2 because only 2 has one even and one odd factor

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Re: What is the value of a positive integer x? (1) x has exactly two disti  [#permalink]

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GMATinsight wrote:
Bunuel wrote:
What is the value of a positive integer x?

(1) x has exactly two distinct factors.
(2) The difference between any two distinct factors of x is odd.

Question: WHat is the value of Positive integer x?

Statement 1: x has exactly two distinct factors.

i.e. x is Prime Number
but x may be 2, 3, 5, 7, 11 etc hence
NOT SUFFICIENT

Statement 2: The difference between any two distinct factors of x is odd.
This is possible only if the number has exactly two factors (i.e.e x is Prime number) and one of them must be odd (i.e. 1) and other must be even
which is possible only if x is 2 because only 2 has one even and one odd factor

How can we deduce that the number is prime?
It doesn't say that the number has only 2 factors that are distinct.

Eg. 14 has two set of factors say (14,1) & (2,7), the difference is odd.

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Re: What is the value of a positive integer x? (1) x has exactly two disti  [#permalink]

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RustagiABC wrote:
GMATinsight wrote:
Bunuel wrote:
What is the value of a positive integer x?

(1) x has exactly two distinct factors.
(2) The difference between any two distinct factors of x is odd.

Question: WHat is the value of Positive integer x?

Statement 1: x has exactly two distinct factors.

i.e. x is Prime Number
but x may be 2, 3, 5, 7, 11 etc hence
NOT SUFFICIENT

Statement 2: The difference between any two distinct factors of x is odd.
This is possible only if the number has exactly two factors (i.e.e x is Prime number) and one of them must be odd (i.e. 1) and other must be even
which is possible only if x is 2 because only 2 has one even and one odd factor

How can we deduce that the number is prime?
It doesn't say that the number has only 2 factors that are distinct.

Eg. 14 has two set of factors say (14,1) & (2,7), the difference is odd.

It explicitly mentions that x has exactly two distinct factors

So there are only two factors of number that are distinct.
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Re: What is the value of a positive integer x? (1) x has exactly two disti  [#permalink]

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The second statement says

The difference between any two distinct factors of x is odd.
CEO  D
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What is the value of a positive integer x? (1) x has exactly two disti  [#permalink]

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1
RustagiABC wrote:
The second statement says

The difference between any two distinct factors of x is odd.

RustagiABC

Suppose a number has three factors --- In that case
1) either two of them will be odd and one will be even OR
2) two will be even and one will be odd OR
3) All will be even OR
4) all will be odd

The difference of any two factors in first case or second case can't be ODD cause in first case odd-odd will be even and in second case even-even will be even

theerfore for the difference of any two factors of the number to be odd

ONE FACTOR MUST BE EVEN
and ONE FACTOR MUST BE ODD

I hope this explains your doubt now... _________________
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Originally posted by GMATinsight on 01 Oct 2018, 06:12.
Last edited by GMATinsight on 01 Oct 2018, 06:15, edited 1 time in total.
Intern  B
Joined: 30 Jan 2018
Posts: 17
Re: What is the value of a positive integer x? (1) x has exactly two disti  [#permalink]

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1
RustagiABC wrote:
GMATinsight wrote:
Bunuel wrote:
What is the value of a positive integer x?

(1) x has exactly two distinct factors.
(2) The difference between any two distinct factors of x is odd.

Question: WHat is the value of Positive integer x?

Statement 1: x has exactly two distinct factors.

i.e. x is Prime Number
but x may be 2, 3, 5, 7, 11 etc hence
NOT SUFFICIENT

Statement 2: The difference between any two distinct factors of x is odd.
This is possible only if the number has exactly two factors (i.e.e x is Prime number) and one of them must be odd (i.e. 1) and other must be even
which is possible only if x is 2 because only 2 has one even and one odd factor

How can we deduce that the number is prime?
It doesn't say that the number has only 2 factors that are distinct.

Eg. 14 has two set of factors say (14,1) & (2,7), the difference is odd.

Hi

You are overlooking the info provided in option B , number 14 has 4 factors such as 1,2,7,14 and the difference between 14-2=12 which is an even number. You are just taking the pairs but the option says the difference between any two factors is odd.

hope its clear now.

Anurag Jain

I don't mind Kudos Manager  S
Joined: 21 Nov 2016
Posts: 71
GMAT 1: 640 Q47 V31 Re: What is the value of a positive integer x? (1) x has exactly two disti  [#permalink]

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From statement 1 we get that x has exactly 2 distinct factors = meaning its a prime number.
So it could be any prime number. 2,3,5,etc..
So, statement 1 is insufficient.

From statement 2 we get that the difference between any two distinct factors of x is odd.
That is one of the factors is even and the other odd. Because, if any of the two distinct factors were odd then the difference would be odd- odd = even, or if any of two distinct factors were even then also we would have got the difference as even - even = even.
So, the only way one can get the difference of the ANY 2 distinct factors odd is even - odd = odd or odd - even = odd.
So, only number 2 satisfies this quality. Because it has only 2 factors and ANY 2 factors are those 2 factors, ie 1 and 2.
So, 2-1 = 1 (odd).
So, statement 2 itself is sufficient.

Corollary: This is a type of question where one may take the help of Statement 1 to get the answer and hence mark the wrong answer C.
Since, statement 2 is itself is sufficient. Answer is B. Re: What is the value of a positive integer x? (1) x has exactly two disti   [#permalink] 01 Oct 2018, 20:45
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