What is the value of a positive integer x? (1) x has exactly two disti

Question

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.

GMATinsight · Answer

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

Answer: Option B

RustagiABC · Answer

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.

Please clarify

GMATinsight · Answer

Please read the statement more carefully

It explicitly mentions that  x has  exactly  two distinct factors

So there are only two factors of number that are distinct.

RustagiABC · Answer

The second statement says

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

GMATinsight · Answer

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...

jainanurag470 · Answer

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

harsha3699 · Answer

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.

Pranavsawant · Answer

Okay here we are assuming factors only to be positive. Why is that so?
GMATinsight
1 has factors 1 and -1 for instance. The entire question breaks down if we consider negative factors.

I believe GMAT would always specify between positive and negative factors. Based on the posts below, it seems like we are to assume positive factors only on the GMAT. However, in all OG questions I have seen them specify "positive" factors. If they ask us to use negative factors, they state that explicitly.

https://gmatclub.com/forum/can-distinct ... 71724.html
https://gmatclub.com/forum/number-of-di ... l#p1121158

What is the value of a positive integer x? (1) x has exactly two disti

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