1. Good post? |

## factors

From Gmat review 11th

If the integer n is greater than 1 , is n equal to 2?

1) n has exactly two positive factors
2) the difference of any two distinct positive factors of n is odd.

SPOILER: B

Can someone tell me what am I doing wrong here?

From stmt1) n could be any number so Insufficient

from stmt 2) say n has two factors a and b , so that n = a * b
If a-b or b-a is odd, that means that either a=even, b=odd, OR a=odd, b=even, in any there are many numbers that fit this description for a and b.
Now, the question statement asks to find whether n = 2.
If n =2, then there can only be two factors, such that 2 = 1 * 2. So the difference of 1 and 2 is always odd, which fits the description of stm2, but there are many combinations of numbers that fit stm2 description. So my answer was E.

2. Good post? |
For stmnt 2, I took 4 = 2*2*1 the difference two distinct positive factors of n is odd (2-1).

Stmnt 2 doesnot say that n has only two factors, right?

Can some please explain my mistake? Thanks.

3. Good post? |
1 and the number(n) itself are factors of the number.

Now, if the number is odd, n-1 must be even. So statement2 does not hold.

Now, for n being even, consider 2 cases: n>2 and n=2
For n>2 and n being even, 2 has to be a factor of n. However, since n is even, n-2 is even. So statement2 does not hold.

Now for n=2, the only factors are 1 and 2 and the difference is odd.

Hence statement2 is enough.

4. Good post? |
Originally Posted by tank
1 and the number(n) itself are factors of the number.

Now, if the number is odd, n-1 must be even. So statement2 does not hold.

Now, for n being even, consider 2 cases: n>2 and n=2
For n>2 and n being even, 2 has to be a factor of n. However, since n is even, n-2 is even. So statement2 does not hold.

Now for n=2, the only factors are 1 and 2 and the difference is odd.

Hence statement2 is enough.
Thanks Tank!! now i see my mistake. For 4 --> 1, 2 and 4 are factors, before I was considering 1, 2 (only prime factors)

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