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GMATPrep Test1 Question

by limestone » Sun Aug 22, 2010 9:52 am
If the integer n is greater than 1, is n equal to 2
(1) n has exactly 2 positive factors
(2) The difference of any two distinct positive factors of n is odd

OA is B

When I came to this question, I considered "1" not to be a factor, so I took E. However, if "1" is considered as a factor, then (2) suggests that "n" has only 2 factors : 1 & 2, so n is equal to 2. As all factors are odd - except for 2, then differences among them must be even. Is this the explanation for my false choice, E?
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by Gurpinder » Sun Aug 22, 2010 10:46 am
hey,

so the question is basically is n=2?

(1) n has exactly 2 positive factors

This is true for any prime number. So its insufficient.

(2) The difference of any two distinct positive factors of n is odd

For any prime number greater than 2, the difference will always be even. Since for this one the difference is odd, the number is 2.

Therefore (B) is sufficient.


1 is a factor of EVERY NUMBER. When we talk about prime numbers having only 2 factors, 1 is one of those 2 factors.


I hope that helps!
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by missrochelle » Sun Aug 22, 2010 3:03 pm
Gurpinder wrote:hey,


(2) The difference of any two distinct positive factors of n is odd

For any prime number greater than 2, the difference will always be even. Since for this one the difference is odd, the number is 2.

Therefore (B) is sufficient.
I chose C because I didn't think statement 2 told us that the number was prime. The fact that the difference of any two distinct factors is odd doesn't tell us the number is prime. What if it were N=4. 4-1 =3? Can you explain how we deduce from statement 2 that N is prime?
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by vijaynaik » Sun Aug 22, 2010 3:58 pm
it doesn't have to be a prime.

if n=4 then 4 has 1, 2, 4 as factors. 4 - 2 will give 2 which is even.
n=6 , then 1, 2, 3, 6 are factors. 6 - 2 is even. So B is suff.
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by skprocks » Sun Aug 22, 2010 6:57 pm
limestone wrote:If the integer n is greater than 1, is n equal to 2
(1) n has exactly 2 positive factors
(2) The difference of any two distinct positive factors of n is odd

OA is B

When I came to this question, I considered "1" not to be a factor, so I took E. However, if "1" is considered as a factor, then (2) suggests that "n" has only 2 factors : 1 & 2, so n is equal to 2. As all factors are odd - except for 2, then differences among them must be even. Is this the explanation for my false choice, E?
Your explannation is not proper.How can the difference among the factors of 2 be even?Or you are trying to make a different point.Stmt 2 alone is Sufficient,as 2 is the only number the difference of the factors of which is always odd.
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by Gurpinder » Sun Aug 22, 2010 7:07 pm
missrochelle wrote:
Gurpinder wrote:hey,


(2) The difference of any two distinct positive factors of n is odd

For any prime number greater than 2, the difference will always be even. Since for this one the difference is odd, the number is 2.

Therefore (B) is sufficient.
I chose C because I didn't think statement 2 told us that the number was prime. The fact that the difference of any two distinct factors is odd doesn't tell us the number is prime. What if it were N=4. 4-1 =3? Can you explain how we deduce from statement 2 that N is prime?
The answer is (B).

Don't fall into the trap of statement 2. The statement says "The difference of any two distinct positive factors of n is odd."

You said N = 4, factors of 4 = 4,1,2. You said 4-1=3 But WHY NOT 4-2. Statement 2 is saying ANYYY distinct positive factors of N.

No other number follows the rule of Statement 2 except for the number 2.

I hope that helps!
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