B GmatRrep6.JPG ____________ 1. From the first statement we

Question

B GmatRrep6.JPG ____________ 1. From the first statement we can conclude that x is a prime. But we don't know which exactly. So NOT sufficient 2. From the second statement we can conclude that one of the factor of x is 2, thus the difference of two factors is odd. And also we know that the second factor is 1, thus 1 is always a factor for any given number. Hence 2 is the only number that can satisfies this condition. If we took 6 for example (3,2,1 are factors for it) and 3-1=2 so we can't take it. So answer is B

PussInBoots · Answer

(1) Insuff. 1 and 2 VS 1 and 3
(2) Suff. 1 is factor of any positive integer. Since the difference of any factors is 1, and n!=1, n has at least 1 more factor and that factor has to be 2. If n has 3rd factor, then the difference between the 3rd factor and 1 > 1, hence n has only two factors: 1 and 2. n = 2.

meenal8284 · Answer

well.. i think answer is c

statement 1 is insufficient as it states property of every prime no.
statement 2 is insufficient as it is true for numbers like 14, 18 ,28 ... and so on and so forth.

A prime number (which is always odd) having only itself and 1 as its factor can have the difference between two of its factors odd if and only if it is even.. hence.. both statements are imperative for arriving at one unique solution i.e. 2

flyingbunny · Answer

1). n can be 2, 3, 5, 7, any prime number, insuf

2). only 2 can satisfy this condition, suff

answer B

gmate2010 · Answer

B only..
1.) n = any prime number --- 2,3,5,7 ( So, n can be 2 or can not be 2)..not sufficient.

2.) factors of 14 = 1,2,7,14 ...( 2-1 = 1 odd ; 7-1 = 6 even ; 14-2 = 12 even ) not true..
same with 18, 28 etc..

2nd statement is true only when n = 2 ...

LenaA · Answer

It is said the difference of  ANY  two factors should be odd. 14-1=13 and it is still odd.  x-1=odd if and only if x is even. So we need a condition that will eliminate all other even numbers other than 2. This condition is "x is prime". Since there is only one prime even number (2), it is sufficient. Therefore, C is an answer I get. Can someone explain why B is OA?

gmate2010 · Answer

factors of 14 are -- 1,2,7 and 14

Any factors can be 
1,2 or 1,7 or 1,14 or 2,7 or 2,14 or 7,14

The difference is sometimes even and sometimes odd..

Only when n =2 , we have 1,2 are the only factors ..

diff = 2-1 = 1 odd only..

When n is 0dd not a prime..lets n = 9 factors are 1,3,9

diff = 3-1 = 2 even always

LenaA · Answer

I got it. The statement 2 will hold only for number 2...for any other number, we have even or odd difference... which is a violation of statement 2. Thanks!

Bunuel · Answer

Think this way easier:
(1) insuff
(2) Difference of any distinct positive factors is odd.
Every integer has at least two prime factors.
Let's take one is x second is 1 => x-1=odd => x is even and also prime. only one prime even 2. => 2 must be a factor of n => n is even. If n>2 even number itself(factor) - 2(factor) is always even. so n=2 is the only option.

sharkk · Answer

Nice explanations.

B GmatRrep6.JPG ____________ 1. From the first statement we

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