Data Sufficiency

If the integer x is greater than 1, does x = 2?

1) x is evenly divisible by exactly two positive integers.
2) The sum of any two distinct positive factors of x is odd.

OA IS B

My doubt is in stmtn 1 ; what does "evenly divisible mean" ? should the quotient be an even number ?

take for example if x =2 ; then 1 evenly divides i.e. 1 *2 = 2 (quotient = 2)
then 2 oddly divides itself i.e 2 * 1 = 2 (quotient = 1)

is this the reason why A is not sufficient ?

Sir OA for this question cannot be B.

2) The sum of any two distinct positive factors of x is odd.


The sum of any two distinct positive factors of x is odd.
If x = odd, then 1 will be one of the factors of x and 1 + x = even, which means x cannot be odd.
If x = even and x > 2, then since x is even so 2 will be one of its factors. So, 2 + x = even, which means x cannot be more than 2, implies x = 2, as 2 has 2 factors, 1 and 2. Also, 2 + 1 = 3 (odd); SUFFICIENT.


The statement 2 clearly states that any two distinct factors of x is odd. Let us say that the number is 6. The factors are 1, 2, 3, 6.

Now let us say we take any two integers greater than 1, lets say 3 and 2. Now 3 + 2 is also odd ie 5. So x is 6 here and not 2.

According to me the answer should be C and not B.

Kindly see if my explanation is correct...

if 6 is the number then the factors are 1,2,3,6 the summation of these factors is :

1+2 = 3 (odd)
2+3 = 5 (odd)
1+6= 7 (odd)
2+6 = 8 (even)

hence 6 cannot be the number . the question stem says the sum of any two distinct factors is ODD number it happen only for the number 2.

the factors of 2 are 1 & 2 and their summation is 1 +2 = 3 (odd)

hence resolved. hope my explanation makes sense...

thanks

Hey thanx!!! Pappueshwar, I was making a silly mistake,,, This is where the DS actually traps us..
It tries to trap us in its usual format only, forget the concepts and so many formulae.


I think I got the answer...B...