does x = 2?

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pappueshwar: Master | Next Rank: 500 Posts; Posts: 234; Joined: Fri Oct 01, 2010 7:28 pmFollowed by: 4 members; Location: chennai; Thanked: 5 times

by pappueshwar » Fri Mar 16, 2012 9:51 pm

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 ?

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Source: Beat The GMAT — Data Sufficiency | Fri Mar 16, 2012 9:51 pm

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by Anurag@Gurome » Fri Mar 16, 2012 10:07 pm

pappueshwar wrote: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 ?

(1) x is evenly divisible by exactly two positive integers implies x can be any prime (because a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself), say, 2, 3, 5, 7, and so on.
NO definite answer; NOT sufficient.

(2) 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 correct answer is B.

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[email protected]: Legendary Member; Posts: 934; Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members; Location: AAMCHI MUMBAI LOCAL; Thanked: 63 times

by [email protected] » Sat Mar 17, 2012 3:55 am

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...

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pappueshwar: Master | Next Rank: 500 Posts; Posts: 234; Joined: Fri Oct 01, 2010 7:28 pmFollowed by: 4 members; Location: chennai; Thanked: 5 times

by pappueshwar » Sat Mar 17, 2012 4:18 am

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

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[email protected]: Legendary Member; Posts: 934; Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members; Location: AAMCHI MUMBAI LOCAL; Thanked: 63 times

by [email protected] » Sat Mar 31, 2012 4:01 am

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...

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