GMAT Prep Question

[sommukh]

Am I missing out something??

Statement 1: k = n* 2^6 (where n is some integer)
n can be either odd or even ... in either case it's insufficient (e.g if n=6 then K can not be 2^r for some positive integer r whereas if n=2,4,8 etc then it's possible)

Statement 2: K is not divisible by any odd integer>1
IMO this is also insufficient (e.g again K is divisible by 6 ... now it can not be 2^r for some positive integer r)

when we combine 1 & 2 still it's not sufficient (assume K= 6*2^6 .... both conditions satisfied but still k !=2^r where r is a integer on other hand if we have k = 4*2^6 it's possible ...) So it turns ou to be E ... Correct me pls ...!!

[bkparikh]

@Sommukh
In Statement 2, K cannot be divisible by 6 because that would mean K is also divisible by 3. The statement says that K is not divisible by any odd integer > 1.

The trick here is understanding prime factorization of a number. A number, K, is divisible by all numbers in its prime factorization. But 2 can be the only even number in a prime factorization (because 2 is the only non-odd prime number). Because the statement says that K is not divisible by any odd numbers greater than 1, the prime factorization of K must be 2^r.

Hope that helps!

[sommukh]

thank you !! ... that was silly on my part ...