mehrasa wrote:is x divisible by 8?
1)x is divisible by 24
2)x is divisible by 16
[spoiler]OA: A[/spoiler]
A lot of integer property questions can be solved using prime factorization.
For divisibility questions, we can say:
If N is divisible by k, then k is "hiding" within the prime factorization of N
Examples:
24 is divisible by
3 <--> 24 = 2x2x2x
3
70 is divisible by
5 <--> 70 = 2x
5x7
330 is divisible by
6 <--> 330 =
2x
3x5x11
So, if x is divisible by 8, then we know an
8 is hiding in the prime factorization of x.
In other words x =
(2)(2)(2)(?)(?)... [notice that we may or may not have primes other than the three 2's in the factorization. All we can be certain of is that there are three 2's (8) within the prime factorization]
Okay, with all of that, we can first take the target question "
Is x divisible by 8?" and reword it as "
Is 8 hiding in the prime factorization of x"
Statement 1: x is divisible by 24
In other words,
24 is hiding in the prime factorization of x
So, we can say that x =
(2)(2)(2)(3)(?)(?)...
From here we can see that 8
is hiding in the prime factorization of x (in the form of three 2's)
So, statement 1 is sufficient.
Statement 1: x is divisible by 16
In other words,
16 is hiding in the prime factorization of x
So, we can say that x =
(2)(2)(2)(2)(?)(?)...
From here we can see that 8
is hiding in the prime factorization of x (in the form of three 2's)
So, statement 2 is sufficient, and the answer is
D
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
