infiniti007 wrote:Is integer x divisible by 24?
1.) x is divisible by 6.
2.) x is divisible by 4.
Target question: Is integer x divisible by 24?
-------------------------------
ASIDE: A lot of integer property questions can be solved using prime factorization.
For questions involving divisibility, divisors, factors and multiples, we can say:
If N is divisible by k, then k is "hiding" within the prime factorization of N
Consider these examples:
24 is divisible by
3 because 24 = (2)(2)(2)
(3)
Likewise, 70 is divisible by
5 because 70 = (2)
(5)(7)
And 112 is divisible by
8 because 112 = (2)
(2)(2)(2)(7)
And 630 is divisible by
15 because 630 = (2)(3)
(3)(5)(7)
----------------------------
Since 24 - (2)(2)(2)(3), we can REPHRASE the target question....
REPHRASED target question: Are there three 2's and one 3 hiding in the prime factorization of x?
Aside: for more on this concept, see our free video: https://www.gmatprepnow.com/module/gmat- ... /video/825
Statement 1: x is divisible by 6.
6 = (2)(3), so we can conclude that x has at least ONE 2 and ONE 3 hiding in its prime factorization.
Of course, there MIGHT be three 2's and one 3 hiding in the prime factorization of x. But we can't say for sure.
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x is divisible by 4.
4 = (2)(2), so we can conclude that x has at least TWO 2's hiding in its prime factorization.
Of course, there MIGHT be three 2's and one 3 hiding in the prime factorization of x. But we can't say for sure.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that that x has at least ONE 2 and ONE 3 hiding in its prime factorization.
Statement 2 tells us that that x has at least TWO 2's hiding in its prime factorization.
Combined, we can be certain that x has at least TWO 2 and ONE 3 hiding in its prime factorization.
Of course, there MIGHT be three 2's and one 3 hiding in the prime factorization of x. But we can't say for sure.
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer =
E
Cheers,
Brent
