Baten80 wrote:
Is x a multiple of 72?
(1) x is a multiple of 16.
(2) x is divisible by 18.
-----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 a multiple of k, then k is "hiding" within the prime factorization of NConsider these examples:
24 is a multiple of
3 because 24 = (2)(2)(2)
(3)Likewise, 70 is a multiple of
5 because 70 = (2)
(5)(7)
And 112 is a multiple of
8 because 112 = (2)
(2)(2)(2)(7)
And 630 is a multiple of
15 because 630 = (2)(3)
(3)(5)(7)
-----ONTO THE QUESTION!---------------------
Target question: Is x a multiple of 72?This is a good candidate for
rephrasing the target question.
72 = (2)(2)(2)(3)(3)
REPHRASED target question: Are three 2's and two 3's hiding in the prime factorization of x?Aside: the video below has tips on rephrasing the target question Statement 1: x is a multiple of 16 16 = (2)(2)(2)(2)
So, this tells us that there are four 2's hiding in the prime factorization of x.
However, we can't be sure whether there are also two 3's hiding in the prime factorization of x.
Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x is divisible by 1818 = (2)(3)(3)
So, this tells us that there is one 2 and two 3's hiding in the prime factorization of x.
This means we have enough 3's, however we can't be sure whether there are also three 2's hiding in the prime factorization of x
Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that there are three 2's hiding in the prime factorization of x
Statement 2 tells us that there are two 3's hiding in the prime factorization of x
So when we COMBINE statements, the answer to the REPHRASED target question is
YES, there are three 2's and two 3's hiding in the prime factorization of xSince we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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