Brent@GMATPrepNow wrote: ↑

Fri Sep 02, 2022 6:16 am

If x and y are positive integers, and K equals the decimal equivalent of x/y, is K a terminating decimal?

(1) x is a divisor of 16
(2) y is a multiple of 30

Answer: C
Source: www.gmatprepnow.com

Given: x and y are positive integers, and K equals the decimal equivalent of x/y

Target question: Is K a terminating decimal?

Key Property: If D = the decimal equivalent of the fraction a/b (written in simplest terms), then D will be a terminating decimal only if the prime factorization of b consists of only 2's and/or 5's
So, for example, if b = 20, the fraction a/b will result in a terminating decimal. The same holds true for other values of b such as 4, 5, 25, 40, 2, 8, and so on.

Statement 1: x is a divisor of 16
Since we have no information about the denominator (y), statement is not sufficient.
Here are two possible cases that yield conflicting answers to the target question:
Case a: x = 2 and y = 5. In this case, K = x/y = 2/5 = 0.4, which means the answer to the target question is YES, K is a terminating decimal
Case b: x = 2 and y = 3. In this case, K = x/y = 2/3 = 0.666666...., which means the answer to the target question is NO, K is not a terminating decimal
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y is a multiple of 30
Here are two possible cases that yield conflicting answers to the target question:
Case a: x = 15 and y = 30. In this case, K = x/y = 15/30 = 1/2 = 0.5, which means the answer to the target question is YES, K is a terminating decimal
Case b: x = 80 and y = 30. In this case, K = x/y = 80/30 = 8/3 = 2.666666...., which means the answer to the target question is NO, K is not a terminating decimal
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x is a divisor of 16, which means x = 1, 2, 4, 8, or 15
Statement 2 tells us that y is a multiple of 30, which means y = (2)(3)(5)(n) for some integer n
Since x cannot be a multiple of 3, the simplified version of the fraction x/y will always have a 3 in the prime factorization of the denominator.
Since we can be certain that x/y will always have a 3 in the prime factorization of the denominator, the decimal equivalent of x/y (aka K) will not be a terminating decimal
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C