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Updated on: 02 Sep 2022, 08:19
Originally posted by BrentGMATPrepNow on 01 Sep 2022, 07:23.
Last edited by BrentGMATPrepNow on 02 Sep 2022, 08:19, edited 1 time in total.
Last edited by BrentGMATPrepNow on 02 Sep 2022, 08:19, edited 1 time in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
57% (01:33) correct
43%
(01:09)
wrong
based on 67
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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
(1) x is a divisor of 16
(2) y is a multiple of 30
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BrentGMATPrepNow
A fraction is a terminating decimal when the reduced form of the denominator contains only 2's or/and 5's
(1) x is a divisor of 16
We cannot ascertain anything about the denominator.
INSUFF.
(2) y is a multiple of 30
So the denominator is a multiple of \(5*2*3 .\)
We can see we have an extra 3 in the denominator, however we still cannot tell whether this \(3 \) can be reduced/cancelled using the numerator.
Lets say we have numerator as 3 then the fraction becomes \(\frac{3}{5*2*3} = \frac{1}{5*2} \) This is a terminating decimal .
Lets say we have numerator as 2 then the fraction becomes \(\frac{2}{5*2*3} == \frac{1}{5*3}\)This is a NON terminating decimal.
INSUFF.
1+2
Since we can only have 2's ( factors/divisors of 16 ) in the numerator , the 3 in the denominator remains uncancelled.
Thus the fraction remains a non terminating decimal.
SUFF.
Ans C
Hope its clear
( edited after correction in the question)
Updated on: 02 Sep 2022, 08:35
Originally posted by BrentGMATPrepNow on 02 Sep 2022, 07:17.
Last edited by BrentGMATPrepNow on 02 Sep 2022, 08:35, edited 2 times in total.
Last edited by BrentGMATPrepNow on 02 Sep 2022, 08:35, edited 2 times in total.
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BrentGMATPrepNow
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
