rxs0005 wrote:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 12, 0.13, and 4.068 are three terminating decimals. If j and k are positive integers and the ratio j/k is expressed as a decimal, is j/k a terminating decimal?
(1) k = 3
(2) j is an odd multiple of 3.
We need to determine whether j/k is a terminating decimal given that j and k are positive integers. One thing we should keep in mind is that a fraction (in lowest terms and with a denominator greater than 1) can be expressed as a terminating decimal if and only if the denominator comprises prime factors of only 2 and/or 5. For example, 3/10 and 3/15 = 1/5 are terminating decimals, whereas 3/7 and 3/9 = 1/3 are not. On the other hand, if the denominator is 1, the fraction is always a terminating decimal as long as the numerator is an integer.
Statement One Alone:
k = 3
Depending on the value of j, j/k may or may not be a terminating decimal. For example, if j = 1, then j/k = 1/3 is not a terminating decimal. On the other hand, if j = 3, then j/k = 3/3 = 1/1 = 1 is a terminating decimal. Statement one is not sufficient to answer the question.
Statement Two Alone:
j is an odd multiple of 3.
Depending on the value of k, j/k may or may not be a terminating decimal. For example, if j = 3 and k = 7, then j/k = 3/7 is not a terminating decimal. On the other hand, if j = 3, and k = 3, then j/k = 3/3 = 1/1 = 1 is a terminating decimal. Statement two is not sufficient to answer the question.
Statements One and Two Together:
Since j is an odd multiple of 3, and k = 3, j/k is always an odd integer. Thus, j/k is a terminating decimal.
Answer: C
_________________
See why Target Test Prep is the top rated GMAT course on GMAT Club.
Read Our Reviews