Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE DS
Solution:
In analyzing whether r/s is a terminating decimal, we can use the following rule:
The decimal equivalent of a fraction will terminate if and only if the denominator of the fraction in its lowest terms is 1 or has a prime factorization that contains only 2s and/or 5s. If the prime factorization of the reduced fraction’s denominator contains anything other than 2s or 5s, the decimal equivalent will not terminate.
Thus, if we can determine that s is 1 or has a prime factorization that contains only 2s and/or 5s then we will know that r/s represents a terminating decimal.
Statement One Alone:
90 < r < 100
Since statement one provides no information about s, we do not have enough information to determine whether r/s is a terminating decimal. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
s = 4
Since s = 4, or s = 2 × 2, we know that s has prime factors of 2 only. Thus, r/s is a terminating decimal. Note that we do not need to know the actual value of positive integer r in order to make this assertion. In fact, its value is of no consequence to the outcome. Only the denominator plays a role in determining whether r/s will be a terminating decimal. Statement two alone is sufficient to answer the question.
Answer: B
