Max@Math Revolution wrote:If r and s are positive integers, is r/s a terminating decimal?
1) r is a factor of 100
2) s is a factor of 500
When solving this problem, we should remember that there is a special property about fractions that allows their decimal equivalents to terminate. This property states:
In its most-reduced form, any fraction with a denominator whose prime factorization contains only 2s, only 5s, or both 2s and 5s, produces decimals that terminate. A denominator with any other prime factors produces decimals that do not terminate.
We must determine whether r/s is a terminating decimal, or in other words, whether s has only 2s, 5s, or both as prime factors.
Statement One Alone:
r is a factor of 100.
Since we do not have any information about s, statement one alone is not sufficient to answer the question.
Statement Two Alone:
s is a factor of 500.
Since 500 = 2^2 x 5^3 and s is a factor of 500, s will contain only 2s, 5s, or both as prime factors. If r/s is already in its most-reduced form, then r/s is a terminating decimal. If r/s is not in its most-reduced form, then the most-reduced form of r/s, say r'/s', will also be a terminating decimal since s' will then be a factor of s and it will contains only 2s, 5s or both as prime factors. Statement two alone is sufficient to answer the question.
Answer:
B
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