asveaass wrote:
If r and s are positive integers, can the fraction r/s be expressed as a decimal with only a finite number of nonzero digits?
(1) s is a factor of 100
(2) r is a factor of 100
Target question: Is r/s a terminating decimal? Statement 1: s is a factor of 100 There's a nice rule that says something like,
If the prime factorization of the denominator contains only 2's and/or 5's, then the decimal version of the fraction will be a terminating decimal.Since 100 = (2)(2)(5)(5), any factor of 100 will contain only 2's and/or 5's (or the denominator can be 1, in which case the decimal will definitely terminate).
Since the denominator of r/s must contain only 2's and/or 5's,
r/s must be a terminating decimalSince we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: r is a factor of 100 There are several pairs of values that meet this condition. Here are two:
Case a: r = 1 and s = 4, in which case
r/s = 1/4 = 0.25, which is a terminating decimalCase b: r = 1 and s = 3, in which case
r/s = 1/3 = 0.333.., which is not a terminating decimalSince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent