MathRevolution wrote:
If r, s are positive integers, is r/s a terminating decimal?
1) 1/r is a terminating decimal
2) 1/s is a terminating decimal
* A solution will be posted in two days.
Target question: Is r/s a terminating decimal?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.So, r/s will be a terminating decimal if the prime factorization of s (the denominator) contains only 2's and/or 5's.
Statement 1: 1/r is a terminating decimal If 1/r is a terminating decimal, then we know that the prime factorization of r contains only 2's and/or 5's.
This, however, tells us nothing about about the value of the denominator in the fraction r/s
Consider these two pairs of conflicting values of r and s:
Case a: r = 2 and s = 4, in which case
r/s = 2/4 = 0.5, which is a terminating decimalCase b: r = 2 and s = 3, in which case
r/s = 2/3 = 0.666.., which is not a terminating decimalSince we can't answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 1/s is a terminating decimal If 1/s is a terminating decimal, then we know that the prime factorization of s contains only 2's and/or 5's.
Since the prime factorization of s (the denominator) contains only 2's and/or 5's, we know that
the decimal version of the fraction will be a terminating decimalSince we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent