If r and s are positive integers, can the fraction r/s be expressed as a decimal with only a finite number of non-zero digits?
(1) s is a factor of 100.
(2) r is a factor of 100.
IN OTHER WORDS, is decimal version of r/s a terminating decimal?
Aside: A terminating decimal is one that does not repeat.
For example, 1/4 = 0.25 so this is a terminating decimal.
Conversely, 1/3 = 0.333333.... so this is a non-terminating decimal
Target question:
Is r/s a terminating decimal?
Statement 1: 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 is a terminating decimal
Case b: r = 1 and s = 3, in which case
r/s is not a terminating decimal
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 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 = 2x2x5x5, any factor of 100 will contain only 2's and/or 5'2 (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 decimal
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
