terminating decimals

[GmatGreen]

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?

1) 90 < r < 100

2) s = 4

[Brent@GMATPrepNow]

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?

1) 90 < r < 100
2) s = 4

Target question: Is r/s a terminating decimal?

Statement 1: 90 < r < 100
There are several pairs of values that meet this condition. Here are two:
Case a: r = 91 and s = 2, in which case r/s = 91/2 = 45.5 = a terminating decimal
Case b: r = 91 and s = 3, in which case r/s = 91/3 = 30.33333.... = a non-terminating decimal
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: s = 4
Notice that 1/4 = 0.25, 2/4 = 0.5 and 3/4 = 0.75
So, if the denominator is 4, the resulting decimal will definitely be a terminating decimal.
In other words, if s = 4 then r/s must be a terminating decimal.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Aside: 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 the denominator, 4 = (2)(2), the rule tells us that r/s must be a terminating decimal.

Answer = B

Cheers,
Brent

[Patrick_GMATFix]

To know whether r/s will terminate, we need either some information about the ratio r/s, or information about the denominator s that guarantees termination (example if s=1, 2, 4, 5, or 10, the ratio will always result in a terminating decimal). The full solution below is taken from the GMATFix App.



-Patrick

[GMATGuruNY]

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?

1) 90 < r < 100

2) s = 4

Many DS problems involve number properties.
If you don't know the relevant rule, DON'T STARE.
Instead, TEST CASES.

Statement 1: 90 < r < 100
If r=92, and s=2, then r/s = 92/2 = 46.
In this case, r/s is terminating.
If r=92 and s=3, then r/s = 92/3 = 30.666.....
In this case, r/s is NOT terminating.
INSUFFICIENT.

Statement 2: s=4
If r=1 and s=4, then r/s = 1/4 = .25.
If r=2 and s=4, then r/s = 1/2 = .5.
If r=3 and s=4, then r/s = 3/4 = .75.
If r=4 and s=4, then r/s = 4/4 = 1.
If r=5 and s=4, then r/s = 5/4 = 1.25.
In EVERY case, r/s is terminating.
SUFFICIENT.

The correct answer is B.