terminating decimal question

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Taniuca: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Aug 02, 2010 3:25 pm; Thanked: 3 times

terminating decimal question

by Taniuca » Sat Aug 14, 2010 5:26 pm

Please someone help me out. Problem 139, The official guide for theGmat 12th edition review

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24.0/82, 5.096 are three terminating decimals. If r and s are positive intergers and theratio r/s is expressed as a decimal, is r/x a terminating decimal?
1) 90<r<100
2) s=4

Quote

Source: Beat The GMAT — Data Sufficiency | Sat Aug 14, 2010 5:26 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Sat Aug 14, 2010 5:48 pm

Taniuca wrote:Please someone help me out. Problem 139, The official guide for theGmat 12th edition review

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

Hi! I fixed a couple of small typos in your post.

We want to know if positive integer r divided by positive integer s is a terminating decimal. What do we need? Info about r and/or s.

(1) 90<r<100

No info about s, so we can quickly pick numbers to get both a yes and a no.

If r=95 and s=5, then r/s IS a terminating decimal.
If r=95 and s=3, then r/s is NOT a terminating decimal (since 95/3 = 31.66666666...).

INSUFFICIENT, eliminate A and D.

(2) s = 4

We don't know anything about r, but does that matter? As it turns out, no.

When you divide by 4, there are only 4 possible results: remainder 1/4, remainder 2/4, remainder 3/4 or no remainder. Accordingly, when you divide by 4, after the decimal you'll have:

.25
.5
.75
or
nothing.

Accordingly, dividing by 4 ALWAYS creates a terminating decimal... SUFFICIENT.

(2) is sufficient, (1) isn't: choose B.