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r,s,t, are nonzero integers...

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Source: — Data Sufficiency |
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by nipunranjan » Sat Aug 03, 2013 11:10 am
Answer is (C). That is both the options together are sufficient for the solution.

In (r^3)(s^2)(t^4), (s^2) and (t^4) will always be positive as they have even powers.

So the solution depends only upon (r^3) and its sign.

r will have same sign as r^3.

Now let's check the options.

1) "s is negative". In this case r can take any sign. So this option is not sufficient.

2) "rs is negative". In this option, either of the r or s is negative. If r is negative(and s is positive) then the expression is negative. But if s is negative(and r is positive) then the expression will be positive. So this statement is not sufficient in giving a unique solution by itself.

1 and 2 combined. "s is negative" and "rs is negative". This means r is positive. Since r is positive, the expression will be positive. So 1 and 2 combined can give a unique solution.
Hence option (C) is correct.
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by Brent@GMATPrepNow » Sat Aug 03, 2013 11:19 am
topspin20 wrote:If r, s, and t are nonzero integers, is (r^3)(s^2)(t^4) positive?

1) s is negative

2) rs is negative
Target question: Is (r^3)(s^2)(t^4) positive?

IMPORTANT: If s and t are nonzero integers, then s^2 and t^4 are always positive.

So, our target question looks more like this:
Target question: Is (r^3)(some positive #)(some positive #) positive?
As you can see, the answer to the target question depends solely on whether or not r is positive.
So, we can rephrase the target question to get . . .

Rephrased target question: Is r positive?

Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: s is negative
Since there's no info about r, we cannot answer the rephrased target question with certainty.
So, statement 1 is NOT SUFFICIENT

Statement 2: rs is negative
This doesn't tell us much. r could be positive, or r could be negative.
Since we cannot answer the rephrased target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
If s is negative, and rs is negative, we can be certain that r is positive
Since we can answer the rephrased target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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