Problem Solving

SavageDetective wrote:If r, s and t are nonzero integers, is (r^5)(s^3)(t^4) negative?

(1) rt is negative
(2) s is negative

Target question: Is (r^5)(s^3)(t^4) < 0?

IMPORTANT: When working with inequalities, we can safely divide both sides by a variable as long as we are certain that we are dividing by a positive value.

NOTE: if r, s and t are nonzero integers, then r^4 is ALWAYS POSITIVE, s^2 is ALWAYS POSITIVE, and t^4 is ALWAYS POSITIVE,

So, let's take the target inequality, (r^5)(s^3)(t^4) < 0, and divide both sides by r^4 to get: (r)(s^3)(t^4) < 0
Then divide both sides by s^2 to get: (r)(s)(t^4) < 0
And divide both sides by t^4 to get: (r)(s) < 0

This means we can rephrase our target question as...
REPHRASED target question: Is rs < 0?

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

Statement 1: rt is negative
There are several values of r, s and t that satisfy this condition. Here are two:
Case a: r = 1, s = -1, t = -1, in which case rs < 0
Case b: r = -1, s = -1, t = 1, in which case rs > 0
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: s is negative
There are several values of r, s and t that satisfy this condition. Here are two:
Case a: r = 1, s = -1, t = -1, in which case rs < 0
Case b: r = -1, s = -1, t = 1, in which case rs > 0
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several values of r, s and t that satisfy both statements. Here are two:
Case a: r = 1, s = -1, t = -1, in which case rs < 0
Case b: r = -1, s = -1, t = 1, in which case rs > 0
Since we cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent