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If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]

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11 Apr 2012, 14:52

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If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative?

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

Could someone kindly render a more easily understood explanation than that found in the Quantitative Review 2nd Edition. It would be really appreciated.

If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative?

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

Could someone kindly render a more easily understood explanation than that found in the Quantitative Review 2nd Edition. It would be really appreciated.

Since r, s, and t are nonzero integers then in order r^5*s^3*t^4 to be negative, only one condition should hold: r and s must have the opposite signs, in this case (r^5*s^3)*t^4=(negative)*(positive)=negative. Notice that if we were not told that given variables are nonzero then there would be one more condition that t must not be zero.

(1) rt is negative --> r and t have the opposite signs. Not sufficient, since no info about s. (2) s is negative. Clearly insufficient.

(1)+(2) If r is positive then the answer will be YES (since r^5*s^3*t^4=positive*negative*positive=negative) but if r is negative then the answer will be NO (r^5*s^3*t^4=negative*negative*positive=positive). Not sufficient.

Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]

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05 Sep 2012, 04:25

Once you realize that two exponents are odd and one is even, you know that the you only have to worry about the signs of r and s, thus reducing the complexity. Picking numbers might also help, I think, even though it might take a bit too long.

Thank you Bunuel and Cyberjadugar.
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Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]

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23 Dec 2015, 00:02

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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