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If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]
 11 Apr 2012, 15:52
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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.
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Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]
11 Apr 2012, 16:11
dzodzo85 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
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. Answer: E. Similar questions to practice: is-x-2-y-5-z-0-1-xz-y-0-2-y-z-98341.htmlm21-q30-96613.htmlis-x-7-y-2-z-3-0-1-yz-0-2-xz-95626.htmlHope it helps.
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Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]
13 Jun 2012, 11:56
Hi, r^5s^3t^4 < 0? Using (1); rt is -ve, so, r^5s^3t^4 = (rt)^4r^1s^3, no clue about s, Insufficient. Using (2), s is -ve, r & t are unknown, Insufficient. Using (1) & (2), (rt)^4r^1s^3(rt)^4 > 0, and s < 0so the expression reduces to r^1(-ve), but we still don't know if r is +ve/-ve. Thus, Answer is (E). Regards,
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Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]
05 Sep 2012, 05:25
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]
05 Sep 2012, 05:25
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