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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.
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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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11 Apr 2012, 15:11
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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: isx2y5z01xzy02yz98341.htmlm21q3096613.htmlisx7y2z301yz02xz95626.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]
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13 Jun 2012, 10:56
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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 \(s < 0\) so the expression reduces to\(r^1(ve)\), but we still don't know if r is +ve/ve.
Thus, Answer is (E).
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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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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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31 Jan 2018, 03:59
Bunuel wrote: 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. Hope it helps. For (1)+(2), how could R be positive? Isn't T automatically positive because it is T^4? Statement 1 says RT is negative, so I assumed that R has to be negative. I'm sure this is an elementary question, but can you please show me an example of how T^4 could be negative? Thanks in advance.



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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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31 Jan 2018, 04:08
msurls wrote: Bunuel wrote: 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. Hope it helps. For (1)+(2), how could R be positive? Isn't T automatically positive because it is T^4? Statement 1 says RT is negative, so I assumed that R has to be negative. I'm sure this is an elementary question, but can you please show me an example of how T^4 could be negative? Thanks in advance. t^4 cannot be negative. A number in an even power is always nonnegative, so 0 or positive. Since we are told that t is nonzero, then t^4 is positive only. But t itself could be positive as well as negative. For example, t^4 = 16 = positive, t = 2 or t = 2.
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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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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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31 Jan 2018, 11:36
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. The given expression can be written as  \((rt)^4*r*s^3\) Statement I: \(rt = ve\).... In \((rt)^4*r*s^3\), we don't know anything about r & s... So, Insufficient. Statement II: \(s = ve\). But still we dont know anything about \(r\). Combined, still we don't know about \(r\) sign. Hence, E.
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Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative
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