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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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07 Jan 2014, 05:20
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The Official Guide For GMAT® Quantitative Review, 2ND EditionIf r, s, and t are nonzero integers, is r^5*s^3*t^4 negative? (1) rt is negative (2) s is negative Data Sufficiency Question: 24 Category: Arithmetic Properties of numbers Page: 154 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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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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07 Jan 2014, 05:20
SOLUTIONIf r, s, and t are nonzero integers, is r^5*s^3*t^4 negative?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.html
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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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07 Jan 2014, 10:03
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf r, s, and t are nonzero integers, is r^5*s^3*t^4 negative? (1) rt is negative (2) s is negative Data Sufficiency Question: 24 Category: Arithmetic Properties of numbers Page: 154 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! Has to be E. We need to know if rs<0 Statement 1 Doesn't help much Statement 2 Well, ok but what about the others? Statement 1 and 2 together well let's see If rt<0 and s<0 then r<0 and t>0 or r>0 and t<0 We get to different values so Insuff E Cheers! J



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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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07 Jan 2014, 21:49
Since r,s and t are nonzero integers, they can be either +ve or ve. The question asks to find whether r^5*s^3*t^4 is negative?
Here, since t has an even power, we can conclude that the value of t^4 will be positive. Therefore, we need to find out whether r*s<0 or which of the 2(r & s) has a negative value?
Statement (1): rt<0; Either r<0 and t>0 or r>0 and t<0; No definite value of r could be found. Also, no information about s is given; Insufficient.
Statement (2): s<0 or s is negative; Also, no information about r is given; Insufficient.
Combining both statements, we still cannot get a definite value for r(r could be < or >0); Insufficient
Hence, (E) is the answer.



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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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08 Jan 2014, 09:09
Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND EditionIf r, s, and t are nonzero integers, is r^5*s^3*t^4 negative? (1) rt is negative (2) s is negative r^5*s^3*t^4 is ve or +ve depends on value of r and s both as only they have odd powers. power of t is even, so should be always +ve. Statement 1) rt is negative. if r is ve, t is +ve if r is +ve, t is ve. We don't know the value of r and nothing is said about the value of s. Not sufficient. Statement 2) s is ve. we don't know about r. Not sufficient. Combining the two statements. Still we don't know the sign of r, hence Option 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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11 Jan 2014, 07:23
SOLUTIONIf r, s, and t are nonzero integers, is r^5*s^3*t^4 negative?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.html
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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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02 Feb 2014, 03:31
\(r^5s^3t^4\) can be rewritten as \((rt)^2(rst)^2*rs\) Now \((rt)^2\) and \((rst)^2\) are always positive. The question boils down to IS rs negative? Stmt1: rt is negative. Either r is ve or t is ve. No info about s. INSUFF Stmt2: No info about r. INSUFF Together: still no info about r, it could be +ve or ve. E is the solution.
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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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