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Each 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.

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Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]
07 Jan 2014, 04:20

Expert's post

SOLUTION

If 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.

Each 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.

Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]
07 Jan 2014, 20:49

Since r,s and t are non-zero 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

If 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]
11 Jan 2014, 06:23

Expert's post

SOLUTION

If 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.

Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative [#permalink]
02 Feb 2014, 02:31

r^5s^3t^4 can be re-written 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]
02 Feb 2014, 02:31