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

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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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63% (02:09) correct 37% (00:59) wrong based on 447 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If 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

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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
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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.

Similar questions to practice:
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m21-q30-96613.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
1
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If 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 Project

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:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
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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

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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
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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

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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 Edition

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]

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11 Jan 2014, 07:23
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.

Similar questions to practice:
is-x-2-y-5-z-0-1-xz-y-0-2-y-z-98341.html
m21-q30-96613.html
is-x-7-y-2-z-3-0-1-yz-0-2-xz-95626.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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02 Feb 2014, 03:31
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$$r^5s^3t^4$$ 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]

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

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Re: If r, s, and t are nonzero integers, is r^5*s^3*t^4 negative   [#permalink] 11 Apr 2017, 16:52
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