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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] New post 07 Jan 2014, 04:20
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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] New post 07 Jan 2014, 04:20
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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.

Answer: E.

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] New post 07 Jan 2014, 09:03
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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


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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] New post 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

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] New post 08 Jan 2014, 08:09
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] New post 11 Jan 2014, 06:23
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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.

Answer: E.

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
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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] New post 02 Feb 2014, 02:31
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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] 02 Feb 2014, 02:31
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