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07 Jan 2014, 05:20
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E
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Difficulty:
25%
(medium)
Question Stats:
76% (01:26) correct
24%
(01:14)
wrong
based on 2332
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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
(1) rt is negative
(2) s is negative
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.
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
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
General Discussion
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
Hence, (E) is the answer.
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.
