nonzero integers

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seema19: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Wed Sep 14, 2011 12:34 am

by seema19 » Tue Oct 18, 2011 9:23 am

If r,s and t are nonzero integers, is (r^5)(s^3)(t^4) negative ?
1) rt is negative
2) s is negative

Answer: E

My doubt: t^4 will always be positive. So, to determine whether the question at hand is either positive or negative, we have to find out the sign of r and s.

Statement 1 states rt is negative, which means r is negative. But it states nothing reg the sign of s. So it is INSUFFICIENT.

Statement 2 states that s is negative but does not state anything abt the sign of r. So it is INSUFFICIENT.

Combined - We now know that (r^5)(s^3)(t^4) not negative.

But the answer is E

Can somebody please explain why C is wrong.

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Source: Beat The GMAT — Data Sufficiency | Tue Oct 18, 2011 9:23 am

sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Tue Oct 18, 2011 10:01 am

Statement 1

rt < 0

Case 1
r=+, t=-
Case 2
r=- , t=+
Insufficient

Statement 2
s < 0. Insufficient

Combining 1 and 2

t^4 is positive regardless of its sign. Let's look at s and r
Case 1
r=+,s=-, Then the result is negative
Case 2
r=-,s=-, Then the result is positive. Hence Insufficient

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Tue Oct 18, 2011 10:13 am

(r^5)(s^3)(t^4) remains positive for any value of t.

We need to find if rs is -ve.

1) rt is -ve. (r can be -ve or t can be -ve) Insuff
2) s is negative (Insuff alone)

Together, if r and s both are -ve, exp is +ve
If r and t are -ve, expression is -ve.

Insufficient. E

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Brian@VeritasPrep: GMAT Instructor; Posts: 1031; Joined: Thu Jul 03, 2008 1:23 pmFollowed by: 255 members; Location: Malibu, CA; Thanked: 716 times; GMAT Score:750

by Brian@VeritasPrep » Tue Oct 18, 2011 11:12 am

Wow - phenomenal question that I have to admit had me stumped for at least a second there until I took a step back.

Here's what they did - by power of suggestion, they got you thinking that the value of t is irrelevant because it's taken to the 4th power and therefore t^4 will be positive. So from the question stem they have you thinking that "only the values of r and s really matter".

But wait - with statement 1, the value of t now matters again. Because if t is negative, then that means that r is positive. Because in statement 1, t no longer has its even exponent. So your assumption (and I'm sure a very, very common one on this question) is that "t has to be positive because it's taken to the 4th". But t ALONE doesn't have that "negative protection", so it's full eligible to be either negative or positive, and that's the wrench in the system.

With both statements we know that:

s is negative, so s^3 is negative
t could be positive or negative, but t^4 must be positive, so it all hinges on:
r could be positive or negative...it just has to be the opposite of t. And because it could be either, both statements are insufficient.

_____________________________________

Now, strategically this question looks like a pretty easy C if you fall victim to that power-of-suggestion about t. Which is why you should have embedded in your mind that you should never accept an "easy C". If C comes to you within 30 seconds or less, there's a huge probability that it's wrong and that your job is now to go back and figure out why. This question is a classic example - C is bait, all the way, but most probably fall for it. Those who are leery of that easy C will go back and reconsider, and that's where you're more likely to notice that t itself, stripped from its exponent, actually does matter.

Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep

Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Oct 19, 2011 2:37 am

seema19 wrote:My doubt: t^4 will always be positive.
...
Statement 1 states rt is negative, which means r is negative. But it states nothing reg the sign of s.

t^4 is always positive doesn't mean t is negative.
rt is negative implies r and t have opposite signs.

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Wed Oct 19, 2011 3:41 am

If r,s and t are nonzero integers, is (r^5)(s^3)(t^4) negative ?

t^4 is always positive, so you need not bother about the sign of it!

1) rt is negative

r > 0 and t < 0
r < 0 and t > 0 are the only conditions

Insufficient as we are not aware of the sign of s

2) s is negative

S < 0

Insufficient as we are not aware of the sign of r

Combine the options, you get two different solutions
r > 0 and t < 0, s < 0 => (r^5)(s^3)(t^4) is -ve
r < 0 and t > 0, s < 0 => (r^5)(s^3)(t^4) is +ve

Hence Option E

Anil Gandham
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nandy1984: Master | Next Rank: 500 Posts; Posts: 105; Joined: Fri Nov 05, 2010 8:29 pm; Thanked: 4 times

by nandy1984 » Wed Oct 19, 2011 9:11 am

seema19 wrote:If r,s and t are nonzero integers, is (r^5)(s^3)(t^4) negative ?
1) rt is negative
2) s is negative

Answer: E

My doubt: t^4 will always be positive. So, to determine whether the question at hand is either positive or negative, we have to find out the sign of r and s.

Statement 1 states rt is negative, which means r is negative. But it states nothing reg the sign of s. So it is INSUFFICIENT.

Statement 2 states that s is negative but does not state anything abt the sign of r. So it is INSUFFICIENT.

Combined - We now know that (r^5)(s^3)(t^4) not negative.

But the answer is E

Can somebody please explain why C is wrong.

Statement (1) rt is negative
Lets simplify the above problem
(r^5)(s^3)(t^4) = (r*s*t)^2 * (r^3) * (s) * (t^2)
So since (r*s*t)^2 and (t^2) is always positive the sign of the expression depends on (r^3) * (s)....since we don't know whats the value of s.... we cannot say whether the expression is positive or negative

Statement (2)
S is negative
Using the same simplification above inorder to find the sign of the above expression we need to find the sign of the expression (r^3) * (s)....but the statement gives only the info of "s" it doesn't say anything about "r" so we cannot find the sign...INSUFFICIENT

Combining the two statements:

We know s is negative and (rt) is negative means
(i) s NEGATIVE, r NEGATIVE , t POSITIVE ------------ (r^3) * (s)....POSITIVE so the expression , is (r^5)(s^3)(t^4) negative NO
(ii) s NEGATIVE, r POSITIVE, t NEGATIVE------------ (r^3) * (s)....NEGATIVE so the expression , is (r^5)(s^3)(t^4) negative YES
Here we have two answers after combining so INSUFFICIENT...

Answer: E
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bpdulog: Master | Next Rank: 500 Posts; Posts: 105; Joined: Sun Jan 25, 2009 6:55 pmFollowed by: 1 member; Thanked: 2 times

by bpdulog » Fri Oct 21, 2011 9:16 am

If either R or S is negative, the entire statement is negative.

If R and S is both positive/negative, the entire statement is positive.

So you need to figure out what about sign R and S is.

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