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

(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

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.

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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.

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

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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If iam WRONG correct me, If I am correct and cleared your doubt thank me

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.