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(2) q^2 is positiveNight reader wrote:Is q positive?
(1) qp^2 is not negative
(2) q^2 is positive
First look, I was for A. But the question is testing the fundamentals:bblast wrote:I fell for C, but shovan's explanation makes it clear that it should be E ?
this is what I worked out before reading shovan's answer.aleph777 wrote:I believe the answer is C.
The wording in the statements is very subtle:
(1) qp^2 is not negative. This means the value could be zero or positive. Whenever you square either a positive or a negative number squared the result is positive number. But we also need to check for zero, and zero squared is zero. So p^2 could be + or 0. And the same goes for q. In order to get a positive number, if p^2 is positive, then q must also be positive. But because we can't rule out a value of qp^2 = 0, q could = 0 or +.
INSUFFICIENT
(2) q^2 is positive. Following the logic of exponents above, a negative or a positive squared creates a positive, so q could either be negative or positive.
INSUFFICIENT
Together, we know qp^2 is not negative and we know that q^2 is positive. Through statement 2 we know that q is not zero, and therefore q must be a positive number in order to make statement 1 true.
Thus, the answer is C.
Great point, Clock60!clock60 wrote:hi aleph777
i think you miss that p^2 can be equals to 0, as we have no restrictions on p, if p^2=0, then
(-q)*0>=0 here q-ve
(q)*0>=0 here q+ve
Night reader wrote:Is q positive?
(1) qp^2 is not negative
(2) q^2 is positive
thp510 wrote:Night reader wrote:Is q positive?
(1) qp^2 is not negative
(2) q^2 is positive
If (1) was re-worded to say: q(p^2) is not positive than the OA would be A correct? I initially thought it was q(p^2) and not (qp)^2
Thanks Anurag. Yes, I forgot about 0 (which is like a "third" sign).Anurag@Gurome wrote:thp510 wrote:Night reader wrote:Is q positive?
(1) qp^2 is not negative
(2) q^2 is positive
If (1) was re-worded to say: q(p^2) is not positive than the OA would be A correct? I initially thought it was q(p^2) and not (qp)^2
So the question will be :
Is q positive?
(1) q(p^2) is not positive
(2) q^2 is positive
Solution:
Let us first consider (1) alone.
This means q(p^2) <= 0
Let q = 3 and p = 0.
Here, q(p^2) = 0 and q is positive.
Next, let q = -3 and p = 0.
Again, q(p^2) = 0 and q is negative.
So, we cannot say from (1) that q is always positive or not.
Hence, (1) alone is not sufficient to answer the question.
Next consider (2) alone.
It only means that q is not zero.
But we cannot say whether q is positive or not.
Or (2) alone is not sufficient.
Next, combine both the statements together and check.
Even on combining, we get that q can be positive or negative.
This can be verified using (p,q) as (0,-3) and (0, 3) respectively.
Or both statements together are not sufficient to answer the question.
The correct answer is (E).
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