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# Is q positive?

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Math Expert
Joined: 02 Sep 2009
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14 Jan 2015, 02:29
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43% (00:52) correct 57% (00:37) wrong based on 118 sessions

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Is q positive?

(1) qp^2 is not negative
(2) q^2 is positive

Kudos for a correct solution.
[Reveal] Spoiler: OA

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14 Jan 2015, 11:20
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Bunuel wrote:
Is q positive?

(1) qp^2 is not negative
(2) q^2 is positive

Kudos for a correct solution.

st.1
if q=1, p=0 then answer to the original question is yes
if q=0, p=1 then answer to the original question is no.

hence st.1 alone is not sufficient

st.2
for both positive and negative values of q , q^2 can be positive. hence st.2 alone is not sufficient

st.1 + st.2

we know that q=0 is not a possible solution.because if q=0, then q^2 will not be positive. but if q takes some negative value, then p can still take zero as a value and can satisfy the condition given in st.1. hence st.1 and st.2 together are not sufficient. as both positive and negative values of q are possible.

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14 Jan 2015, 11:22
1
KUDOS
We can't really rewrite the information in the question, so we directly go into the statements:

(1) Since 0 is not negative, we don't know enough about q. q can be either 0, positive or negative, as the product of q and $$p^2$$ will be 0 if p is 0.

(2) $$q^2$$ is positive, that only tells us that q cannot be 0, but nothing more. It is also insufficient.

Both statements combined: From the second statement we know that q cannot be 0, but q can still be positive or negative, as either way, $$qp^2$$ can be 0 and therefore fulfil the condition in statement 1.

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19 Jan 2015, 04:17
Bunuel wrote:
Is q positive?

(1) qp^2 is not negative
(2) q^2 is positive

Kudos for a correct solution.

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07 Feb 2015, 11:22
Yep also agree.

q>0?

[1] (qp)^2 >= 0.
If it is equal to zero, then q or p equal to zero.
If it is positive, then q,p are both positiive or both negative. So, NS.

[2] q^2>0. So, q cannot be zero. But, q could be positive or negative. NS.

[1,2] q is not zero (statement 2), but it could be positive or negative, statements 1 and 2. NS. ANS E
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24 Aug 2017, 05:41
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Re: Is q positive?   [#permalink] 24 Aug 2017, 05:41
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