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# If p q and r are integers, is p+q+r> 0 ?

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Board of Directors
Joined: 01 Sep 2010
Posts: 3430
If p q and r are integers, is p+q+r> 0 ? [#permalink]

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19 Apr 2012, 03:20
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Difficulty:

35% (medium)

Question Stats:

74% (01:20) correct 26% (01:29) wrong based on 74 sessions

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If p, q, and r are integers, is p+q+r> 0 ??

(1) p + r = q

(2) r^2 < -q

The first one is insufficient : 3 + 2 = 5 > 0 YES or 0+0=0 NO

The second one we do not know about p

Combined: from 2 q is negative (this is the meaning), so 1 is also as consequence = to a negative value .......... negative + negative < 0 always. answer is NO Suff.

here is the tricky thing: if i look at the problem as if I were during the exam and under time pressure I could say: p + r = q so we have 2q > 0 .....NO sufficient and the answer would be A not C.

BUT if I use the two statement combined with the substitution method I have

q is postive ( we know from second statement that q per se is negative but time minus we have q: positive in the end) so p + r = q --------> r = q - p

So we have p + q + q - p > 0 -------- > 2q >0 Suff, answer would be C, again.

Please clarify this weird situation. Thanks

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Joined: 02 Sep 2009
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Re: If p q and r are integers, is p+q+r> 0 ? [#permalink]

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19 Apr 2012, 03:42
4
carcass wrote:
If p, q, and r are integers, is p+q+r> 0 ??

(1) p + r = q

(2) r^2 < -q

The first one is insufficient : 3 + 2 = 5 > 0 YES or 0+0=0 NO

The second one we do not know about p

Combined: from 2 q is negative (this is the meaning), so 1 is also as consequence = to a negative value .......... negative + negative < 0 always. answer is NO Suff.

here is the tricky thing: if i look at the problem as if I were during the exam and under time pressure I could say: p + r = q so we have 2q > 0 .....NO sufficient and the answer would be A not C.

BUT if I use the two statement combined with the substitution method I have

q is postive ( we know from second statement that q per se is negative but time minus we have q: positive in the end) so p + r = q --------> r = q - p

So we have p + q + q - p > 0 -------- > 2q >0 Suff, answer would be C, again.

Please clarify this weird situation. Thanks

If p, q, and r are integers, is p+q+r> 0 ?

(1) p + r = q --> original question becomes is $$q+q>0$$? --> is $$2q>0$$? --> is $$q>0$$? We don't know that, hence this statement is not sufficient.

(2) r^2 < -q --> $$q<0$$ (because if q is positive (or zero) then we would have that $$r^2<negative$$ (or $$r^2<0$$), which is not possible since square of a number is always non-negative). Not sufficient.

(1)+(2) From (1) the question became: "is $$q>0$$?" while (2) say that $$q<0$$, hence the answer to the question is NO. Sufficient.

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Re: If p q and r are integers, is p+q+r> 0 ? [#permalink]

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19 Apr 2012, 05:59
mmmmmmmm................study, study, study.......practice, practice, practice.

Thanks Mod.
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Posts: 1734
Re: If p q and r are integers, is p+q+r> 0 ? [#permalink]

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06 Oct 2017, 08:34
[quote="carcass"]If p, q, and r are integers, is p+q+r> 0 ??

(1) p + r = q

(2) r^2 < -q

FROM 1

it is possible that p+r = q = 0 or p+r = q = 3 .... insuff

from 2

r^2 < -q .... r is 0 or any integer and q is -ve integer .... insufficient

both

p+r = -ve = q , thus question becomes is is 2q > 0 , answer is definitely not .......C
Re: If p q and r are integers, is p+q+r> 0 ?   [#permalink] 06 Oct 2017, 08:34
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