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

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

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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
[Reveal] Spoiler: OA

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Kudos [?]: 9523 [0], given: 1203

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

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New post 19 Apr 2012, 02:42
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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.

Answer: C.
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Kudos [?]: 135771 [4], given: 12708

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

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New post 19 Apr 2012, 04:59

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

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New post 06 Oct 2017, 07:34
[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

Kudos [?]: 447 [0], given: 49

Re: If p q and r are integers, is p+q+r> 0 ?   [#permalink] 06 Oct 2017, 07:34
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