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If p and q are negative, is p/q > 1 [#permalink]
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07 Feb 2011, 07:08
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If p and q are negative, is p/q > 1 (1) The positive difference between p and q is 2. (2) q  p < 1
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Re: Algebra DS [#permalink]
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07 Feb 2011, 07:49
rxs0005 wrote: If p and q are negative, is p / q > 1
(1) The positive diff erence between p and q is 2. (2) q  p < 1 If p and q are negative, is p / q > 1 Given: \(p<0\) and \(q<0\). Question: is \(\frac{p}{q}>1\) > multiply both sides by \(q\) and as it's negative flip the sign: is \(p<q\)? or is \(pq<0\)? (1) The positive diff erence between p and q is 2 > \(pq=2\): either \(pq>0\) (answer NO) and \(pq=2\) or \(pq<0\) (answer YES) and \(pq=2\). Not sufficient. (2) q  p < 1 (\(pq>1\)) > if \(q=1\) and \(p=1\) then the answer will be NO but if \(q=1\) and \(p=1.5\) then the answer will be YES. Not sufficient. (1)+(2) As from (2) \(pq>1\) then from (1) \(pq=2\) so \(pq>0\) and we have the answer NO. Sufficient. Answer: C.
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Re: Algebra DS [#permalink]
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07 Feb 2011, 08:00
Stmt 1: let p=5, q=3 Ans : YES, but as its given positive difference is 2 the values can be interchanged Ans : NO insuff
Stmt 2 : q  p < 1 > q < 1 + p ,, p = 1, q=2 Ans : NO. p = 3, q = 4, Ans : NO, insuff
Combining,, p = 2, q= 4, NO.. p=1,q=3 NO Suff..
very lengthy method.. can anyone pls post easier way to deal with this sort of probs



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Re: Algebra DS [#permalink]
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03 Apr 2012, 20:43
Bunuel wrote: rxs0005 wrote: If p and q are negative, is p / q > 1
(1) The positive diff erence between p and q is 2. (2) q  p < 1 If p and q are negative, is p / q > 1 Given: \(p<0\) and \(q<0\). Question: is \(\frac{p}{q}>1\) > multiply both sides by \(q\) and as it's negative flip the sign: is \(p<q\)? or is \(pq<0\)? (1) The positive diff erence between p and q is 2 > \(pq=2\): either \(pq>0\) (answer NO) and \(pq=2\) or \(pq<0\) (answer YES) and \(pq=2\). Not sufficient. I'm very confused. First why do you have absolute value? How did you derive pq>0? pq<0? pq=2? Any way to demonstrate? or explain the concepts? Thank you very much. rxs0005 wrote: (2) q  p < 1 (\(pq>1\)) > if \(q=1\) and \(p=1\) then the answer will be NO but if \(q=1\) and \(p=1.5\) then the answer will be YES. Not sufficient. How can q and p both equal 1? [/quote]



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Re: Algebra DS [#permalink]
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04 Apr 2012, 01:35
bohdan01 wrote: Bunuel wrote: rxs0005 wrote: If p and q are negative, is p / q > 1
(1) The positive diff erence between p and q is 2. (2) q  p < 1 If p and q are negative, is p / q > 1 Given: \(p<0\) and \(q<0\). Question: is \(\frac{p}{q}>1\) > multiply both sides by \(q\) and as it's negative flip the sign: is \(p<q\)? or is \(pq<0\)? (1) The positive diff erence between p and q is 2 > \(pq=2\): either \(pq>0\) (answer NO) and \(pq=2\) or \(pq<0\) (answer YES) and \(pq=2\). Not sufficient. I'm very confused. First why do you have absolute value? How did you derive pq>0? pq<0? pq=2? Any way to demonstrate? or explain the concepts? Thank you very much. rxs0005 wrote: (2) q  p < 1 (\(pq>1\)) > if \(q=1\) and \(p=1\) then the answer will be NO but if \(q=1\) and \(p=1.5\) then the answer will be YES. Not sufficient. How can q and p both equal 1? "The positive difference between p and q is 2" means that the distance between p and q is 2, which can be expressed as \(pq=2\). For example positive difference between 5 and 3 is 2: 5(3)=2. Next: Absolute value properties:When \(x\leq{0}\) then \(x=x\), or more generally when \(some \ expression\leq{0}\) then \(some \ expression={(some \ expression)}\). For example: \(5=5=(5)\); When \(x\geq{0}\) then \(x=x\), or more generally when \(some \ expression\geq{0}\) then \(some \ expression={some \ expression}\). For example: \(5=5\); So, for \(pq=2\): If \(pq>0\) then \(pq=pq=2\) (example: \(p=3\) and \(q=5\)); If \(pq<0\) then \(pq=(pq)=qp=2\) (example: \(p=5\) and \(q=3\)); Check Absolute Value chapter of Math Book for more: mathabsolutevaluemodulus86462.htmlAs for \(p=q=1\): unless it is explicitly stated otherwise, different variables can represent the same number. Hope it's clear.
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Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]
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04 Apr 2012, 06:21
C
bookmarking
given p<0 & q<0
find p/q>1 or p < q
(A) The positive diff erence between p and q is 2.
there pq = 2 so we have
if (pq) = 2 then p > q
(pq) = 2 then q > p
datanot sufficient
(B) q  p < 1 or pq > 1 (multiply both sides by ve and flip the sign)
if(p>q) p = 0.5 q = 1
then pq > 1
if(p<q) p = 1 q = 0.5
then pq > 1
datanot sufficient
(C)
only possibility if(p>q) p = 0.5 / 3 q = 1 / 5 then pq > 1 also if (pq) = 2 then p > q
opposite not true if(p<q) p = 5 q = 3
(pq) = 2 then q > p but pq not > 1
then pq > 1 [not possible]



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Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]
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05 Apr 2012, 00:06
rxs0005 wrote: If p and q are negative, is p / q > 1
(1) The positive diff erence between p and q is 2. (2) q  p < 1 It is a good question and you can solve it logically too. Given p and q are negative so p/q must be positive (negative/negative). Whether p/q is greater than 1 depends on whether p < q. If p < q, then yes, p/q > 1 (if p is more negative, it has higher absolute value). Else p/q is not greater than 1. So we have to find out whether p is less than q. (1) The positive diff erence between p and q is 2. This only tells us that the difference between them is 2. It doesn't tell us which one is greater so not sufficient. (2) q  p < 1 This tells us that if q is greater than p, it is less than 1 greater than p. q can be equal to p or less than p but if it is greater than p, it is certainly less than 1 greater than p. This means (q = 1.2, p = 1.9), (q = 23, p = 23.4), (q = 3, p = 3), (q = 4, p = 2) are possible pairs (and many more). Again, we don't know whether p is greater or q so not sufficient. Using both together, we know that the difference between p and q is 2 and if q is greater than p, it is less than 1 greater than p. Since the difference between them is 2, q cannot be greater than p so p must be greater than q. We can say that "No. p is not less than q." Hence sufficient. Answer (C)
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Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]
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06 Apr 2012, 23:26
rxs0005 wrote: If p and q are negative, is p / q > 1
(1) The positive diff erence between p and q is 2. (2) q  p < 1 st. (1) the +ve difference = pq = 2 implies pq > 0 or pq < 0 if pq > 0 then p>q then p/q> 1 But if pq < 0 then p<q or p/q cannot be greater than 1 anyway st. (1) gives two options which leads "insufficient" st. (2) qp<1 (this could be pq < 1 which mean pq> 1 ) implies qp = 0 or qp is ve if qp=0then p/q > 1 is not possible But if qp is ve then it gives different values of p and q which says both  p/q>1 or p/q<1 however st.(2) insufficient Combining together st. (1) and st. (2) pq > 1 and pq =2 implies p>q or we can say p/q>1 Sufficient hope i got it correct frm bunnel and karishma



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Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]
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07 Apr 2012, 04:36
rxs0005 wrote: If p and q are negative, is p / q > 1
(1) The positive diff erence between p and q is 2. (2) q  p < 1 st. (1) the +ve difference = pq = 2 implies pq > 0 or pq < 0 if pq > 0 then p>q then p/q> 1 But if pq < 0 then p<q or p/q cannot be greater than 1 anyway st. (1) gives two options which leads "insufficient" pq = 2 gives you two cases: Either pq = 2 or qp = 2 We do not know whether p is smaller than q.st. (2) qp<1 (this could be pq < 1 which mean pq> 1 ) qp < 1 is the same as pq > 1 (when you multiply both sides by 1) implies qp = 0 or qp is ve if qp=0then p/q > 1 is not possible But if qp is ve then it gives different values of p and q which says both  p/q>1 or p/q<1 however st.(2) insufficient If qp<1, q could be greater or p could be greater. So we again cannot figure whether p is smaller than q Combining together st. (1) and st. (2) pq > 1 and pq =2 implies p>q or we can say p/q>1 Sufficient Combining, stmnt 1 tells us that either pq = 2 or qp = 2. Stmnt 2 tells us that qp<1. Hence qp cannot be 2. Therefore, pq must be 2. p must be greater than q. We know that p is greater so p/q is not greater than 1 (since p and q are both negative) Answer (C).
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Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]
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27 Nov 2012, 18:56
Luckily I went for the diagram and was able to do it in under 2 minutes. Draw a line with 0 in the middle. p and q are both to the left of 0. We only know this much. We don't know their position with respect to 0, i. e we don't know whether q or p is closer to 0 or even whether p and q are the same number, both negative. Question asks whether p/q>1 meaning is p more negative than q? This suggests that the question is about the position of p and q with respect to each other and 0. 1. the positive difference between them is 2 suggests that the distance between p and q is 2 units. this only tells us the distance and not which one is more negative than the other. Not Sufficient. 2. qp<1 suggests that the difference between the two is less than 1. but their degree of negativity is not clear. by itself, this statement points to the possibility that q and p may be the same number; 2(2)=0<1, or one of them could be slightly more negative and still have satisfy qp<1. so Not Sufficient. when you take 1 and 2 together, the possibility that the two are the same number is eliminated because 1 says that the two numbers are 2 units apart. so now, the number line will have p and q standing at 2 units apart and based on statement 2, q has to be more negative than p. Hence C. vikram4689 wrote: i was able to solve but within 3 minutes.... how to solve this question in less than 2 min.



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Re: Algebra DS [#permalink]
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17 Feb 2014, 12:35
Bunuel wrote: rxs0005 wrote: If p and q are negative, is p / q > 1
(1) The positive diff erence between p and q is 2. (2) q  p < 1 If p and q are negative, is p / q > 1 Given: \(p<0\) and \(q<0\). Question: is \(\frac{p}{q}>1\) > multiply both sides by \(q\) and as it's negative flip the sign: is \(p<q\)? or is \(pq<0\)? (1) The positive diff erence between p and q is 2 > \(pq=2\): either \(pq>0\) (answer NO) and \(pq=2\) or \(pq<0\) (answer YES) and \(pq=2\). Not sufficient. (2) q  p < 1 (\(pq>1\)) > if \(q=1\) and \(p=1\) then the answer will be NO but if \(q=1\) and \(p=1.5\) then the answer will be YES. Not sufficient. (1)+(2) As from (2) \(pq>1\) then from (1) \(pq=2\) so \(pq>0\) and we have the answer NO. Sufficient. Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that pq>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because pq>1 (from I) could mean that pq<0 or pq>0 .. Answer: C. Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that pq>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because pq>1 (from I) could mean that pq<0 or pq>0 ..



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Re: Algebra DS [#permalink]
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17 Feb 2014, 14:16
damamikus wrote: Bunuel wrote: rxs0005 wrote: If p and q are negative, is p / q > 1
(1) The positive diff erence between p and q is 2. (2) q  p < 1 If p and q are negative, is p / q > 1 Given: \(p<0\) and \(q<0\). Question: is \(\frac{p}{q}>1\) > multiply both sides by \(q\) and as it's negative flip the sign: is \(p<q\)? or is \(pq<0\)? (1) The positive diff erence between p and q is 2 > \(pq=2\): either \(pq>0\) (answer NO) and \(pq=2\) or \(pq<0\) (answer YES) and \(pq=2\). Not sufficient. (2) q  p < 1 (\(pq>1\)) > if \(q=1\) and \(p=1\) then the answer will be NO but if \(q=1\) and \(p=1.5\) then the answer will be YES. Not sufficient. (1)+(2) As from (2) \(pq>1\) then from (1) \(pq=2\) so \(pq>0\) and we have the answer NO. Sufficient. Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that pq>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because pq>1 (from I) could mean that pq<0 or pq>0 .. Answer: C. Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that pq>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because pq>1 (from I) could mean that pq<0 or pq>0 .. As @grumpytesttaker said the best way to solve such problems is to use the number line. The question stem says that p and q are negative so we can have 2 scenarios (p to the left of q or p to the right of q) Now to definitively say whether p/q>1 we need to find if p > q as both are negative so there is no question of signs. Since both are negative nos p > q only if p is to the left of q on the Number Line. So we just need to find if p is to the left or right of q. (1) p  q = 2, this means p and q have a separation of 2. But this is possible if p is to the left of q or p is to the right of q. So this statement doesn't help us. Not Sufficient. (2) q  p < 1, Since both nos are negative we can rewrite this statement as p  q < 1. Now if p is to the left of q (p > q) then the separation between p and q have to be less than 1. But if p is to the right of q (p < q) then the separation can be anything. Since this statement doesn't say if p is to the left or right of q, it is Not Sufficient. (1) & (2) Now if we combine the 2 statements we can see that p cannot be to the left of q because (1)  p  q = 2 and (2)  p  q < 1 together is not possible. So the only possibility is p is to the right of q, which answers the question, since p < q hence p/q < 1 So (1) & (2) put together answers the question. Sufficient. Answer C
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Re: Algebra DS [#permalink]
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18 Feb 2014, 01:28
damamikus wrote: Bunuel wrote: rxs0005 wrote: If p and q are negative, is p / q > 1
(1) The positive diff erence between p and q is 2. (2) q  p < 1 If p and q are negative, is p / q > 1 Given: \(p<0\) and \(q<0\). Question: is \(\frac{p}{q}>1\) > multiply both sides by \(q\) and as it's negative flip the sign: is \(p<q\)? or is \(pq<0\)? (1) The positive difference between p and q is 2 > \(pq=2\): either \(pq>0\) (answer NO) and \(pq=2\) or \(pq<0\) (answer YES) and \(pq=2\). Not sufficient. (2) q  p < 1 (\(pq>1\)) > if \(q=1\) and \(p=1\) then the answer will be NO but if \(q=1\) and \(p=1.5\) then the answer will be YES. Not sufficient. (1)+(2) As from (2) \(pq>1\) then from (1) \(pq=2\) so \(pq>0\) and we have the answer NO. Sufficient. Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that pq>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because pq>1 (from I) could mean that pq<0 or pq>0 .. Answer: C. Hi Bunuel! Could you please explain to me, why you concluded from (1) + (2) that pq>0? The question doesn't say that p and q are integers, so shouldn't the answer be E then? because pq>1 (from I) could mean that pq<0 or pq>0 .. Sure. From (1) we have two possible cases: \(pq=2\) or \(pq=2\). Since from (1) we have that \(pq>1\), then \(pq\neq{2}\), thus \(pq=2>0\). Does this make sense?
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Re: If p and q are negative, is p/q > 1 [#permalink]
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