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# If p and q are negative, is p / q > 1 (1) The positive

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If p and q are negative, is p / q > 1 (1) The positive [#permalink]  07 Feb 2011, 07:08
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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
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Re: Algebra DS [#permalink]  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 p-q<0?

(1) The positive diff erence between p and q is 2 --> |p-q|=2: either p-q>0 (answer NO) and p-q=2 or p-q<0 (answer YES) and p-q=-2. Not sufficient.

(2) q - p < 1 (p-q>-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) p-q>-1 then from (1) p-q=2 so p-q>0 and we have the answer NO. Sufficient.

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Re: Algebra DS [#permalink]  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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Negative integers P & Q [#permalink]  02 Apr 2012, 03:14
If p and q are negative, is \frac{p}{q} greater than 1 ?

(1) The positive di¤erence between p and q is 2.
(2) q - p < 1

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Re: Negative integers P & Q [#permalink]  02 Apr 2012, 03:29
enigma123 wrote:
If p and q are negative, is \frac{p}{q} greater than 1 ?

(1) The positive di¤erence between p and q is 2.
(2) q - p < 1

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Re: Algebra DS [#permalink]  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 p-q<0?

(1) The positive diff erence between p and q is 2 --> |p-q|=2: either p-q>0 (answer NO) and p-q=2 or p-q<0 (answer YES) and p-q=-2. Not sufficient.

I'm very confused. First why do you have absolute value? How did you derive p-q>0? p-q<0? p-q=-2? Any way to demonstrate? or explain the concepts? Thank you very much.

rxs0005 wrote:
(2) q - p < 1 (p-q>-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?

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Re: Algebra DS [#permalink]  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 p-q<0?

(1) The positive diff erence between p and q is 2 --> |p-q|=2: either p-q>0 (answer NO) and p-q=2 or p-q<0 (answer YES) and p-q=-2. Not sufficient.

I'm very confused. First why do you have absolute value? How did you derive p-q>0? p-q<0? p-q=-2? Any way to demonstrate? or explain the concepts? Thank you very much.

rxs0005 wrote:
(2) q - p < 1 (p-q>-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 |p-q|=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|\leq{-(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|\leq{some \ expression}. For example: |5|=5;

So, for |p-q|=2:
If p-q>0 then |p-q|=p-q=2 (example: p=-3 and q=-5);
If p-q<0 then |p-q|=-(p-q)=q-p=2 (example: p=-5 and q=-3);

Check Absolute Value chapter of Math Book for more: math-absolute-value-modulus-86462.html

As 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]  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 |p-q| = 2
so we have

if (p-q) = 2 then p > q

(p-q) = -2 then q > p

datanot sufficient

(B) q - p < 1 or p-q > -1 (multiply both sides by -ve and flip the sign)

if(p>q)
p = -0.5
q = -1

then p-q > -1

if(p<q)
p = -1
q = -0.5

then p-q > -1

datanot sufficient

(C)

only possibility
if(p>q)
p = -0.5 / -3
q = -1 / -5
then p-q > -1
also if (p-q) = 2 then p > q

opposite not true
if(p<q)
p = -5
q = -3

(p-q) = -2 then q > p but p-q not > -1

then p-q > -1 [not possible]
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Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]  05 Apr 2012, 00:06
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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."
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Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]  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 = |p-q| = 2
implies p-q > 0 or p-q < 0
if p-q > 0 then
p>q then p/q> 1

But if p-q < 0 then p<q or p/q cannot be greater than 1
anyway st. (1) gives two options which leads "insufficient"

st. (2) q-p<1 (this could be p-q < -1 which mean p-q> -1 )
implies q-p = 0 or q-p is -ve
if q-p=0then p/q > 1 is not possible

But if q-p 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)
p-q > -1 and p-q =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]  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 = |p-q| = 2
implies p-q > 0 or p-q < 0
if p-q > 0 then
p>q then p/q> 1

But if p-q < 0 then p<q or p/q cannot be greater than 1
anyway st. (1) gives two options which leads "insufficient"

|p-q| = 2 gives you two cases: Either p-q = 2 or q-p = 2
We do not know whether p is smaller than q.

st. (2) q-p<1 (this could be p-q < -1 which mean p-q> -1 )

q-p < 1 is the same as p-q > -1 (when you multiply both sides by -1)

implies q-p = 0 or q-p is -ve
if q-p=0then p/q > 1 is not possible

But if q-p 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 q-p<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)
p-q > -1 and p-q =2 implies
p>q or we can say p/q>1
Sufficient

Combining, stmnt 1 tells us that either p-q = 2 or q-p = 2. Stmnt 2 tells us that q-p<1. Hence q-p cannot be 2. Therefore, p-q 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)

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Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]  23 Apr 2012, 21:40
Guess this is a 700+ level problem.
Anyway, excellent explanation Karishma
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Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]  22 May 2012, 18:26
i was able to solve but within 3 minutes.... how to solve this question in less than 2 min.
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Re: If p and q are negative, is p / q > 1 (1) The positive [#permalink]  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. q-p<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 q-p<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.
Re: If p and q are negative, is p / q > 1 (1) The positive   [#permalink] 27 Nov 2012, 18:56
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