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# Are positive integers p and q both greater than n ?

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Manager
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Are positive integers p and q both greater than n ? [#permalink]

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14 Jul 2010, 13:40
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Are positive integers p and q both greater than n

(1) p-q is greater than n
(2) q>p
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Jun 2013, 04:24, edited 2 times in total.
Edited the question and added the OA
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Re: p and q greater than n [#permalink]

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14 Jul 2010, 15:06
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zisis wrote:
are positive integers p and q both greater than n

(1) p-q is greater than n
(2) q>p

Given: $$p=integer>0$$ and $$q=integer>0$$. Question: is $$p>n$$ and $$q>n$$?

(1) $$p-q>n$$. Clearly insufficient.

(2) $$q>p$$, no info about $$n$$. Not sufficient.

(1)+(2) Sum (1) and (2) (we can safely do this as their signs are in the same direction): $$p-q+q>n+p$$ --> $$n<0$$. As given that both $$p$$ and $$q$$ are positive then they are greater than negative $$n$$. Sufficient.

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Re: DS: positive integers p and q [#permalink]

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17 Feb 2011, 06:59
(i) Clearly, not sufficient;
(ii) Clearly, not sufficient.

Taken together:
We can subtract two inequalities with different signs:
p-q > n -----p > n+q
q > p -------p < q
Subtract and get 0 > n

Since n is less than zero and p and q are positive integers, then obviously n < p or q
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Are p and q both greater than n? [#permalink]

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21 Feb 2011, 23:13
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Are p and q both greater than n?

(1) p - q is greater than n
(2) q>p

EDIT:

p and q are positive integers.... I missed that part

Sorry!
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Last edited by AmrithS on 22 Feb 2011, 01:00, edited 1 time in total.
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Re: Are p and q both greater than n? [#permalink]

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22 Feb 2011, 00:46
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Are you sure the correct answer is C?

Let's do two cases for which the stated conditions hold.

Case 1: p= 2, q=3
From condition 1 it follows that n < -1, i.e. n is smaller than both p and q.

Case 2: p=-3, q=-2

From condition 1 it follows that n <-1, i.e. it is unclear whether n is smaller or larger than p and q.

Unless the question states that p and q are positive (integers) I think the correct solution is E (not C).
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Re: Are p and q both greater than n? [#permalink]

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22 Feb 2011, 00:59
stanford2012 wrote:
Are you sure the correct answer is C?

Let's do two cases for which the stated conditions hold.

Case 1: p= 2, q=3
From condition 1 it follows that n < -1, i.e. n is smaller than both p and q.

Case 2: p=-3, q=-2

From condition 1 it follows that n <-1, i.e. it is unclear whether n is smaller or larger than p and q.

Unless the question states that p and q are positive (integers) I think the correct solution is E (not C).

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Re: Are p and q both greater than n? [#permalink]

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22 Feb 2011, 01:03
stanford2012 wrote:
Are you sure the correct answer is C?

Let's do two cases for which the stated conditions hold.

Case 1: p= 2, q=3
From condition 1 it follows that n < -1, i.e. n is smaller than both p and q.

Case 2: p=-3, q=-2

From condition 1 it follows that n <-1, i.e. it is unclear whether n is smaller or larger than p and q.

Unless the question states that p and q are positive (integers) I think the correct solution is E (not C).

Gotcha man
Thanks!
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Re: Are p and q both greater than n? [#permalink]

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22 Feb 2011, 02:06
Expert's post
Merging similar topics.

Entwistle wrote:
Are p and q both greater than n?

(1) p - q is greater than n
(2) q>p

EDIT:

p and q are positive integers.... I missed that part

Sorry!

Entwistle you should type the question EXACTLY as it's given in the source.
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Re: Are p and q both greater than n? [#permalink]

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22 Feb 2011, 07:15
Bunuel wrote:
Merging similar topics.

Entwistle wrote:
Are p and q both greater than n?

(1) p - q is greater than n
(2) q>p

EDIT:

p and q are positive integers.... I missed that part

Sorry!

Entwistle you should type the question EXACTLY as it's given in the source.

Wont happen in the future!
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Re: p and q greater than n [#permalink]

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22 Feb 2011, 08:25
Bunuel wrote:
zisis wrote:
are positive integers p and q both greater than n

(1) p-q is greater than n
(2) q>p

Given: $$p=integer>0$$ and $$q=integer>0$$. Question: is $$p>n$$ and $$q>n$$?

(1) $$p-q>n$$. Clearly insufficient.

(2) $$q>p$$, no info about $$n$$. Not sufficient.

(1)+(2) Sum (1) and (2) (we can safely do this as their signs are in the same direction): $$p-q+q>n+p$$ --> $$n<0$$. As given that both $$p$$ and $$q$$ are positive then they are greater than negative $$n$$. Sufficient.

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Re: p and q greater than n [#permalink]

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22 Feb 2011, 09:07
(1) is not sufficient, as p is greater but we don't know about q
(2) this statement doesn't relate p and q with n, so it is insufficient as well.

With both statements together, we know that n is negative.
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Re: p and q greater than n [#permalink]

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23 Feb 2011, 13:11
Baten80 wrote:
Bunuel wrote:
zisis wrote:
are positive integers p and q both greater than n

(1) p-q is greater than n
(2) q>p

Given: $$p=integer>0$$ and $$q=integer>0$$. Question: is $$p>n$$ and $$q>n$$?

(1) $$p-q>n$$. Clearly insufficient.

(2) $$q>p$$, no info about $$n$$. Not sufficient.

(1)+(2) Sum (1) and (2) (we can safely do this as their signs are in the same direction): $$p-q+q>n+p$$ --> $$n<0$$. As given that both $$p$$ and $$q$$ are positive then they are greater than negative $$n$$. Sufficient.

I second that! In my attempt to solve it i did a whole bunch of things but this was the easiest!
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Re: p and q greater than n [#permalink]

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23 Feb 2011, 18:42
From 1) p-q is greater than n

=> p-n > q (a +ve value) so p > n, but nothing can be inferred about q, so (1) is not sufficient.

From (2) q > p but nothing is given about n, so (2) is not sufficient.

So combining (1) and (2) we can see that q > p > n.

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Re: p and q greater than n [#permalink]

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11 Mar 2011, 04:36
subhashghosh wrote:
From 1) p-q is greater than n

=> p-n > q (a +ve value) so p > n, but nothing can be inferred about q, so (1) is not sufficient.

From (2) q > p but nothing is given about n, so (2) is not sufficient.

So combining (1) and (2) we can see that q > p > n.

I like this different approach!!
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20 Mar 2012, 17:45
Another one...

many thanks,
V.
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Re: Gmatprep DS Questions 3 [#permalink]

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20 Mar 2012, 18:35
1. A is insufficient because we know p-q>n. This means p>n but q need not be greater than n. We have no further information on q. e.g. 5-2 > 2 but here q = n. So, rule out A.

2. B is insufficient as no information is given on n. So, we can't compare n to p and q.

Together C: we know that q-p MUST be negative and that makes n negative. Since p and q are positive integers its sufficient to answer the question that BOTH p and Q are greater than n.

I suppose the mistake you made is that you didn't read the key word POSITIVE INTEGERS.
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Re: Gmatprep DS Questions 3 [#permalink]

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20 Mar 2012, 23:22
Expert's post
vix wrote:
Another one...

many thanks,
V.

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Re: Are positive integers p and q both greater than n ? [#permalink]

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04 Nov 2013, 05:50
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Re: Are positive integers p and q both greater than n ? [#permalink]

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07 Jan 2015, 05:15
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Re: Are positive integers p and q both greater than n ?   [#permalink] 07 Jan 2015, 05:15
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