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Are positive integers p and q both greater than n ?

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zisis
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Are positive integers p and q both greater than n ? [#permalink] New post  Updated on: 16 Oct 2019, 05:56
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Are positive integers p and q both greater than n ?

(1) p - q is greater than n
(2) q > p
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Originally posted by zisis on 14 Jul 2010, 13:40.
Last edited by Bunuel on 16 Oct 2019, 05:56, edited 3 times in total.
Edited the question and added the OA
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Are positive integers p and q both greater than n ? [#permalink] New post  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.

Answer: C.
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Matt1177
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Re: Are positive integers p and q both greater than n ? [#permalink] New post  17 Feb 2011, 06:59
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(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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Re: Are positive integers p and q both greater than n ? [#permalink] New post  Updated on: 22 Feb 2011, 01:00
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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 :P

Sorry!

Originally posted by AmrithS on 21 Feb 2011, 23:13.
Last edited by AmrithS on 22 Feb 2011, 01:00, edited 1 time in total.
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Re: Are positive integers p and q both greater than n ? [#permalink] New post  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 positive integers p and q both greater than n ? [#permalink] New post  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.

Answer: C.


Your approach is too good
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Re: Are positive integers p and q both greater than n ? [#permalink] New post  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.

Answer: C.


Your approach is too good


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

Answer is C.
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Re: Are positive integers p and q both greater than n ? [#permalink] New post  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: Are positive integers p and q both greater than n ? [#permalink] New post  11 Apr 2023, 04:56
after eliminating the two statements we can line them up


p-q-n>0
q-p>0

adding them together we get

-n>0 , therfore n <0

since we know p and q are positive integers, we know that both p and q are greater than n

or

p-q>n
q>p

p>n+p

0>n

therefore P and Q both > n
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Re: Are positive integers p and q both greater than n ? [#permalink]
11 Apr 2023, 04:56
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