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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) pq is greater than n (2) q>p
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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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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: pq > 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). I'm uploading the screenshot
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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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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. I'm sorry about that man 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) pq is greater than n (2) q>p Given: \(p=integer>0\) and \(q=integer>0\). Question: is \(p>n\) and \(q>n\)? (1) \(pq>n\). 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): \(pq+q>n+p\) > \(n<0\). 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: 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) pq is greater than n (2) q>p Given: \(p=integer>0\) and \(q=integer>0\). Question: is \(p>n\) and \(q>n\)? (1) \(pq>n\). 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): \(pq+q>n+p\) > \(n<0\). 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: p and q greater than n [#permalink]
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23 Feb 2011, 18:42
From 1) pq is greater than n => pn > 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: p and q greater than n [#permalink]
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11 Mar 2011, 04:36
subhashghosh wrote: From 1) pq is greater than n
=> pn > 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. I like this different approach!!



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Gmatprep DS Questions 3 [#permalink]
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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 pq>n. This means p>n but q need not be greater than n. We have no further information on q. e.g. 52 > 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 qp 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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