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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.
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.
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!
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.
Re: Are positive integers p and q both greater than n ?
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01 Jul 2018, 18:45
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65% (01:37) correct 
