Are positive integers p and q both greater than n ?

Question

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

Bunuel · Accepted Answer

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.

Matt1177 · Answer

(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

AmrithS · Answer

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!

stanford2012 · Answer

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).

MHIKER · Answer

Your approach is too good

mbafall2011 · Answer

I second that! In my attempt to solve it i did a whole bunch of things but this was the easiest!

subhashghosh · Answer

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.

mourinhogmat1 · Answer

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.

yannichc · Answer

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

bumpbot · Answer

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Are positive integers p and q both greater than n ?

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Are positive integers p and q both greater than n ?

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