consecutive integers

[wilson4mba]

If p , q , r, and s are consecutive integers, with p <q < r <s , is pr< qs ?
(1) pq<rs
(2) ps<qr

[Rahul@gurome]

If p , q , r, and s are consecutive integers, with p <q < r <s , is pr< qs ?
(1) pq<rs
(2) ps<qr

Given: p , q , r, and s are consecutive integers, with p <q < r <s.
Thus, q = (p + 1), r = (p + 2) and s = (p + 3)

Let's find the condition for which pr < qs holds true!
... pr < qs
=> p*(p + 2) < (p + 1)*(p + 3)
=> (p² + 2p) < (p² + 4p + 3)
=> 2p < (4p + 3)
=> 2p > -3
=> p > -3/2

Therefore pr < qs if p is greater than -3/2.

Statement 1: pq < rs
... pq < rs
=> p*(p + 1) < (p + 2)*(p + 3)
=> (p² + p) < (p² + 5p + 6)
=> p < (5p + 6)
=> 4p > -6
=> p > -3/2

This is the same condition. Thus pr < qs!

Sufficient.

Statement 1: ps < qr
... ps < qr
=> p*(p + 3) < (p + 1)*(p + 2)
=> (p² + 3p) < (p² + 3p + 2)
=> 3p < (3p + 2)
=> 0 < 2

This means ps < qr for any four consecutive integers. Thus this is a redundant information as this information is already hidden in the question itself.

Not sufficient.

The correct answer is A.

[wilson4mba]

i found it one of the forum's free practice test. I have copied the question correctly. I guess then there could be mistake in the question itself.

[Night reader]

Rahul, I got the same solution independently. Theoretically, 0<2 for statement(2)

[TOPGMAT]

Hi Rahul,
p,q,r,s
0,1,2,3

=> ps < qr ?

why did you say

=> 3p < (3p + 2)
=> 0 < 2

This is effectively not a condition.?

[Rahul@gurome]

Hi Rahul,

why did you say

=> 3p < (3p + 2)
=> 0 < 2

This is effectively not a condition.?

Because this doesn't add any new information to the question. This means ps < qr for any four consecutive integers. Thus statement 2 is redundant.