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wilson4mba
- Junior | Next Rank: 30 Posts
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If p , q , r, and s are consecutive integers, with p <q < r <s , is pr< qs ?
(1) pq<rs
(2) ps<qr
(1) pq<rs
(2) ps<qr
Given: p , q , r, and s are consecutive integers, with p <q < r <s.wilson4mba wrote:If p , q , r, and s are consecutive integers, with p <q < r <s , is pr< qs ?
(1) pq<rs
(2) ps<qr
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.
