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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pm; Thanked: 165 times; Followed by:70 members

PS - Inequality

by karthikpandian19 » Wed Jul 04, 2012 7:21 pm

If p, q and r are positive numbers such that p = (40((r^2) + r) / (q+r)) - 17, and 1 < q < r, which of the following could be the value of p?

(A) 10

(B) 15

(C) 17

(D) 23

(E) 24

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Source: Beat The GMAT — Problem Solving | Wed Jul 04, 2012 7:21 pm

eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pm; Thanked: 339 times; Followed by:49 members; GMAT Score:770

by eagleeye » Wed Jul 04, 2012 7:42 pm

karthikpandian19 wrote:If p, q and r are positive numbers such that p = (40((r^2) + r) / (q+r)) - 17, and 1 < q < r, which of the following could be the value of p?

We are given r>q>1, and asked for a possible value of p, when all of p,q,r are positive.

we have p = 40 * (r^2 + r)/(q+r) -17

Now r>q so r^2>q ( since r is greater than 1)
=> r^2 + r > q + r
=> (r^2 + r)/(q+r) > 1
So p = 40*(something greater than 1) - 17
=> p > 40 -17
=> p > 23.

Only p= 24 works.

hence E is the correct answer.