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
PS - Inequality
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- karthikpandian19
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- eagleeye
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We are given r>q>1, and asked for a possible value of p, when all of p,q,r are positive.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 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.
- karthikpandian19
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OA is E
Regards,
Karthik
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