If p, q, and r are positive numbers such that 40 * (r+r²)/(q+r) -17 = p, and 1 < q < r, which of the following could be the value of p?
A 10
B 15
C 17
D 23
E 24
Since r > q > 1, r² > q.
Thus:
(r+r²) / (q+r) = (r + greater value) / (r + smaller value) = (greater value)/(smaller value) = more than 1.
Thus:
p = 40 * (r+r²)/(q+r) - 17 = [40 * (more than 1)] - 17 = (more than 40) - 17 = more than 23.
Eliminate A, B, C and D.
The correct answer is
E.
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