I'm going to assume you meant to write it so that the entire expression (q+r) is in the denominator. Otherwise, I don't think this will work out.

40(r+r^2)/(q+r)-17=p.

First note that that 40-17=23. But 40 is getting multiplied by (r^2+r)/(q+r). Notice that this expression MUST be greater than 1. We can see this if we compare the numerator and denominator term by term: r^2 must be greater than q, because we are told that 1<q<r, and r=r, so r^2+r>q+r. Therefore this entire expression must be greater than 1. As a result, 40 will be increased when it is multiplied by (r^2+r)/(q+r), so p must be greater than 23.

Ans: E

rahulvsd wrote:If p, q, and r are positive numbers such that (40(r+r^2)/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

[spoiler]OA:E[/spoiler]

(40(r+r^2)/(q+r))-17=p
((40 * r * r+1) / (q + r))-17 = p

r*r+1/(q+r) > 1 Assume r = q = 1, then the value of r*r+1/(q+r) = 1 As you know 1<q<r, the value of the expression r*r+1/(q+r) > 1

So, 40*a number greater than 1 - 17 = A number greater than 23, i.e. 24 from the options