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KN1: Equation

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Source: — Problem Solving |

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by Anurag@Gurome » Mon Feb 21, 2011 10:33 pm
Solution:
It is given that q < r.
Or q+r < 2r.
Or 1/(q+r) > 1/2r.
Or r/(q+r) > 1/2.
Or r^2/(q+r) > r/2.
Or (r+r^2)/(q+r) > (1/2 + r/2).
Or 40 * (r+r^2)/(q+r) - 17 > 20(r+1) - 17.
Or p > 20(r+1) - 17.
Or [(p+17)/20] - 1 > r.
Now, r > 1.
Or [(p+17)/20] - 1 > 1.
Or p > 23.
The only possibility is p = 24 which is (E).
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by kevincanspain » Tue Feb 22, 2011 12:01 am
yellowho wrote:Is there a way to do this without testing?

Think that since 0< q < r , (r +r^2)/(q + r) > (r + r^2/2r) = 1/2 + r/2.

Since r > 1, 1/2 + r/2 is greater than 1
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