KN1: Equation

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Mon Feb 21, 2011 8:51 pm

Is there a way to do this without testing?

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Source: Beat The GMAT — Problem Solving | Mon Feb 21, 2011 8:51 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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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kevincanspain: GMAT Instructor; Posts: 613; Joined: Thu Mar 22, 2007 6:17 amFollowed by: 64 members; Location: madrid; Thanked: 171 times; GMAT Score:790

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

Kevin Armstrong
GMAT Instructor
Gmatclasses
Madrid

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