Problem Solving

infiniti007 wrote:Would appreciate any help on approach and solving the following problem. Is there a way to set it up algebraically?

On Monday, an animal shelter housed 55 cats and dogs and by Friday, exactly 1/5 of the cats and 1/4 of the dogs had been adopted. If no new cats or dogs were brought to the shelter during this period, what is the greatest possible number of pets that could have been adopted from the animal shelter between Monday and Friday?

A) 11
B) 12
C) 13
D) 14
E) 20

Hi infiniti007,

One more take on algebraic route...

Say #of cats = x and #of dogs = y.

Thus, x + y = 55 ----(1).

We have to maximize (x/5 + y/4).

From eqn (1), we get y = 55 - x

By plugging in the value of y = 55 - x in (x/5 + y/4), we get,

x/5 + y/4 = x/5 + (55-x)/4

=> (275+4x-5x)/20

=> (275-x)/20

=> (260+15-x)/20

=> 13 + (15-x)/20

We have to maximize (15-x)/20. Since (15-x)/20 must be an integer and x cannot be negative, the minimum value of x would be 15.

Thus, the maximum number of pets could be = 13 + (15-15)/20 = 13 + 0 = 13.

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
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