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Probability with rectangles GMAT, GRE

How many unique rectangles are possible that have a perimeter of not more than 258cm and integers for the length of each side?

A. 65
B. 129
C. 4158
D. 4160
E. 130





Let's set a constraint for the area and dimensions:

2(l+w) <=258
(l+w) <=129


case1
l+w=129
128,1
127,2
126,3

65,64
64 pairs

Case2
l+w=128
127,1
126,2
125,3

65,63
64,64
64 pairs

for (l+w)=127 and 126 we will get 63 pairs
for (l+w)=3 and 2 we get 1 pair.

SUM formula= (1+64)2264 = 64*65 = Answer D



Jeremiah LaBrash


1 comment:

Rum Tan said...

There was a time when I used to practice for GMAT & GRE exams. At that time I was pro at math section especially at solving rectangle and square kind of questions. The way you have solved this question is absolutely correct but it is quite lengthy. Nowadays students are looking for more and more short tricks to solve questions like these in a few seconds. So try to provide some short tricks to solve these questions.