giobas wrote:
A student cuts 80 rectangles from construction paper, all of which are at least 10 inches in length and in width, and 20 percent of rectangles that are greater than 10 inches long are exactly 10 inches wide. if 40 of the rectangles have a length of exactly 10 inches and 50 of the rectangles are greater than 10 inches wide. How many rectangles have a perimeter of greater than 40 inches? (Note: assume that width and length are interchangeable; in other words, width does not have to be shorter than length)
(A) 18
(B) 22
(C) 32
(D) 58
(E) 66
Given by the question:
.................Exactly 10 ................ > 10......... Total
Length ........40 ...............................................80
Width .......... .................................50..............80
We can infer the:
.................Exactly 10 ................ > 10 ......... Total
Length ........40 .............................40 .............80
Width ...........30.............................50 .............80
20% of 40 rectangles (>10 length) are 8 rectangles. They are a part of 30 that have exactly 10 width. So other 22 rectangles must have exactly 10 length too.
So only 22 rectangles have exactly 10 length and exactly 10 width which gives exactly 40 perimeter.
Rest 80 - 22 = 58 rectangles must have perimeter greater than 40.
_________________
Karishma
Veritas Prep GMAT Instructor
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