Question: The Dimensions of A Ream of Paper are \(8{1\over2}\)Inches by 11 Inches by \(2{1\over2}\)Inches. The inside dimensions of a carton that will hold exactly 12 reams of paper could be:

1. \(8{1\over2}\)in by 11 in by 12 in
2. 17 in by 11 in by 15 in
3. 17 in by 22 in by 3 in
4. 51 in by 66 in by 15 in
5. 102 in by 132 in by 30 in

Answer:
Approach Solution (1):
Let’s analyze each answer choice:
A) Since\({12\over{2.5}}=4.8\), the dimensions in choice A can only hold 4.8 reams of paper
B) Since\({17\over{8.5}}=2,{15\over{2.5}}=6, and 2\times6=12,\)the dimensions in choice B can hold 12 reams of paper. To fill the carton, then, two reams will be placed side-by-side in the bottom and then 5 reams will be stacked on the top of each of the two reams, making 2 stacks of 6 reams each
Correct option: B

Approach Solution (2):
Given dimensions are\({17\over2},11and{5\over2}\)
Total number of boxes to be filled is 12
Thus 12 can be written as\((1,1,12),(2,2,3),(1,2,6)..\)in any form
Where each of these in (x,y,z) represent the total number divisible by corresponding side of the carton for
quick solution
Let’s start looking at options:
A. \(8{1\over2}\)in by 11 in by 12 in divisible by corresponding l, b, h in 1, 1 and not divisible (the divisor must be an integer)
B. 17 in by 11 in by 15 in divisible by l, b, and h in 2, 1, 6
Correct option: B

Approach Solution (3):
A ream measures = 8.5 x 11 x 2.5, and we need to fit in exactly 12 reams in the box.
Therefore, of the answer choices whichever option will give 12 will be the answer, as in,
Option A = 8.5 x 11 x 12
This means that we can fit,
8.5/8.5 x 11/11 x 12/2.5
= 1 x 1 x 4 = 4 reams, not our answer
(2.5 x 5 = 12.5, thus for the given size (anything, height , length or width) of 12 we cannot completely fit 5 reams and can only fit 4. Therefore, 1 x 1 x 4)
Option B = 17 x 11 x 15
We can fit:
17/8.5 x 11/11 x 15/2.5
= 2 x 1 x 6 = 12 reams
Correct option: B

“The dimensions of a ream of paper are\(8{1\over2}\)inches by 11 inches by\(2{1\over2}\)inches. The inside dimensions of a carton that will hold exactly 12 reams of paper could be:”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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