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Rectangular box wrapped with paper...

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Rectangular box wrapped with paper...

by sairamGmat » Thu Jul 15, 2010 4:01 pm
17. The figure above shows the dimensions of a rectangular box that is to be completely wrapped with paper. If a single sheet of paper is to be used without patching, then the dimensions of the paper could be
(A) 17 in by 25 in
(B) 21 in by 24 in
(C) 24 in by 12 in
(D) 24 in by 14 in
(E) 26 in by 14 in

Image

Official Answer is B

But not sure how this value arrived.. I got it about 24 in because- length wise is is 20 inch + 2 inch + 2 inch = 24 inch when wrapped on one side of the box.

The other remaining side should be 2+ 8+ 8 + 2 = 20 inch.. So, it should be 20 inch by 24 inch.. But OA says the other way.

Any explanation on why is it so?

Thanks,
sairamGmat
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by indiantiger » Thu Jul 15, 2010 5:14 pm
You need to calculate the total surface area of the rectangular box as that will give you the minimum area of the wrapping paper needed

Total surface area of rectangular box = 2(lb+bh+hl) = 2(8*20+20*2+8*2) = 432

now you need an answer choice that has area equal to 432 or greater than 432

(A) 17 in by 25 in (425)
(B) 21 in by 24 in (504)
(C) 24 in by 12 in (288)
(D) 24 in by 14 in (336)
(E) 26 in by 14 in (334)

Hence B
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by Testluv » Fri Jul 16, 2010 12:57 am
sairam,

if the question was asking for the MINIMAL area of the wrap, then you would be right. But since the question asks for what the area of the wrap COULD be, we know it COULD be the minimal area or any area that is larger. We know we need one side of the wrap to be at least 24, and the other to be at least 20. Only choice B satisfies this.

Here's one to see the concept:

If 5<=x<=10, which of the following must be true?

a) x<8
b) 3<x<8
c) 2<x<9
d) 5<=x<10
e) -1000<x<1000
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