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The figure above shows the dimensions of a rectangular box that is to

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Intern
Joined: 15 Sep 2005
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The figure above shows the dimensions of a rectangular box that is to  [#permalink]

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Updated on: 01 Aug 2018, 10:09
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Difficulty:

55% (hard)

Question Stats:

65% (02:30) correct 35% (02:22) wrong based on 315 sessions

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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

Attachment:

Untitled.png [ 1.11 KiB | Viewed 9754 times ]

Originally posted by sarojpatra on 17 Nov 2005, 01:02.
Last edited by Bunuel on 01 Aug 2018, 10:09, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: The figure above shows the dimensions of a rectangular box that is to  [#permalink]

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09 Aug 2014, 10:21
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1
Surface area of the box with dimensions a,b,c is $$S=2(ab+bc+ac)$$

Here we have S=2(20*2+2*8+20*8)=2*216=432. Now check the answers:
(A) 17*25=16*25+25=425 Less.
(B) 21*24=20*24+24=504 Good!
(C) 24*12 definitely less than A
(D) 24*14 less than A
(E) 26*14=25*14+14 less than A

General Discussion
Director
Joined: 17 Oct 2005
Posts: 762
Re: The figure above shows the dimensions of a rectangular box that is to  [#permalink]

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17 Nov 2005, 02:08
1
I got B

21 * 24=504

Surface area = 2lw + 2hw + 2hl =432

B is the only answer that is larger than 432
VP
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Posts: 1100
Re: The figure above shows the dimensions of a rectangular box that is to  [#permalink]

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17 Nov 2005, 08:13
B.
length =20, width = 8+8+2+2=20
so the dimensions are 20x20. only B has dimensions greater than 20x20.
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Re: The figure above shows the dimensions of a rectangular box that is to  [#permalink]

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17 Nov 2005, 09:55
The area of the rectangular box= 2(8*20)+2(2*8)+2(2*20)= 432,

The only option B has area more than 432.

So it B.
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Re: The figure above shows the dimensions of a rectangular box that is to  [#permalink]

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17 Nov 2005, 18:55
2
1
joemama142000 wrote:
himilaya im not sure how you came to the same conclusion. Can you explain more in depthly.? thanks

area doesnot tell you all you need. you cannot slelect B because its area is 504, which is greater than 432. an area with 504 can have the following dimensions as under:

2x252
4x126
8x63
21x24
28x18
36x14
42x12
or so on....

all the dimensions have area 504 but only a paper sheet with 21x24 can cover the box. if we take any paper sheet other than 21x24 dimensions, we have to cut it and patch the piece. so only dimension 21x24 works for the purpose of rapping the whole box.

the 20x20 is derrived from adding the height and width. if we surfaced the box, its dimension becomes 20x20.

hope it is clear........
Director
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Re: The figure above shows the dimensions of a rectangular box that is to  [#permalink]

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19 Nov 2005, 03:29
Total surface area is 432. B alone allows us to cover the box without patching!
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Joined: 29 Jan 2005
Posts: 3540
Re: The figure above shows the dimensions of a rectangular box that is to  [#permalink]

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19 Nov 2005, 06:45
HIMALAYA wrote:
joemama142000 wrote:
himilaya im not sure how you came to the same conclusion. Can you explain more in depthly.? thanks

area doesnot tell you all you need. you cannot slelect B because its area is 504, which is greater than 432. an area with 504 can have the following dimensions as under:

2x252
4x126
8x63
21x24
28x18
36x14
42x12
or so on....

all the dimensions have area 504 but only a paper sheet with 21x24 can cover the box. if we take any paper sheet other than 21x24 dimensions, we have to cut it and patch the piece. so only dimension 21x24 works for the purpose of rapping the whole box.

the 20x20 is derrived from adding the height and width. if we surfaced the box, its dimension becomes 20x20.

hope it is clear........

Himalaya> As crazy as this may sound, what if we very carefully snake wrapped that 2X252 inch long skinny piece all the way around the box 10 times with a slight fold on each end to cover each exposed section of the box. Definately a "jimmy rigged" wrap job, but theoretically possible because 252/20= 12.6; enough for 10 full wraps and 1 on each end (folded over) to cover the entire box. Granted you would need a lot of tape!
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Re: The figure above shows the dimensions of a rectangular box that is to  [#permalink]

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24 Nov 2005, 09:28
Total area of the box =

8*2*2 + 20*2*2 + 8*20*2 = 432

Only B gives a value that is greater than 432.
Hence B
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Re: The figure above shows the dimensions of a rectangular box that is to  [#permalink]

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11 Aug 2014, 02:46
Total sides = 6

Total surface area = 2(20*2 + 2*8+8*20) = 2(40+16+160) = 2 * 216 = 432

Only 21 * 24 = 504 fits in

Attachments

box.png [ 2.96 KiB | Viewed 9480 times ]

Intern
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Re: The figure above shows the dimensions of a rectangular box that is to  [#permalink]

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11 Oct 2014, 10:00
3
Above two images show three ways to cover the rectangular ways. We can easily see that option B (21 X 24) covers the second method with (20 X 24). hence B.
Attachments

File comment: Wrapping the rectangular box with paper

Slide2.JPG [ 14.97 KiB | Viewed 9296 times ]

File comment: Wrapping the rectangular box with paper

Slide1.JPG [ 32.78 KiB | Viewed 9289 times ]

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Re: The figure above shows the dimensions of a rectangular box that is to  [#permalink]

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01 Aug 2018, 09:16
sarojpatra wrote:
Attachment:
Untitled.png
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

OA:B
Total Surface area of box =2(2*8+2*20+8*20) =432
B i.e 21 in by 24 in=504 is the only answer that is larger than 432
Director
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Re: The figure above shows the dimensions of a rectangular box that is to  [#permalink]

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03 Aug 2018, 13:13
sarojpatra wrote:

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

Attachment:
Untitled.png

The Total Surface Area of the box is 2*(20*2 + 2*8 + 20*8) = 432 sq. inches

Checking the answer choices, we find choice B, 21 * 24 = 504 > 432, therefore no need to check further.

Thanks,
GyM
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Re: The figure above shows the dimensions of a rectangular box that is to  [#permalink]

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07 Aug 2019, 00:06
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Re: The figure above shows the dimensions of a rectangular box that is to   [#permalink] 07 Aug 2019, 00:06
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