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

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sarojpatra
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The figure above shows the dimensions of a rectangular box that is to [#permalink] New post   Updated on: 01 Aug 2018, 10:09
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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


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B

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] New post   09 Aug 2014, 10:21
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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

The correct answer is B.
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Re: The figure above shows the dimensions of a rectangular box that is to [#permalink] New post   11 Oct 2014, 10:00
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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.
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Re: The figure above shows the dimensions of a rectangular box that is to [#permalink] New post   17 Nov 2005, 02:08
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I got B

21 * 24=504

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

B is the only answer that is larger than 432
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Re: The figure above shows the dimensions of a rectangular box that is to [#permalink] New post   17 Nov 2005, 08:13
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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] New post   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] New post   17 Nov 2005, 18:55
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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........
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Re: The figure above shows the dimensions of a rectangular box that is to [#permalink] New post   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! :lol: :sa
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Re: The figure above shows the dimensions of a rectangular box that is to [#permalink] New post   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

Answer = B
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Re: The figure above shows the dimensions of a rectangular box that is to [#permalink] New post   07 Dec 2017, 06:56
Total surface area = 2(lb*bh*lh) = 432
The only option with area above 432 is E. No other dimensions can completely wrap the box.
So, option E
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The figure above shows the dimensions of a rectangular box that is to [#permalink] New post   07 Dec 2017, 08:43
anudeep133 wrote:
Total surface area = 2(lb*bh*lh) = 432
The only option with area above 432 is E. No other dimensions can completely wrap the box.
So, option E


But option E only gives you 364. It's not above 432.

The only option with an area above 432 is B.

Appreciate if you could let me know if i get anything wrong.
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Re: The figure above shows the dimensions of a rectangular box that is to [#permalink] New post   07 Dec 2017, 09:46
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Bunuel 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 inches by 25 inches
(B) 21 inches by 24 inches
(C) 24 inches by 12 inches
(D) 24 inches by 14 inches
(E) 26 inches by 14 inches

Show Spoiler
Attachment:
2017-12-07_0956.png



Hi..

the choices here have not made it tricky, and that is why just by looking at the area you have got your answer inspite of missing on words WITHOUT PATCHING.

SAY I gave you a choice 30*15... so this gives you an area 450>432. would that be an answer...NO
the trick is to look at the dimensions and then visualize wrapping it..

few dimensions that could be the answer..
1) \((20+2+2) * (2+8+2+8) = 24*20\)
2) \(( 8+2+2) * (2+20+2+20) = 12*44\)
there can be others too.
But our answer 24*21 is just bigger than 24*20

For above ways and other ways too think of opening the box as one paper
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The figure above shows the dimensions of a rectangular box that is to [#permalink] New post   22 Aug 2020, 11:45
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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


Show Spoiler
Attachment:
The attachment Untitled.png is no longer available


Solution:

The best way to solve this problem is to draw a picture with the box unfolded (see diagram below):

Attachment:
Box No Patch.png
Box No Patch.png [ 8.02 KiB | Viewed 12598 times ]


We see that the sheet of paper has to be at least 20 inches by 24 inches in order to completely wrap the box without patching.

Answer: B
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Re: The figure above shows the dimensions of a rectangular box that is to [#permalink] New post   19 Apr 2024, 08:02
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Re: The figure above shows the dimensions of a rectangular box that is to [#permalink]
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