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Chocolates are packed in boxes that measure six inches long,
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Updated on: 20 Oct 2018, 03:24

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Question Stats:

Chocolates are packed in boxes that measure six inches long, three inches wide, and two inches high. If four individual boxes are packaged together in bulk by either arranging them in a single row or stacking them, what could be the total surface area of the bulk unit?

Indicate ALL that apply.

[ ] 168

[ ] 180

[ ] 192

[ ] 204

[ ] 252

[ ] 294

Indicate ALL that apply.

[ ] 168

[ ] 180

[ ] 192

[ ] 204

[ ] 252

[ ] 294

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Official Answer

A,B,C,E

Originally posted by amitmathew on 19 Oct 2018, 03:28.

Last edited by chetan2u on 20 Oct 2018, 03:24, edited 2 times in total.

Last edited by chetan2u on 20 Oct 2018, 03:24, edited 2 times in total.

Updated the OA

Re: Chocolates are packed in boxes that measure six inches long,
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19 Oct 2018, 22:17

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Expert Reply

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amitmathew wrote:

Chocolates are packed in boxes that measure six inches long, three inches wide, and two inches high. If four individual boxes are packaged together in bulk by either arranging them in a single row or stacking them, what could be the total surface area of the bulk unit?

Indicate ALL that apply.

[ ] 168

[ ] 180

[ ] 192

[ ] 204

[ ] 252

[ ] 294

Indicate ALL that apply.

[ ] 168

[ ] 180

[ ] 192

[ ] 204

[ ] 252

[ ] 294

The total surface area ÷4*SA of one box = 4*2*(6*2+2*3+6*3)=4*2*36=288

Now let us check cases when they are in single row..

The base 6*3 will always be open to air

Case I..

The faces 2*3 are placed next to each other, so there will be 3 overlaps in four boxes with the result that SIX 3*2 faces will be eliminated while calculating SA

So 288-6*(2*3)=288-36=252

Case II..

The faces 2*6 are placed next to each other, so there will be 3 overlaps in four boxes with the result that SIX 6*2 faces will be eliminated while calculating SA

So 288-6*(2*6)=288-72=216

Now let us check cases when they are in single stack..

The base 6*3 will now be merged with each other

Case I..

The faces 6*3 are placed on top of each other, so there will be 3 overlaps in four boxes with the result that SIX 3*6 faces will be eliminated while calculating SA

So 288-6*(6*3)=288-108=180

So answer would be 180,216 and 252

But if stacking means they can be in form of 2*2, so nice it does not mention that they are stacked in one column, here four faces will be 6*3 that will be eliminated and other 4 will be

The two more cases..

Case 1.. when the overlap is 2*3 faces

So eliminated SA = 4*(2*3+6*3)=4*24=96

So SA = 288-96=192

Case 2.. when the overlap is 2*6 faces

So eliminated SA = 4*(2*6+6*3)=4*30=120

So SA = 288-120=168

So 168, 180, 192, 216, 252

Re: Chocolates are packed in boxes that measure six inches long,
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19 Oct 2018, 18:04

1

Expert Reply

Draw out the figure.

Blue is one choc bar. Red, Green, and Black are 3 possible configurations.

Inkednew_LI.jpg [ 729.03 KiB | Viewed 4661 times ]

NOTE: I have drawn 3 boxes but the question asks for 4 so please modify the calculation accordingly.

Now area of cuboid is given by = 2 (lw + wh + hl) where:

displayImage.jpeg [ 4.98 KiB | Viewed 4690 times ]

Red area= \(180 in^2\)

Green area= \(216 in^2\)

Black area= \(252 in^2\)

Hence 180 and 252 are correct!

Blue is one choc bar. Red, Green, and Black are 3 possible configurations.

Attachment:

Inkednew_LI.jpg [ 729.03 KiB | Viewed 4661 times ]

NOTE: I have drawn 3 boxes but the question asks for 4 so please modify the calculation accordingly.

Now area of cuboid is given by = 2 (lw + wh + hl) where:

Attachment:

displayImage.jpeg [ 4.98 KiB | Viewed 4690 times ]

Red area= \(180 in^2\)

Green area= \(216 in^2\)

Black area= \(252 in^2\)

Hence 180 and 252 are correct!

Re: Chocolates are packed in boxes that measure six inches long,
[#permalink]
20 Oct 2018, 03:04

Thank you for the help sandy and chetan2u! I believe the OA should be A, B, C and E (it was the answer given in class) but it has been marked as only B and E. Kindly change it for the others who may happen upon this question.

Re: Chocolates are packed in boxes that measure six inches long,
[#permalink]
23 Jan 2019, 11:27

amitmathew wrote:

Thank you for the help sandy and chetan2u! I believe the OA should be A, B, C and E (it was the answer given in class) but it has been marked as only B and E. Kindly change it for the others who may happen upon this question.

I think explanation of this need more clarification.

Re: Chocolates are packed in boxes that measure six inches long,
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19 Jun 2019, 08:36

1

by any means such math takes a lot of time. How can we tackle such maths in GRE exam? Any clue , pls?

Re: Chocolates are packed in boxes that measure six inches long,
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19 Jun 2019, 10:12

1

jelal123 wrote:

by any means such math takes a lot of time. How can we tackle such maths in GRE exam? Any clue , pls?

The only way to solve these fairly quickly is to know this type of question like the back of your hand. Familiarizing yourself with challenging/time consuming questions like this will help you prevent costly tip-of-the-tongue moments when you take the GRE. Knowing exactly how to begin and how to move on to the next step subsequently means everything during a timed test.

Re: Chocolates are packed in boxes that measure six inches long,
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12 Jun 2024, 12:11

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Chocolates are packed in boxes that measure six inches long, [#permalink]

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