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A grocer stacked oranges in a pile. The bottom layer was

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A grocer stacked oranges in a pile. The bottom layer was  [#permalink]

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New post Updated on: 26 Jun 2013, 03:06
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Question Stats:

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A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?

(A) 5
(B) 4
(C) 3
(D) 2
(E) 1

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Originally posted by sondenso on 10 Jul 2008, 18:34.
Last edited by Bunuel on 26 Jun 2013, 03:06, edited 2 times in total.
Moved to PS forum and added the OA.
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A grocer stacked oranges in a pile. The bottom layer was  [#permalink]

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New post 05 Dec 2013, 08:35
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jlgdr wrote:
somalwar wrote:
Bottom Layer = 5 x 3 = 15
IInd Layer = (5-1) x (3-1) = 8
IIIrd Layer = (4-1) x (2-1) = 3

Answer = 3 = C


Why do you subtract 1 for each dimension? Would you kindly explain the logic behind this?
Also when they say between 4 oranges does it mean that an orange can be serving to hold to others oranges that might be adjacent? Or is it that one orange is only allowed to 'touch' one other orange from the second layer?

Cheers
J :)


The following image might help:

Image

Attachment:
260px-Close-packed_spheres,_with_umbrella_light_&_camerea.jpg
260px-Close-packed_spheres,_with_umbrella_light_&_camerea.jpg [ 14.08 KiB | Viewed 8455 times ]

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Re: Gmatprep. Find another way to solve this problem!  [#permalink]

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New post 10 Jul 2008, 18:51
1
if bottom layer is 3 by 5
next layer will be 1 less in each dimension, same with the next layer => 1 by 3 = 3 oranges.
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Re: Gmatprep. Find another way to solve this problem!  [#permalink]

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New post 10 Jul 2008, 19:22
1
sondenso wrote:
A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?

(A) 5
(B) 4
(C) 3
(D) 2
(E) 1

Can you solve this prob by making reasoning only, not by drawing it on the paper sheet? Thanks!


5 * 3 - bottom
2 * 4 - second
1 * 3 - top

Thus 3.

I didnt understand why the question uses word "maximum" though.
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Re: from Gmat Prep Question....  [#permalink]

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New post 17 Jul 2010, 04:21
2
As mentioned in the question the first layer of the pile looks like this (each symbol o represents one organge):

o o o o o

o o o o o

o o o o o

Now since each orange of the second layer has to be supported by 4 oranges of the first layer there will be two rows of 4 oranges each (shown in blue font):

o o o o o
o o o o
o o o o o
o o o o
o o o o o

Repeat the same step for the third layer and you'll see that there are 3 oranges in the thrird layer (shown in red font):

o o o o
o o o
o o o o

Hence option c is correct.
Edit:
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Re: from Gmat Prep Question....  [#permalink]

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New post 01 Sep 2010, 23:19
1
gmatJP wrote:
Please help solve this... I dont understand how it comes to 3...

Grocer stacked oranges in a pile. Bottom layer was rectangular with 3 rows of 5 oranges each. In 2nd layer , from bottom , each orange rested on 4 oranges from bottom layer and in the 3rd layer each orange rested on 4 oranges from 2nd layer. Which of the following is max.no. of oranges that could have been in 3rd layer.

a. 5
b. 4
c. 3
d. 2
e. 1

thanks...


My approach:

I believe if you understand that the every single orange above the bottom most layer can rest between the two oranges in the bottom most layer then it is easy to solve this question. Again the 3rd layer requires that the every single orange be rested on top of 4 oranges which is in the immediate bottom (2nd) layer.

stanford2012 has provided the correct approach but the diagrammatic representation is not correctly aligned and hence it is difficult to understand.
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Re: A grocer stacked oranges in a pile. The bottom layer was  [#permalink]

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New post 26 Jun 2013, 03:02
What is this question testing its from GMAT prep...
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Re: A grocer stacked oranges in a pile. The bottom layer was  [#permalink]

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New post 26 Jun 2013, 03:09
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Re: A grocer stacked oranges in a pile. The bottom layer was  [#permalink]

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New post 14 Oct 2013, 01:42
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Bottom Layer = 5 x 3 = 15
IInd Layer = (5-1) x (3-1) = 8
IIIrd Layer = (4-1) x (2-1) = 3

Answer = 3 = C
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Re: A grocer stacked oranges in a pile. The bottom layer was  [#permalink]

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New post 03 Dec 2013, 10:06
somalwar wrote:
Bottom Layer = 5 x 3 = 15
IInd Layer = (5-1) x (3-1) = 8
IIIrd Layer = (4-1) x (2-1) = 3

Answer = 3 = C


Why do you subtract 1 for each dimension? Would you kindly explain the logic behind this?
Also when they say between 4 oranges does it mean that an orange can be serving to hold to others oranges that might be adjacent? Or is it that one orange is only allowed to 'touch' one other orange from the second layer?

Cheers
J :)
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Re: A grocer stacked oranges in a pile. The bottom layer was  [#permalink]

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New post 27 Aug 2017, 19:55
1
sondenso wrote:
A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?

(A) 5
(B) 4
(C) 3
(D) 2
(E) 1

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oranges.png
oranges.png [ 54.77 KiB | Viewed 3249 times ]

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Re: A grocer stacked oranges in a pile. The bottom layer was  [#permalink]

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New post 24 Sep 2017, 04:24
gracie wrote:
sondenso wrote:
A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 5 oranges each. In the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each orange rested on 4 oranges from the second layer. Which of the following is the maximum number of oranges that could have been in the third layer?

(A) 5
(B) 4
(C) 3
(D) 2
(E) 1


hahaha Kudos for the illustrative photos! somehow I found it quite cute.
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A grocer stacked oranges in a pile. The bottom layer was  [#permalink]

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New post 06 Apr 2018, 03:41
Bunuel could you please refer to some similar (visualization) questions?Thanks.
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Re: A grocer stacked oranges in a pile. The bottom layer was  [#permalink]

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New post 06 Apr 2018, 03:54
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Re: A grocer stacked oranges in a pile. The bottom layer was  [#permalink]

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Re: A grocer stacked oranges in a pile. The bottom layer was   [#permalink] 08 Apr 2019, 02:12
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