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

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.

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

Thus 3.

I didnt understand why the question uses word "maximum" though.

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.

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.

What is this question testing its from GMAT prep...

I'd say logic and 3D visualization...

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

Bunuel could you please refer to some similar (visualization) questions?Thanks.

Check GEOMETRY: 3-D Geometry Questions.

Hope it helps.

Bunuel

I got the answer, but I do not understand in what sense did we achieve five oranges in each row ? there's five only at the bottom one. Also, what's with the word maximum ?

KarishmaB is there another way of solving this question other than visualizing? Given the numbers, one could draw and understand BUT what if the numbers were huge, let's say 100 (starting from the bottom layer)?

You don't have to visualise the whole thing - only a part of it to get the pattern. Obviously, once you get the pattern, it can be used for any number.

Think of 4 balls placed together. We can place 1 ball on top of them in the middle. If we add another 2 balls such that we have 2 rows of 3 balls each, we can place another ball on top. So a 3*2 first layer has 2*1 second layer. Put another 3 balls at the back such that the first layer is 3*3. Now you can place 2 more balls on the top.
So a 3*3 first layer has a 2*2 second layer.
So the dimensions of the layer on the top is 1 less for both row and column.

So say 25 * 30 first layer will have 24*29 second layer and 23 * 28 third layer etc.

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