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GMATPrep PS

by GmatKiss » Sat Oct 29, 2011 6:57 am
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?

o 5
o 4
o 3
o 2
o 1
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by user123321 » Sat Oct 29, 2011 7:27 am
GmatKiss 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?

o 5
o 4
o 3
o 2
o 1
With each layer one row and one column cease to exist.
so in third layer = (5-2)*(3-1) = 3
a max of three oranges are possible

is it C?

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by GmatKiss » Sat Oct 29, 2011 7:42 am
Not getting this. OA is C
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by GmatMathPro » Sat Oct 29, 2011 7:49 am
Picture the bottom 3x5 layer of oranges as follows:

OOOOO
OOOOO
OOOOO

The oranges in the next layer have to be resting in the middle of a set of four oranges. There are 8 "middles" like that where you could place an orange in the next level. If you place in orange in all of those, there are 8 oranges:

OOOO
OOOO

Now there are three "middles" or spots for oranges, so you could place a maximum of 3 oranges in that layer.
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by GmatKiss » Sat Oct 29, 2011 8:21 am
Very impressive explanation. Thanks a lot GmatMathPro :)
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