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Maximum number!

by Ahmed MS » Mon Oct 31, 2011 11:02 pm
Q: A grocer stocked orange in a pile. The bottom layer was a rectangular with 3 rows of 5 oranges each. If the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each oranges 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


I do not understand how to start with problem. Please help me guys!
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by smackmartine » Mon Oct 31, 2011 11:30 pm
IMO C
This a visualization problem and I had a lot of fun while drawing it :). The oranges in the third layer (blue) are the max # of oranges possible that satisfies the condition that they are rested on 4 oranges(green).


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by GMATGuruNY » Tue Nov 01, 2011 2:03 am
Ahmed MS wrote:Q: A grocer stocked orange in a pile. The bottom layer was a rectangular with 3 rows of 5 oranges each. If the second layer from the bottom, each orange rested on 4 oranges from the bottom layer, and in the third layer, each oranges 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


I do not understand how to start with problem. Please help me guys!
Another approach:

The dimensions of the bottom layer are 3 oranges by 5 oranges, yielding 3*5 = 15 oranges.
With each subsequent layer, we lose 1 orange off each dimension.
Second layer is 2 by 4, yielding 2*4 = 8 oranges.
Third layer is 1 by 3, yielding 1*3 = 3 oranges.

The correct answer is C.
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