A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 5 oranges each. In the second layer

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Fri Jul 09, 2021 11:37 am

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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

Answer: C

Source: GMAT Prep

Source: Beat The GMAT — Problem Solving | Fri Jul 09, 2021 11:37 am

gmatbyexample: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Fri Jun 14, 2019 11:26 am

Re: A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 5 oranges each. In the second la

by gmatbyexample » Mon Jul 12, 2021 1:54 pm

VJesus12 wrote: ↑
Fri Jul 09, 2021 11:37 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?

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

Answer: C

Source: GMAT Prep

So the second layer is a 2*4 matrix. There are three such possibilities in the third layer where the orange in the top layer will touch 4 oranges in the second layer.

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swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: A grocer stacked oranges in a pile. The bottom layer was rectangular with 3 rows of 5 oranges each. In the second la

by swerve » Tue Jul 13, 2021 7:27 am

VJesus12 wrote: ↑
Fri Jul 09, 2021 11:37 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?

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

Answer: C

Source: GMAT Prep

Bottom Layer $= 5 \times 3 = 15$
2nd Layer $= (5-1) \times (3-1) = 8$
3rd Layer $= (4-1) \times (2-1) = 3$

Therefore, C

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