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Each of the 30 boxes in a certain shipment with either 10

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Joined: 31 Dec 1969
Location: United States
Concentration: Marketing, Other
GMAT 1: 710 Q49 V38
GMAT 2: 660 Q V
GPA: 3.64
WE: Accounting (Accounting)
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Each of the 30 boxes in a certain shipment with either 10 [#permalink] New post 20 Oct 2004, 07:53
Each of the 30 boxes in a certain shipment with either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?

A. 4
B. 6
C. 10
D. 20
E. 24
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 [#permalink] New post 20 Oct 2004, 10:54
D. 20
(Calculations take some time... maybe there is a faster way..)

First, we know the average and that there are 30 boxes.
10A + 20(30-A) = 30*18.
We get A=6 which means there are 24 boxes of 20 pounds.

Now we only remove some of the 20-pound boxes. Let's say we remove X boxes.

6*10 + (24-X)*20 = (30-X)*14.

Solve and get X=20.
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 [#permalink] New post 20 Oct 2004, 12:27
D) 20
Let x = # of 10lbs boxes
10x + 20(30-x) = 18*30
x = 6
Let y = # of 20lbs boxes to be removed
10*6 + 20(24-y) = 14(30-y)
y=20

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Paul

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 [#permalink] New post 20 Oct 2004, 15:01
Also got D, same approach
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 [#permalink] New post 21 Oct 2004, 11:50
Got 20 as well by the same method.
  [#permalink] 21 Oct 2004, 11:50
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