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Boxes to be removed

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by aanikmakaan » Tue Dec 14, 2010 10:54 am
Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and 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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by diebeatsthegmat » Tue Dec 14, 2010 11:08 am
aanikmakaan wrote:Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and 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
]

10 x+20y=30*18=540
10x+20(y-z)=14*(30-z) [ consider z the number of 20 pound boxes which will be reduced)
10 x+20y-20z=420-14z
540-20z=420-14z
z=20
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by GMATGuruNY » Tue Dec 14, 2010 1:57 pm
aanikmakaan wrote:Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and 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
Total current weight = 30*18=540.

We can plug in the answer choices, which represent the number of 20-pound boxes that need to be removed.

Answer choice C: 10 of the 20-pound boxes removed
New total weight = 540 - 10*20 = 340.
New number of boxes = 30-10 = 20.
New average = 340/20 = 17.
Need to remove more boxes.

Answer choice D: 20 of the 20-pound boxes removed
New total weight = 540 - 20*20 = 140.
New number of boxes = 30-20 = 10.
New average = 140/10 = 14. Success!

The correct answer is D.
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by towerSpider » Tue Dec 14, 2010 3:57 pm
aanikmakaan wrote:Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and 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
30 = e + w
w=30-e
18 * 30 = 10e+20(30-e)
540=10e+600-20e
-10e=-60
e=6
w=24


14*(30-(24-A)) = 60+20A
14(6+A)=60+20A
84+14A=60+20A
24=6A
A=4

e=amount of ten p boxes
w=amount of 20 p boxes
a=answer
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