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A shipment has 30 boxes. each is either 10lbs or 20lbs.

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Manager
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A shipment has 30 boxes. each is either 10lbs or 20lbs. [#permalink] New post 07 Sep 2004, 08:00
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A shipment has 30 boxes. each is either 10lbs or 20lbs. Current ave is 18 lbs. ave needs to be reduced to 14 lbs. how mnay 20 lbs boxes must be removed to achive this

a. 4
b. 6
c. 10
d. 20
e. 24
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 [#permalink] New post 07 Sep 2004, 08:09
let X = no. of 10lb boxe. Y = no. of 20lb boxes and A = no. of 20lb boxes to be reduced.

1. (10X + 20Y)/(X+Y) = 18 =>Y=4X
2. X+Y = 30

Solving we have X=6, Y=24

3. Now, we have [10*6 + 20(24-A)]/[6 + (24-A)] = 14

Solving we have A = 20.

So ans is d.
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 [#permalink] New post 07 Sep 2004, 09:17
Alternatively, let n be the number of boxes to be removed.

Current total weight = 30 * 18 = 540

Revised total weight = 14 * (30 - n) = 420 - 14n

Reduction in terms of 20 lb boxes:

540 - (420 - 14n) = 20n
=> n = 20
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 [#permalink] New post 07 Sep 2004, 10:21
hey i am getting the answer as 12
can someone tell me ...whats wrong with this


lets the no of 10lb boxes be x
therefore no of 20 lb boxes is 30-x

10(x) + 20(30-x)/30 = 18
10(x) + 20(30-x)=540-

we get x=6 and 30-x =24

now we want the average = 14

10(x) + 20(30-x)/30=14

we get the answer x=18
there for x-18 = 12

therefore the reduction in 20 lb boxes is 24-12=12

can someone please correct me ?
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 [#permalink] New post 07 Sep 2004, 10:34
I also have D as answer.

6 * 10 + 20 * x / 6 + x = 14
60 + 20x = 84 - 14x
x = 4

24 - 4 = 20

Damit, propably you have picked 4 as answer, but it is tricky cause the answer is 20. With 4 boxes of 20lbs and 6 boxes of 10lbs you get an average of 14. Therefore, 20 boxes of 20 lbs need to be deducted of the original 24 boxes of 20lbs.

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Alex
Joined: 31 Dec 1969
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GMAT 2: 740 Q40 V50
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 [#permalink] New post 08 Sep 2004, 06:47
jimishg wrote:
hey i am getting the answer as 12
can someone tell me ...whats wrong with this


lets the no of 10lb boxes be x
therefore no of 20 lb boxes is 30-x

10(x) + 20(30-x)/30 = 18
10(x) + 20(30-x)=540-

we get x=6 and 30-x =24

now we want the average = 14

10(x) + 20(30-x)/30=14

we get the answer x=18
there for x-18 = 12

therefore the reduction in 20 lb boxes is 24-12=12

can someone please correct me ?



10(x) + 20(30-x)/30=14 is wrong because the total number of boxes is not 30, it will be 6 + a number smaller than 24, but unknown.
I solved this problem in the same way as you, but this second equation should be: [(6*10 + 20*a)/(6+a)] = 14, where a is the number of 20lbs boxes. Solving this we obtain: a=4

Therefore 24 - 4 = 20, answer d.
  [#permalink] 08 Sep 2004, 06:47
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A shipment has 30 boxes. each is either 10lbs or 20lbs.

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