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

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Manager
Joined: 11 Jul 2004
Posts: 120
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A shipment has 30 boxes. each is either 10lbs or 20lbs. [#permalink]  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
Director
Joined: 16 Jun 2004
Posts: 893
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Kudos [?]: 19 [0], given: 0

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.
Manager
Joined: 05 Sep 2004
Posts: 97
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Kudos [?]: 3 [0], given: 0

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
Manager
Joined: 28 Jul 2004
Posts: 54
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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

there for x-18 = 12

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

can someone please correct me ?
_________________

Jim

Manager
Joined: 02 Apr 2004
Posts: 224
Location: Utrecht
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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.

Regards,

Alex
Joined: 31 Dec 1969
Location: India
Concentration: General Management, Strategy
GMAT 1: 710 Q49 V0
GMAT 2: 740 Q40 V50
GMAT 3: 700 Q48 V38
GPA: 3.6
Followers: 0

Kudos [?]: 88 [0], given: 86987

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

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.
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