boxes average problem

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heymayank08: Master | Next Rank: 500 Posts; Posts: 181; Joined: Fri Feb 17, 2012 9:36 amFollowed by: 1 member; Thanked: 1 times; GMAT Score:620

by heymayank08 » Mon Apr 30, 2012 8:48 pm

Q) 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?

pls explain how to proceed with this type of prob..
thanks in advance
[spoiler]OA: D[/spoiler]

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Source: Beat The GMAT — Problem Solving | Mon Apr 30, 2012 8:48 pm

shantanu86: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Sun Mar 11, 2012 8:57 pmFollowed by: 1 member; Location: India; Thanked: 16 times

by shantanu86 » Mon Apr 30, 2012 9:47 pm

heymayank08 wrote:Q) 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?

pls explain how to proceed with this type of prob..
thanks in advance
[spoiler]OA: D[/spoiler]

Total weight of 30 boxes = 30 * (mean weight) = 30*18
Let's suppose that n boxes of 20p were removed..
Therefore, new total weight = 30*18 - 20n
Number of boxes remaining = 30 - n
New average = (30*18 - 20n) / (30-n)

But new average is given to be 14.
Therefore,

14 = (30*18 - 20n) / (30-n) => n= 20

Hope it helps!!

If you feel like it, hit thanks

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heymayank08: Master | Next Rank: 500 Posts; Posts: 181; Joined: Fri Feb 17, 2012 9:36 amFollowed by: 1 member; Thanked: 1 times; GMAT Score:620

by heymayank08 » Mon Apr 30, 2012 10:30 pm

thnx a ton

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