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pradeepkaushal9518: Legendary Member; Posts: 1309; Joined: Wed Mar 17, 2010 11:41 pmFollowed by: 5 members; Thanked: 33 times

by pradeepkaushal9518 » Fri May 07, 2010 12:06 pm

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?

i have the answer but not options

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Source: Beat The GMAT — Problem Solving | Fri May 07, 2010 12:06 pm

clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Fri May 07, 2010 2:44 pm

pradeepkaushal9518 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?

i have the answer but not options

i got 20

x-number of 10 pound boxes

(10*x+20*(30-x))/30=18
solving for x gives us x=6-the number of 10 pounds, and 24 (30-6=24) the number of 20 pounds
y-the number of 20 pounds boxes that must be removed for new mean

(6*10+20*(24-y))/(30-x)=14
solving for y gives us y=20

so 20 boxes weight 20 must be removed

for checking
(6*10+4*20)/10=14

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abhi332: Master | Next Rank: 500 Posts; Posts: 117; Joined: Wed Dec 30, 2009 1:57 pmFollowed by: 1 member; Location: India; Thanked: 4 times

by abhi332 » Fri May 07, 2010 3:07 pm

total weight = 18*30 = 540

reduced avg = 14 = (540-(30-n)*20)/(30-n) where n is no of 20 pond boxed has to be removed

540-600+20n = 420-14n
n=480/34
therefore, n = 14 approx

What you think, you become.

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liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Fri May 07, 2010 5:35 pm

Number of 10pound box|Number of 20 pound box|total weight
x y 10x+20y=30*18=540---1
x z 10x+20z=14*[30-(y-z)]---2

subtraction 2 from 1 we get
20(y-z)=120+14(y-z)
or 6(y-z)=120
or (y-z)=20

hence 20 boxes of wight 20 pound has been removed

Ans 20

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pradeepkaushal9518: Legendary Member; Posts: 1309; Joined: Wed Mar 17, 2010 11:41 pmFollowed by: 5 members; Thanked: 33 times

by pradeepkaushal9518 » Fri May 07, 2010 7:58 pm

thanks buddy the answer is 20 only but i confused with 10 and 20 pounds.

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Fri May 07, 2010 11:11 pm

pradeepkaushal9518 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?

I have the answer but not options

This question is very simple ...just go this way..
Total no. of boxes (including 10 lbs and 20 lbs ) = 30
Avg. weight of boxes = 18
Total weight of boxes = 30 x 18 = 540
Now avg. weight is to be reduced to 14 pounds & let X boxes of 20 pounds is removed.
so total weight now = (30 - X)14 = 540 - 20X --> 420 - 14X = 540 -20X --> 120 = 6X --> X= 20
So Ans 20.

In short if u wanna solve ...
just put this exp. (30 - X)14 = 540 - 20X --> X =20 and u will get the soln in not more than 20 sec.

I would also suggest no to take x , y, z as three variable rather take x as the only variable to solve out what is required..

Hope this helps,.

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