Averages

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sparkle6: Senior | Next Rank: 100 Posts; Posts: 54; Joined: Tue Sep 20, 2011 7:58 amFollowed by: 1 member; Thanked: 1 times

by sparkle6 » Sun Sep 25, 2011 6:12 am

Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average 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

Answer is D, but I got B.

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Source: Beat The GMAT — Problem Solving | Sun Sep 25, 2011 6:12 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Sun Sep 25, 2011 6:23 am

First

Let X be Nos of boxes with 10 pounds weight and 30-X be Nos of 20 pound weight boxes.

So,

10X + 20 (30-X) = 18*30

X = 6 (10 pound)
20 pound boxes = 24.

Now Nos of 10 pound boxes remain unchanged, you remove only 20 pound boxes and Avg is 14.

Weight of 10 pound boxes = 10* 6 = 60

Let Y be Nos of 20 pound boxes (2nd case after removing)

We have

60 + 20Y = 14 (Y+6) --- Equating weights

Y=4.

Hence from 24 to 4 , 20 boxes are removed

sparkle6 wrote:Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average 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

Answer is D, but I got B.

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Sun Sep 25, 2011 6:31 am

Let the number of 10 pound boxes be x. So their total weight will be 10x
The number of 20 pound boxes will be 30-x. So their total weight will be 20(30-x)

Now since their average weight is 18, we have
[10x+20(30-x)]/30=18
x=6 so y=24 since x+y=30

Now, let the number of 20 lb boxes to be reduced be z. So the total number of boxes will be 30-z and the total number of 20 pound boxes will be 20-z. The new weight of the 20 pound boxes will be 20(24-z). And the average has to be brought down to 14 so we have,
[6*10+20(24-z)]/(30-z)=14

Solving we get, z=20 hence D

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Bigred2008: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun Jul 18, 2010 3:09 pm

by Bigred2008 » Tue Sep 27, 2011 11:58 am

Just a question, how/why did you set up the lefthand side of the equation. 10X-20(30-X). I tried to find the total weight of all the boxes 18*30 but wasn't sure where to go after that.

"No Pressure, No Diamonds. "

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Sep 27, 2011 1:41 pm

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