## Weight average

##### This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 68
Joined: 30 Nov 2011

### Weight average

by bobdylan » Tue Jun 12, 2012 4:34 am
Each of the 30 boxes in a certain shipment weighs either 10 pound or 20 pounds, and the arithmetic mean of the boxes in the shipment is 18 pounds. If the average weight of the boxes 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

Legendary Member
Posts: 1159
Joined: 16 Apr 2008
Thanked: 56 times
by raunekk » Tue Jun 12, 2012 5:13 am
IMO : D = 20

a = 10 pound boxes
b = 20 pound boxes

a+b = 30 --- (1)
10(a) +20 (b) = 30* 18 ( given)

10a + 20 b = 540 --(2)

Solving 1 & 2, a= 6, b = 24

To reduce average to 14 by removing some 20 pound boxes

We use equation (2) to form new equation for average 14

10(6) + 20 (24-x) = 14 (30-x) ( Where x is the number of 20 pound boxes to be removed)

Solving, we get x = 20 (D)

Hope this helps!

GMAT Instructor
Posts: 15533
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1898 members
GMAT Score:790
by GMATGuruNY » Tue Jun 12, 2012 6:36 am
bobdylan wrote:Each of the 30 boxes in a certain shipment weighs either 10 pound or 20 pounds, and the arithmetic mean of the boxes in the shipment is 18 pounds. If the average weight of the boxes 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
Total current weight = number*average = 30*18 = 540.
We can plug in the answers, which represent the number of 20-pound boxes that must be removed to reduce the average weight to 14.

Answer choice C: 10 of the 20-pound boxes
New total weight = 540 - 10*20 = 340.
New average for the 20 remaining boxes = 340/20 = 17.
To reduce the average weight further, more 20-pound boxes must be removed.
Eliminate A, B and C.

Answer choice D: 20 of the 20-pound boxes
New total weight = 540 - 20*20 = 140.
New average for the 10 remaining boxes = 140/10 = 14.
Success!

The correct answer is D.
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at [email protected].
Student Review #1
Student Review #2
Student Review #3

• Page 1 of 1