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
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Weight average
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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!
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!
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Total current weight = number*average = 30*18 = 540.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
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.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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