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Two boxes

by alex.gellatly » Tue Jul 17, 2012 9:42 pm
Box W and Box V each contain several blue sticks and red sticks, and all of the red sticks have the same length. The length of each red stick is 18 inches less than the average length of the sticks in Box W and 6 inches greater than the average length of the sticks in Box V. What is the average (mean) length, in inches, of the sticks in Box W minus the average (mean) length, in inches, of the sticks in Box V?

3
6
12
18
24
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by Anurag@Gurome » Tue Jul 17, 2012 10:40 pm
alex.gellatly wrote:Box W and Box V each contain several blue sticks and red sticks, and all of the red sticks have the same length. The length of each red stick is 18 inches less than the average length of the sticks in Box W and 6 inches greater than the average length of the sticks in Box V. What is the average (mean) length, in inches, of the sticks in Box W minus the average (mean) length, in inches, of the sticks in Box V?
Say, the length of each red stick = L inches

Hence, the average length of the sticks in Box W = MW = (L + 18)
And, the average length of the sticks in Box V = MV = (L - 6)

Hence, MW - MV = (L + 18) - (L - 6) = (28 + 6) = 24

The correct answer is E.
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by GMATGuruNY » Wed Jul 18, 2012 2:21 am
alex.gellatly wrote:Box W and Box V each contain several blue sticks and red sticks, and all of the red sticks have the same length. The length of each red stick is 18 inches less than the average length of the sticks in Box W and 6 inches greater than the average length of the sticks in Box V. What is the average (mean) length, in inches, of the sticks in Box W minus the average (mean) length, in inches, of the sticks in Box V?

3
6
12
18
24
Let the length of each red stick = 10.
The length of each red stick is 18 inches less than the average length of the sticks in Box W and 6 inches greater than the average length of the sticks in Box V.
Thus:
W = 10+18 = 28.
V = 10-6 = 4.
W-V = 28-4 = 24.

The correct answer is E.
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by Shalini Suresh » Wed Jul 18, 2012 3:08 am
@Anurag
Request you to explain why avg length is boxes W and V are (L+18) and (L-6) and not(L+18)/2 and(L-6)/2 . Can we just add the two values to get the mean? Please help.
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by Anurag@Gurome » Wed Jul 18, 2012 3:15 am
Shalini Suresh wrote:@Anurag
Request you to explain why avg length is boxes W and V are (L+18) and (L-6) and not(L+18)/2 and(L-6)/2 . Can we just add the two values to get the mean? Please help.
Because I've assumed the length of each red stick to be L and the question says "The length of each red stick is 18 inches less than the average length of the sticks in Box W and 6 inches greater than the average length of the sticks in Box V.

Hence, L is 18 less than the average length of the sticks in Box W and 6 more than the average length of the sticks in Box V.

Hope that helps.
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