Two boxes

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alex.gellatly: Master | Next Rank: 500 Posts; Posts: 435; Joined: Wed Nov 16, 2011 7:27 amFollowed by: 16 members; Thanked: 48 times

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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Source: Beat The GMAT — Problem Solving | Tue Jul 17, 2012 9:42 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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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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 » 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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Shalini Suresh: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Dec 22, 2011 10:22 pmFollowed by: 1 member; Thanked: 4 times

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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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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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