Least Possible Value Problem

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wcheng57: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Tue Dec 08, 2009 1:09 am

Least Possible Value Problem

by wcheng57 » Wed May 26, 2010 4:13 pm

If x, y, z are all positive integers, and 3x=4y=7z, then the least possible value of x+y+z is:

a) 33

b) 40

c) 49

d) 61

e) 84

Can someone explain to me why D is the correct answer?

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Source: Beat The GMAT — Problem Solving | Wed May 26, 2010 4:13 pm

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pm; Location: Milpitas, CA; Thanked: 447 times; Followed by:88 members

by Rahul@gurome » Wed May 26, 2010 4:23 pm

Let 3x=4y=7z = n. Then x = n/3, y = n/4 and z = n/7
x+y+z = n/3 + n/4 + n/ 7 = 61n/84
Since x , y and z are positive integers so x + y + z should also be a positive integer, this implies minimum value of n = 84
Hence, minimum value of x + y + z = 61

The correct answer is (D).

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