Good Number Properties Problem from GMAC paper test

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tonebeeze: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Nov 02, 2009 5:49 pmFollowed by: 3 members; Thanked: 2 times

by tonebeeze » Mon May 16, 2011 2:43 pm

Can someone walk me through this one. thanks

If x, y, and z are 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

OA = D

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Source: Beat The GMAT — Problem Solving | Mon May 16, 2011 2:43 pm

MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 amFollowed by: 2 members; Location: Dominican Republic; Thanked: 31 times; GMAT Score:480

by MAAJ » Mon May 16, 2011 3:23 pm

Prime Factors
3 -> 3
4 -> 2,2
7 -> 7
LCM = 2x2x3x7 = 84

3x/84 = 4y/84 = 7z/84
x/28 = y/21 = z/12

If we make x, y and z equal to 1:
x = 28; y = 21; z = 12 and (x + y + z) = 28 + 21 + 12 = 61

That's how I got [spoiler] D? [/spoiler]

tonebeeze wrote:Can someone walk me through this one. thanks

If x, y, and z are 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

OA = D

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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 » Mon May 16, 2011 7:53 pm

tonebeeze wrote:Can someone walk me through this one. thanks

If x, y, and z are 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

OA = D

Let 3x = 4y = 7z = k.
Or x = k/3,
y = k/4, and z = k/7.
Or, x+y+z = k/3 + k/4 + k/7 = (28k+21k+12k)/84 = 61k/84.
So, the least value of x+y+z is obtained at the least value of k.
Note that since k is a common multiple of 3, 4, and 7, its least value is the LCM of 3, 4, and 7 which is 84.
So, least value of x+y+z = 61.

The correct answer is d.

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