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Sum of integers....Please help

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by JeetGulia » Tue Jul 20, 2010 12:19 pm
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
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by Patrick_GMATFix » Tue Jul 20, 2010 12:20 pm
The question stem tells us that x, y and z are positive integers.

My approach is to focus on 3x=4y=7z. Since the variables are integers, 3x, 4y and 7z must also be integers. They all equal some mystery number. This mystery number is a multiple of 3, 4 and 7. The smallest values of x, y, z will result in the smallest possible mystery number. Thus this number is the least common multiple (LCM) of 3, 4, and 7. This is 84. Thus 3x=4y=7z=84. x=28, y=21, z=12. x+y+z=61

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by Rakan » Thu Jul 22, 2010 2:30 am
Thanks
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by Patrick_GMATFix » Thu Jul 22, 2010 4:48 am
No problem :-)
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by zareentaj » Wed Aug 11, 2010 4:41 am
Patrick_GMATFix wrote:The question stem tells us that x, y and z are positive integers.

My approach is to focus on 3x=4y=7z. Since the variables are integers, 3x, 4y and 7z must also be integers. They all equal some mystery number. This mystery number is a multiple of 3, 4 and 7. The smallest values of x, y, z will result in the smallest possible mystery number. Thus this number is the least common multiple (LCM) of 3, 4, and 7. This is 84. Thus 3x=4y=7z=84. x=28, y=21, z=12. x+y+z=61

Hope that helps,
-Patrick
Thnaks Patrick_GMATFix. Your approach is good. Now I solve these type of questions easily.
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