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
(A) 33
(B) 40
(C) 49
(D) 61
(E) 84
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
