16. 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
Hi,
I though the answer was E) but turned out to be D) -- can anyone please explain?
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16. 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
3x = 4y
So x = 4y/3
and 4y = 7z
so 4y/7
For both x and z to be integers it is important that y = LCM of 7&3 (i.e. 21)
Now x = (4*21)/3 = 28
Ans z = (4*21)/7 = 12
y = 21
Hence sum = 28+12+21 = 61
(A) 33
(B) 40
(C) 49
(D) 61
(E) 84
3x = 4y
So x = 4y/3
and 4y = 7z
so 4y/7
For both x and z to be integers it is important that y = LCM of 7&3 (i.e. 21)
Now x = (4*21)/3 = 28
Ans z = (4*21)/7 = 12
y = 21
Hence sum = 28+12+21 = 61