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test23 #16

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test23 #16

by dunkin77 » Tue Apr 24, 2007 5:47 pm
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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by Neo2000 » Tue Apr 24, 2007 5:52 pm
Let 3x = 4y = 7z = k

Find the LCM of 3,4,7 i.e. 84

Since we want the lowest value k = 84
If 3x = 84 X = 28
Similarly Y = 21
Z = 12

Sum total = 61
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by Cybermusings » Wed Apr 25, 2007 5:10 am
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
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