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GMAT past paper - Ratio

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GMAT past paper - Ratio

by akay » Sat Aug 11, 2007 9:37 pm
I am going in circles on this one.

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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Re: GMAT past paper - Ratio

by veekay » Sat Aug 11, 2007 10:18 pm
akay wrote:I am going in circles on this one.

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
Ans is D


3x=t the x=t/3
4y=t then y=t/4
7z=t then z=t/7

x+y+z = t/3 + t/4 + t/7 = 61t/84
Since x,y, z are (+)ive integer, x+y+z should be a (+)ive integer

therefore for min value of x+y+z, t should be 84 and the min value is 61

Let me know if there is a simpler approach to this problem
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by krishnamurthyu » Sat Aug 11, 2007 11:53 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
Given: 3x=4y=7z=A
LCM of 3,4,7 = 84 [ They are co-prime hence LCM= 3*4*7 ]
= 3*(4*7) = 4 *(3*7) = 7 (3*4)
x+y+z = (4*7) + (3*7) + (3*4)
=28 +21+12
=61
=D.
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by akay » Sun Aug 12, 2007 5:33 am
tks krishnamurthyu & veekay appreciate your taking the time.
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