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by kao521547 » Mon Aug 13, 2012 4:04 pm
if 6x=8y=14z, what is a possible sum of positive integers x,y and z

A. 52
B. 58
C. 84
D. 122
E. 168

thank you for your help
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by adthedaddy » Mon Aug 13, 2012 4:27 pm
Take LCM of 6,8,14. It will be 168.
Normalizing each term, we get

(x/28)=(y/21)=(z/12)

Taking sum of the terms - 28+21+12=61
Since its not a part of the options, multiply it by 2 (61x2 = 122)

Ans: D
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by GMATGuruNY » Mon Aug 13, 2012 6:29 pm
kao521547 wrote:if 6x=8y=14z, what is a possible sum of positive integers x,y and z

A. 52
B. 58
C. 84
D. 122
E. 168

thank you for your help
(2*3)x = (2*2*2)y = (2*7)z.

The smallest possible value of each product is 2*2*2*3*7.
Smallest possible x = (2*2*2*3*7)/(2*3) = 28.
Smallest possible y = (2*2*2*3*7)/(2*2*2) = 21.
Smallest possible z = (2*2*2*3*7)/(2*7) = 12.
Thus:
The smallest possible value of x+y+z = 28+21+12 = 61.

x+y+z must be a multiple of 61.
Of the answer choices, only D is a multiple of 61.

The correct answer is D.
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by cypherskull » Tue Aug 14, 2012 12:16 pm
6x = 8y = 14z

x + y + z = ?

First, I'd write each of x,y & z in terms of any one variable. Say I choose x.
So,

y = 3x/4
z = 3x/7

The required sum would be -

x + 3x/4 + 3x/7 = 61x/28

Now look at the answer choices. The correct answer should be divisible by 61. Looking at the answer choices, I'd immediately eliminate A,B and C. 61 times 2 yields 122.

Therefore, our answer is D
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