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Re: If x, y, and z are positive integers and 3x = 4y = 7z, then [#permalink]
05 Oct 2012, 07:14

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kingb wrote:

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

Notice that since 3, 4, and 7 are co-prime (they don't share any common factor but 1), then:

x must be a multiple of 4 and 7, so the least value of x is 28 (LCM of 4 and 7); y must be a multiple of 3 and 7, so the least value of y is 21; z must be a multiple of 3 and 4, so the least value of z is 12;

So, the least possible value of x + y + z is 28+21+12=61.

Re: If x, y, and z are positive integers and 3x = 4y = 7z, then [#permalink]
15 Jun 2013, 12:47

1

This post received KUDOS

kingb wrote:

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

We know x,y and z are postive integers so based on given information, we can say x= 4/3y and z= 4/7y

then x+y+z= 4/3y+y+4/7y-------> (4/3y+4/7y)+ y ------> 40y/21 +y -----> 61 y/21

61y/21= Sum of positive integers x,y and z. This sum also is a postive integer. Let us say it as Integer "a"

therefoee 61y/21= a now this implies y= a*21/61 ----For y to be an integer, we see that "a" has to be multiple of 61 and the smallest multiple of 61 is 1

Hence ans should D i.e 61 _________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Re: If x, y, and z are positive integers and 3x = 4y = 7z, then [#permalink]
29 Jul 2014, 11:37

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