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Intern
Joined: 26 Jul 2006
Posts: 5
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If x, y, and z are positive integers and 3x=4y=7z, then the [#permalink]
 06 Sep 2006, 16:37
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
I used the following approach in order to try and solve this problem:
First I set all variable in terms of x which resulted in
x+y+z = x+(3/4)x+(3/7)x
simplifying, x+(3/4)x+(3/7)x = (61/28)x
This is where I got stuck. Any suggestions?
Thanks!
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VP
Joined: 02 Jun 2006
Posts: 1278
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(D) 61
Given 3x = 4y = 7z
LCM(3,4,7) = 84
=> x = 28, y = 21, z = 12
Sum = 61.
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VP
Joined: 29 Dec 2005
Posts: 1356
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Re: very interesting #'s properties q [#permalink]
06 Sep 2006, 18:10
chrismeiyu 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
I used the following approach in order to try and solve this problem:
First I set all variable in terms of x which resulted in
x+y+z = x+(3/4)x+(3/7)x
simplifying, x+(3/4)x+(3/7)x = (61/28)x
This is where I got stuck. Any suggestions?
Thanks!
since 3, 4 and 7 has no common factors, the only way to have 3x=4y=7z is 3 (4x7) = 4 (3x7) = 7 (3x4). so x = 28, y= 21, and z = 12.
therefore x + y + z = 28+21+12 = 61.
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Senior Manager
Joined: 11 May 2006
Posts: 262
Followers: 1
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Re: very interesting #'s properties q [#permalink]
06 Sep 2006, 22:33
chrismeiyu 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
I used the following approach in order to try and solve this problem:
First I set all variable in terms of x which resulted in
x+y+z = x+(3/4)x+(3/7)x
simplifying, x+(3/4)x+(3/7)x = (61/28)x
This is where I got stuck. Any suggestions?
Thanks!
you are almost there 
now x + y + z will be a +ve integer since x,y, and z each are +ve integers.
so (61/28)x will be a integer => x is a multiple of 28.
now (61/28)x will be minimum when x = 28
hence x+y+z = 61
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Re: very interesting #'s properties q
[#permalink]
06 Sep 2006, 22:33
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