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If x, y, and z are positive integers and 3x = 4y = 7z, then [#permalink]
 05 Oct 2012, 07:53
Question Stats:
82% (01:56) correct
17% (00:52) wrong based on 3 sessions
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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Last edited by Bunuel on 05 Oct 2012, 08:14, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If x, y, and z are positive integers and 3x = 4y = 7z, then [#permalink]
05 Oct 2012, 08:14
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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. Answer: D.
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Re: If x, y, and z are positive integers and 3x = 4y = 7z, then [#permalink]
05 Oct 2012, 08:37
i did wrong..  .. i was luking at the choice that must be multiple of all 3 4 and 7.. so i tuk 84 .. Thanks bunuel  .. bunuel..is there any other way too to do this question ?
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Re: If x, y, and z are positive integers and 3x = 4y = 7z, then [#permalink]
05 Oct 2012, 08:40
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 The LCM of 3, 4, and 7 = 84. (Easy to figure out - since 3, 4, and 7 are prime, the LCM is 3*4*7) 3(x) = 84 -> x = 284(y) = 84 -> y = 217(z) = 84 -> z = 1228+21+12 = 61. Hope this helps.
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Re: If x, y, and z are positive integers and 3x = 4y = 7z, then
[#permalink]
05 Oct 2012, 08:40
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