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If x, y, and z are positive integers and 3x = 4y = 7z, then

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If x, y, and z are positive integers and 3x = 4y = 7z, then [#permalink]  05 Oct 2012, 06:53
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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
[Reveal] Spoiler: OA

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Last edited by Bunuel on 05 Oct 2012, 07:14, 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, 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.

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Re: If x, y, and z are positive integers and 3x = 4y = 7z, then [#permalink]  15 Jun 2013, 12:47
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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
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Re: If x, y, and z are positive integers and 3x = 4y = 7z, then [#permalink]  05 Oct 2012, 07:37
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, 07:40
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BOOKMARKED
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 = 28
4(y) = 84 -> y = 21
7(z) = 84 -> z = 12

28+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]  14 Jun 2013, 04:26
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Re: If x, y, and z are positive integers and 3x = 4y = 7z, then [#permalink]  29 Jul 2014, 11:37
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Re: If x, y, and z are positive integers and 3x = 4y = 7z, then [#permalink]  31 Jul 2014, 20:05
LCM of 3, 4 & 7 is 84

Least value of x+y+z

$$= \frac{84}{3} + \frac{84}{4} + \frac{84}{7}$$

= 28 + 21 + 12 = 61

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Re: If x, y, and z are positive integers and 3x = 4y = 7z, then   [#permalink] 31 Jul 2014, 20:05
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