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# If x, y, and z are positive integers, and 4x = 5y = 6z, then the least

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Joined: 02 Sep 2009
Posts: 58381
If x, y, and z are positive integers, and 4x = 5y = 6z, then the least  [#permalink]

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28 Aug 2016, 10:50
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25% (medium)

Question Stats:

73% (01:33) correct 27% (01:17) wrong based on 94 sessions

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If x, y, and z are positive integers, and 4x = 5y = 6z, then the least possible value of x + y + z is

A. 15
B. 28
C. 37
D. 42
E. 60

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Re: If x, y, and z are positive integers, and 4x = 5y = 6z, then the least  [#permalink]

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28 Aug 2016, 11:30
1
Bunuel wrote:
If x, y, and z are positive integers, and 4x = 5y = 6z, then the least possible value of x + y + z is

A. 15
B. 28
C. 37
D. 42
E. 60

Answer is C.

4x = 5y = 6z = K (say)

or x = K/4 ; y = K/5; Z = K/6

We need to find the minimum value of K such that X,Y and Z are integers and have minimum value.

For that we can find the LCM of 4,5,6 = 60

So, Take K = 60

X= 15;Y=12;Z=10

or x+y+z = 37.
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Re: If x, y, and z are positive integers, and 4x = 5y = 6z, then the least  [#permalink]

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28 Aug 2016, 11:41
1
Bunuel wrote:
If x, y, and z are positive integers, and 4x = 5y = 6z, then the least possible value of x + y + z is

A. 15
B. 28
C. 37
D. 42
E. 60

Take LCM of 4,5 and 6 = 60

Now 4x = 60 => x =15
5y = 60 => y = 12
6z = 60 => z =10

115+12+10 = 37.

Option C.
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Re: If x, y, and z are positive integers, and 4x = 5y = 6z, then the least  [#permalink]

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14 Jan 2018, 14:29
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Re: If x, y, and z are positive integers, and 4x = 5y = 6z, then the least   [#permalink] 14 Jan 2018, 14:29
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# If x, y, and z are positive integers, and 4x = 5y = 6z, then the least

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