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X, Y and Z are three positive integers such that the least common mult

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X, Y and Z are three positive integers such that the least common mult  [#permalink]

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New post 17 Mar 2019, 11:48
3
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A
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Difficulty:

  45% (medium)

Question Stats:

66% (02:05) correct 34% (02:12) wrong based on 77 sessions

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X, Y and Z are three positive integers such that the least common multiple of X & Y is 12, while the least common multiple of Y & Z is 18. Which of the following could be the value of Y?

I) 6
II) 9
III) 3
IV) 4

A. III only
B. IV only
C. I and III only
D. III and IV only
E. I and III and IV only
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Re: X, Y and Z are three positive integers such that the least common mult  [#permalink]

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New post 17 Mar 2019, 23:22
amanvermagmat wrote:
X, Y and Z are three positive integers such that the least common multiple of X & Y is 12, while the least common multiple of Y & Z is 18. Which of the following could be the value of Y?

I) 6
II) 9
III) 3
IV) 4

A. III only
B. IV only
C. I and III only
D. III and IV only
E. I and III and IV only




X*Y =12 ; 2^2 * 3 or 6*2
Y*Z= 18 ; 3^2*2 or 6*3

so value of y = 6 or 3
IMO C
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Re: X, Y and Z are three positive integers such that the least common mult  [#permalink]

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New post 22 May 2019, 18:55
amanvermagmat wrote:
X, Y and Z are three positive integers such that the least common multiple of X & Y is 12, while the least common multiple of Y & Z is 18. Which of the following could be the value of Y?

I) 6
II) 9
III) 3
IV) 4

A. III only
B. IV only
C. I and III only
D. III and IV only
E. I and III and IV only


12: 2,2,3
18: 2,3,3

1. Maximum number of '2' that can be is only 1, coz 18 has only 1 '2'
2. Simultaneously, max number of '3' that can be also only 1, coz 12 has only 1 '3'

So, possible varients of Y: 2,3 or 2*3

So the answer is C
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Re: X, Y and Z are three positive integers such that the least common mult  [#permalink]

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New post 22 May 2019, 19:27
amanvermagmat wrote:
X, Y and Z are three positive integers such that the least common multiple of X & Y is 12, while the least common multiple of Y & Z is 18. Which of the following could be the value of Y?

I) 6
II) 9
III) 3
IV) 4

A. III only
B. IV only
C. I and III only
D. III and IV only
E. I and III and IV only


LCM of x,y = 12
LCM of y,z = 18

Let's check possibility of each option-
Option X Y Z
6 12 6 18
3 12 3 18
9 Not possible
4 Not possible

Answer= 6 and 3.
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Re: X, Y and Z are three positive integers such that the least common mult  [#permalink]

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New post 17 Aug 2019, 11:49
Hello VeritasKarishma ,

Any Other method to solve this question. Any algebraic approach. I found above approach little difficult.
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Re: X, Y and Z are three positive integers such that the least common mult   [#permalink] 17 Aug 2019, 11:49
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