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If x, y and z are distinct positive integers where x and y are prime

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Joined: 18 Feb 2019
Posts: 602
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
If x, y and z are distinct positive integers where x and y are prime  [#permalink]

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New post 23 Mar 2019, 23:00
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Difficulty:

  85% (hard)

Question Stats:

19% (02:13) correct 81% (02:23) wrong based on 16 sessions

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If x, y and z are distinct positive integers where x and y are prime numbers, find the number of prime factors of the lowest number that has x, y and z as its factors?

I. z is equal to the least common multiple of x, y and z.
II. z is equal to 15 times the highest number that divides each of x, y and z completely.
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Re: If x, y and z are distinct positive integers where x and y are prime  [#permalink]

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New post 24 Mar 2019, 07:54
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If x, y and z are distinct positive integers where x and y are prime numbers, find the number of prime factors of the lowest number that has x, y and z as its factors?

We are looking for the LCM of x, y and z.

I. z is equal to the least common multiple of x, y and z.
This tells us that x and y are factors of z as x and y are prime numbers.
But we do not know any value of variables
Insuff

II. z is equal to 15 times the highest number that divides each of x, y and z completely.
Since x and y are prime numbers, their greatest divisor would be 1, so z is 15 times 1 or 15*1=15.
But we do not know anything about 15..
say x=2, y =7, and z is 15, the answer is 210, but say x =3 and y =5, and z is 15, the answer is 15.
Insuff

Combined.
x and y are prime factors of z, and z is LCM of z, x and y. z is 15, thus answer is 15.
Suff
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Re: If x, y and z are distinct positive integers where x and y are prime   [#permalink] 24 Mar 2019, 07:54
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If x, y and z are distinct positive integers where x and y are prime

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