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Math Expert V
Joined: 02 Sep 2009
Posts: 58445
If x, y, and z are positive integers, what is the value of x?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 66% (01:09) correct 34% (01:19) wrong based on 140 sessions

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If x, y, and z are positive integers, what is the value of x?

(1) (2^x)(3^y)(5^z)=300n
(2) n is a multiple of 5.

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Marshall & McDonough Moderator D
Joined: 13 Apr 2015
Posts: 1684
Location: India
Re: If x, y, and z are positive integers, what is the value of x?  [#permalink]

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St1: (2^x) * (3^y) * (5^z) = (2^2) * (3^1) * (5^1) * n
n can be a multiple of 2, 3, 5 or any other prime.
Hence St1 is not sufficient to determine the value of x.

St2: n is a multiple of 5. Not Sufficient

Combining St1 and St2,
n can still be a multiple of 2, 3 or any other prime even though n is a multiple of 5
For instance,
(2^x) * (3^y) * (5^z) = (2^2) * (3^1) * (5^1) * (5) --> Value of x = 2
(2^x) * (3^y) * (5^z) = (2^2) * (3^1) * (5^1) * (5 * 2) --> Value of x = 3
Not Sufficient

Manager  Joined: 12 Jun 2015
Posts: 78
Re: If x, y, and z are positive integers, what is the value of x?  [#permalink]

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Statement A:
(2^x) (3^y) (5^z) = (2^2) (3^1) (5^2) * n
n can be a multiple of any prime number. So, we cannot determine the value of x.

Hence, Statement A : Not sufficient

Statement B:
n is a multiple of 5.
This statement gives us no information about the value of x

Hence, Statement B : Not sufficient

Combining both statements,
n can still be a multiple of any other prime even though n is a multiple of 5
For instance,
(2^x) (3^y) (5^z) = (2^2) (3^1) (5^1) (25)
Here, value of x = 2
(2^x) (3^y) (5^z) = (2^2) (3^1) (5^1) (400)
Here, value of x = 6

Not Sufficient

Correct Option: E
Non-Human User Joined: 09 Sep 2013
Posts: 13275
Re: If x, y, and z are positive integers, what is the value of x?  [#permalink]

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_________________ Re: If x, y, and z are positive integers, what is the value of x?   [#permalink] 18 Dec 2018, 19:01
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