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# For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ

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Math Expert
Joined: 02 Sep 2009
Posts: 43810
For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ [#permalink]

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16 Feb 2017, 02:31
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For integers x, y, and z, $$3^x4^y5^z=54675$$. What is the value of product xyz?

A. 0
B. 15
C. 30
D. 45
E. Cannot be determined
[Reveal] Spoiler: OA

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For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ [#permalink]

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16 Feb 2017, 02:44
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Bunuel wrote:
For integers x, y, and z, $$3^x4^y5^z=54675$$. What is the value of product xyz?

A. 0
B. 15
C. 30
D. 45
E. Cannot be determined

Given that $$3^x4^y5^z=54675$$, notice that 54675is not divisible by 4 (using divisibility rule of 4)
so y=0 and therefore x*y*z =0

Hence Option A is correct.
Hit Kudos if you liked it

Last edited by 0akshay0 on 16 Feb 2017, 20:53, edited 2 times in total.
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Re: For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ [#permalink]

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16 Feb 2017, 02:45
if we do prime factorization of 382725 we will result : 5^2 *3^7 *7.
if so 4^y should be 7, which is not possible from the argument.

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Re: For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ [#permalink]

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16 Feb 2017, 06:16
prime factorize..

4^y should account for 7, hence cannot be determined.

Ans E
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Re: For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ [#permalink]

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16 Feb 2017, 07:07
Bunuel wrote:
For integers x, y, and z, $$3^x4^y5^z=382725$$. What is the value of product xyz?

A. 0
B. 15
C. 30
D. 45
E. Cannot be determined

$$3^x*4^y*5^z=382725 = 3^7 * 5^2 * 7^1$$

So, we do not have any 4's in the Factorization, thus, answer must be (E) Cannot be determined
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Posts: 5655
Re: For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ [#permalink]

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16 Feb 2017, 08:09
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Expert's post
Bunuel wrote:
For integers x, y, and z, $$3^x4^y5^z=382725$$. What is the value of product xyz?

A. 0
B. 15
C. 30
D. 45
E. Cannot be determined

Hi,

It is given that x, y and z are integers...
So 4^y cannot be 7...
Value of y as an integer has to be 0, so product xyz is 0..

Bunuel, some error in Q, could be typo..
There has to be 7 on left hand side..
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Math Expert
Joined: 02 Sep 2009
Posts: 43810
Re: For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ [#permalink]

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16 Feb 2017, 09:48
chetan2u wrote:
Bunuel wrote:
For integers x, y, and z, $$3^x4^y5^z=382725$$. What is the value of product xyz?

A. 0
B. 15
C. 30
D. 45
E. Cannot be determined

Hi,

It is given that x, y and z are integers...
So 4^y cannot be 7...
Value of y as an integer has to be 0, so product xyz is 0..

Bunuel, some error in Q, could be typo..
There has to be 7 on left hand side..

You are right but the original question does not have it. Edited the question to correct the issue. Thank you for noticing.
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Re: For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ [#permalink]

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16 Feb 2017, 11:03
Option A

Given: $$3^x4^y5^z = 54675; xyz = ?$$

:54675 is an odd number, hence can't have any even factors or in other words y = 0 ($$4^0 = 1$$).
: xyz = 0
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Re: For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ   [#permalink] 16 Feb 2017, 11:03
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