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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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Bunuel
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For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ [#permalink] New post  16 Feb 2017, 03:31
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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
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For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ [#permalink] New post  Updated on: 16 Feb 2017, 21:53
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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 8-)

Originally posted by 0akshay0 on 16 Feb 2017, 03:44.
Last edited by 0akshay0 on 16 Feb 2017, 21:53, edited 2 times in total.
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giobas
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Re: For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ [#permalink] New post  16 Feb 2017, 03:45
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.

i think answer is E
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mohshu
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Re: For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ [#permalink] New post  16 Feb 2017, 07:16
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] New post  16 Feb 2017, 08:07
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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Re: For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ [#permalink] New post  16 Feb 2017, 09:09
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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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Bunuel
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Re: For integers x, y, and z, 3^x4^y5^z=382725. What is the value of produ [#permalink] New post  16 Feb 2017, 10:48
Expert Reply
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] New post  16 Feb 2017, 12:03
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] New post  21 Sep 2023, 11:52
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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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