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For integers x and y
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06 Mar 2021, 06:51
06 Mar 2021, 06:51
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42% (01:14) correct
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For integers x and y, \(3^{(4x+12)}=5^{(3x+y)}\). What is the value of y?
A. -12
B. -3
C. 0
D. 9
E. Cannot be determined
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. -12
B. -3
C. 0
D. 9
E. Cannot be determined
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Joined: 10 Apr 2015
Posts: 6218
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Re: For integers x and y
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06 Mar 2021, 07:07
06 Mar 2021, 07:07
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Carcass wrote:
For integers x and y, \(3^{(4x+12)}=5^{(3x+y)}\). What is the value of y?
A. -12
B. -3
C. 0
D. 9
E. Cannot be determined
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. -12
B. -3
C. 0
D. 9
E. Cannot be determined
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
The key word in this question is INTEGERS
Notice that, if x is an integer, then 4x+12 is an integer, which means 3^(4x+12) will equal the product of a bunch of 3's
Likewise, if x and y are integers, then 3x+y is an integer, which means 5^(3x+y) will equal the product of a bunch of 5's
Given these conditions, it seems impossible that 3^(4x+12) could ever equal 5^(3x+y)
HOWEVER, if the exponents 4x+12 and 3x + y both equal ZERO, then we get 3^0 and 5^0, and both of these evaluate to equal 1 - PERFECT!
So, let 4x+12 = 0 and let 3x+y = 0
Now we'll solve this system of equations for x and y.
First, if 4x+12 = 0, then x = -3
If x = -3, then we can take 3x+y = 0 and replace x with -3 to get: 3(-3) + y = 0
Simplify: -9 + y = 0
Solve: y = 9
So, x = -3 and y = 9, is a solution to the equation 3^(4x+12) = 5^(3x+y)
Answer: D
Cheers,
Brent
General Discussion
Retired Moderator
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Re: For integers x and y
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06 Mar 2021, 22:20
06 Mar 2021, 22:20
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Carcass wrote:
For integers x and y, \(3^{(4x+12)}=5^{(3x+y)}\). What is the value of y?
A. -12
B. -3
C. 0
D. 9
E. Cannot be determined
A. -12
B. -3
C. 0
D. 9
E. Cannot be determined
\(3^{(4x+12)}=5^{(3x+y)}\)
If base \(3\) and base \(5\) are equal, then, their powers must be zero
i.e. \(3^0 = 5^0 = 1\)
So, \(4x + 12 = 0\) which means \(x = -3\)
And, \(3x + y = 0\) which means \(y = 9\)
Hence, option D
