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655-705 (Hard)|   Exponents|      
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Bunuel
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For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y? 21 Feb 2017, 05:17
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D
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53% (01:40) correct 47% (01:54) wrong based on 807 sessions

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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
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D
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GMATinsight
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For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y? 21 Feb 2017, 05:43
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Bunuel
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
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3^(4x+12)=5^(3x+y)

This relation will hold true if the power of 3 and 5 on both sides of equation become zero because \({anything}^0 = 1\)

i.e. 4x+12 = 0 and 3x+y=0
i.e. x = -2 and y = 9

Answer: Option D
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For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y? 22 Feb 2017, 08:34
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Bunuel
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
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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
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For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y? 22 Feb 2017, 08:35
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GMATinsight


i.e. 4x+12 = 0 and 3x+y=0
i.e. x = -2 and y = 9

Answer: Option D
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Small error with the x-value above. Should be x = -3

Cheers,
Brent
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For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y? 23 Feb 2017, 10:45
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Bunuel
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
Show more

In order for the two sides of the equation to be equal, the exponent (4x+12) must equal zero and the exponent (3x+y) must equal zero, since 3^0 = 1 and 5^0 = 1. Thus:

4x + 12 = 0

4x = -12

x = -3

and

3x + y = 0

y = -3x

Since x = -3, y = -3(-3) = 9.

Answer: D
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For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y? 17 Jul 2017, 06:10
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Bunuel
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

3^(4x+12)=5^(3x+y)

This relation will hold true if the power of 3 and 5 on both sides of equation become zero because \({anything}^0 = 1\)

i.e. 4x+12 = 0 and 3x+y=0
i.e. x = -2 and y = 9

Answer: Option D
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Hello GMATinsight - You solution is really the quickest way to do! Somehow I spent 4 mins to solve this.

Just one correction, the value you mentioned for x is incorrect, x should be -3
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For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y? 17 Jul 2017, 06:14
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For integers x and y, \(3^{4x+12}=5^{3x+y}\). What is the value of y?

\(3^{4x+12}=5^{3x+y}\)

This is only possible when both 3 and 5 are raised to the power of ZERO.

4x + 12 = 0

3x + y = 0

Solving these two equations we get:

\(x = -3\)

\(y = 9\)

Hence, Answer is D

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For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y? 18 Aug 2018, 18:25
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Bunuel
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
Show more

Since 3^(4x+12) = 5^(3x+y) and 3 and 5 are relatively prime to each other (that is, they don’t have a common factor other than 1), the only way those two expressions can be equal is if each base is raised to the zero power and thus each side is equal to 1.

Thus:

4x + 12 = 0

4x = -12

x = -3

Substituting, we have:

3(-3) + y = 0

-9 + y = 0

y = 9

Answer: D
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For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y? 04 Feb 2019, 23:02
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Bunuel
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
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Had thought of an approach, but still forgot to consider this

5^0 * 3^(4x+12)=5^(3x+y) 3^0

3x +y = 0 & 4x+12 = 0, x =-3

y = 3*3 = 9

D
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For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y? 05 Feb 2019, 16:20
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Bunuel
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
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My reasoning:

In order for these two values to be equal each other \(3^{(4x+12}) and 5^{(3x+y)}\) must BOTH be equal to 1.

The reason is because 5 raised to any power will never equal 3 raised to any power unless they are both raised to the power of 0.

Explained even further: \(5^3\) = 5*5*5. Notice how there are no 3s in the prime factorization.

So we can set 4x+12 = 0 and see that x = -3. If x =-3, y must equal 9
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For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y? 06 Feb 2019, 20:51
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Bunuel
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
Show more

In order for a power in base 3 to equal a power in base 5, the exponents of each base must equal zero. In other words, 3^0 = 1 and 5^0 = 1, and so 3^0 = 5^0. This is the only way that the original equation can be satisfied. Thus, since each exponent must equal 0, we have:
4x + 12 = 0

4x = -12

x = -3

Solving for y, we have:

3(-3) + y = 0

-9 + y = 0

y = 9

Answer: D
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For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y? 08 Sep 2022, 21:04
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Given that For integers x and y, \(3^{(4x+12)}=5^{(3x+y)}\) and we need to find the value of y

Now 3 and 5 are prime numbers and their powers will be equal ONLY when value of both of them will be equal to 1, which happens at \(3^0\) and \(5^0\)

=> \(3^{(4x+12)}=5^{(3x+y)}\) = 1
=> 4x+12 = 0 and 3x + y = 0
=> 4x = -12
=> x = \(\frac{-12}{4}\) = -3

3x + y = 0
=> 3*-3 + y = 0
=> y - 9 = 0
=> y = 9

So, Answer will be D
Hope it helps!
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For integers x and y,3^(4x+12)=5^(3x+y). What is the value of y? 19 Jul 2025, 04:44
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