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If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?
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08 Mar 2021, 11:08
08 Mar 2021, 11:08
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If \(3^a – 3^{(a – 2)} = 8(3^{27})\), what is the value of 2a ?
A. 20
B. 25
C. 27
D. 29
E. 58
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 20
B. 25
C. 27
D. 29
E. 58
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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Posts: 6218
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Re: If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?
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08 Mar 2021, 12:32
08 Mar 2021, 12:32
1
Carcass wrote:
If \(3^a – 3^{(a – 2)} = 8(3^{27})\), what is the value of 2a ?
A. 20
B. 25
C. 27
D. 29
E. 58
A. 20
B. 25
C. 27
D. 29
E. 58
Given: \(3^a – 3^{(a – 2)} = 8(3^{27})\)
Factor \(3^{(a – 2)}\) from the left side to get: \(3^{(a – 2)}(3^2 – 1) = 8(3^{27})\)
Evaluate the part in the brackets: \(3^{(a – 2)}(8) = 8(3^{27})\)
Divide both sides by 8 to get: \(3^{(a – 2)} = 3^{27}\)
This means: \(a - 2 = 27\)
Solve: a = 29
So, 2a = (2)(29) = 58
Answer: E
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Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
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Location: India
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If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?
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08 Mar 2021, 23:18
08 Mar 2021, 23:18
Carcass wrote:
If \(3^a – 3^{(a – 2)} = 8(3^{27})\), what is the value of 2a ?
A. 20
B. 25
C. 27
D. 29
E. 58
A. 20
B. 25
C. 27
D. 29
E. 58
\(3^a – 3^{(a – 2)} = 8(3^{27})\)
\(3^a – \frac{3^a}{3^2} = (2^3)(3^{27})\)
\((3^a)(3^2) - (3^a) = (2^3)(3^{27})(3^2)\)
\(3^a (3^2 - 1) = (2^3)(3^{29})\)
\(3^a = 3^{29}\)
When the bases are equal, the powers are also equal;
i.e \(a = 29\)
Therefore, \(2a = 58\)
Hence, option E
