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2^n + 2^n + 2^n + 2^n = 4^n+3
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02 Dec 2018, 09:52
02 Dec 2018, 09:52
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Question Stats:
81% (00:55) correct
18% (01:52) wrong based on 116 sessions
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\(2^n + 2^n + 2^n + 2^n = 4^{n+3}\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
Quantity A |
Quantity B |
n |
4 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
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Joined: 10 Apr 2015
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Re: 2^n + 2^n + 2^n + 2^n = 4^n+3
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03 Dec 2018, 10:31
03 Dec 2018, 10:31
3
Carcass wrote:
\(2^n + 2^n + 2^n + 2^n = 4^{n+3}\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
Quantity A |
Quantity B |
n |
4 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
--------ASIDE------------------------
Many students will fail to correctly simplify the terms on the left side of the given equation.
Notice that k + k + k + k = 4k
And x² + x² + x² + x² = 4x²
And 2m + 2m + 2m + 2m = 4(2m) = 8m
Likewise, \(2^n + 2^n + 2^n + 2^n = 4(2^n)\)
-----ONTO THE QUESTION!!---------------
GIVEN: \(2^n + 2^n + 2^n + 2^n = 4^{n+3}\)
Simplify left side: \(4(2^n) = 4^{n+3}\)
Rewrite both 4's as follows: \((2^2)(2^n) = (2^2)^{n+3}\)
Simplify both sides: \(2^{2+n} = 2^{2n+6}\)
Since we now have the same base on each side, we can conclude that: \(2+n = 2n+6\)
Solve to get: \(n = -4\)
We have:
QUANTITY A: -4
QUANTITY B: 4
Answer: B
RELATED VIDEO FROM OUR COURSE
2^n+2^n+2^n+2^n=4^n+3
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27 Sep 2022, 02:25
27 Sep 2022, 02:25
Expert Reply
1
Bookmarks
\(2^n+2^n+2^n+2^n=4^{n+3}\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
n |
4 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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GRE Math Essentials (2022)
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GRE - Math Book
