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# 2^n + 2^n + 2^n + 2^n = 4^n+3

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Kudos [?]: 1051 [0], given: 4710

2^n + 2^n + 2^n + 2^n = 4^n+3 [#permalink]  02 Dec 2018, 09:52
Expert's post
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Question Stats:

90% (00:39) correct 10% (04:25) wrong based on 10 sessions
$$2^n + 2^n + 2^n + 2^n = 4^{n+3}$$

 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
[Reveal] Spoiler: OA

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Posts: 1253
Followers: 47

Kudos [?]: 1159 [1] , given: 7

Re: 2^n + 2^n + 2^n + 2^n = 4^n+3 [#permalink]  03 Dec 2018, 10:31
1
KUDOS
Expert's post
Carcass wrote:
$$2^n + 2^n + 2^n + 2^n = 4^{n+3}$$

 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

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Re: 2^n + 2^n + 2^n + 2^n = 4^n+3   [#permalink] 03 Dec 2018, 10:31
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