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If \(2^{4x}=3,600\), what is the value of \((2^{(1-x)})^2\)?

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If \(2^{4x}=3,600\), what is the value of \((2^{(1-x)})^2\)?

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Source: Official Guide

If \(2^{4x}=3,600\), what is the value of \((2^{(1-x)})^2\)?

A. \(-\frac{1}{15}\)
B. \(\frac{1}{15}\)
C. \(\frac{3}{10}\)
D. \(-\frac{3}{10}\)
E. \(1\)

The OA is B

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2^(4x) = 3600, so (2^2)^2x = 3600, and 4^(2x) = 3600. Taking square roots, 4^x = 60.

We want to find the value of (2^(1-x))^2 = (2^2)^(1-x) = 4^(1-x) = 4^1 * 4^(-x)

Since 4^x = 60, 4^(-x) is equal to 1/60, so 4^1 * 4^(-x) = 4 * (1/60) = 4/60 = 1/15

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If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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Alternatively:

2^(4x) = 3600
2^(2x) = 60
2^x = √60

So

(2^(1-x))^2 = (2 / 2^x)^2 = (2/√60)^2 = 4/60 = 1/15

_________________
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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BTGmoderatorLU wrote:
Source: Official Guide

If \(2^{4x}=3,600\), what is the value of \((2^{(1-x)})^2\)?

A. \(-\frac{1}{15}\)
B. \(\frac{1}{15}\)
C. \(\frac{3}{10}\)
D. \(-\frac{3}{10}\)
E. \(1\)
\((2^{(1-x)})^2\) = \(2^{2-2x}\) = \(2^2/2^{2x}\) = \(4/2^{2x}\)

We need to know the value of \(2^{2x}\):
\(2^{4x}=3,600\)
\((2^{2x})^2=3,600\)
\(2^{2x}= 60\)

Substituting \(2^{2x}= 60\) into \(4/2^{2x}\), we get:
4/60 = 1/15

The correct answer is B.

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BTGmoderatorLU wrote:
Source: Official Guide

If \(2^{4x}=3,600\), what is the value of \((2^{(1-x)})^2\)?

A. \(-\frac{1}{15}\)
B. \(\frac{1}{15}\)
C. \(\frac{3}{10}\)
D. \(-\frac{3}{10}\)
E. \(1\)

The OA is B
Let’s first simplify the expression we want to evaluate. We see that [2^(1-x)]^2 can be simplified as (2 * 2^(-x))^2 = 2^2 * 2^(-2x) = (2^2)/(2^(2x))

Thus, if we can determine 2^2x, then we have an answer.

Taking the square root of both sides of the given equation, which is 2^(4x) = 3600, we have 2^(2x) = 60; thus:

(2^2)/(2^(2x)) = 4/60 = 1/15

Answer: B

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Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



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