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Algebra, Exponents/Powers

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Algebra, Exponents/Powers

by swerve » Wed Nov 25, 2020 6:36 am

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If x is a positive integer and \(4^x-3=y\), which of the following CANNOT be a value of \(y\)?

A. 1
B. 7
C. 13
D. 61
E. 253

The OA is B

Source: Official Guide
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Re: Algebra, Exponents/Powers

by Scott@TargetTestPrep » Mon Nov 30, 2020 9:16 am
swerve wrote: ↑
Wed Nov 25, 2020 6:36 am
 If x is a positive integer and \(4^x-3=y\), which of the following CANNOT be a value of \(y\)?

A. 1
B. 7
C. 13
D. 61
E. 253

The OA is B

Source: Official Guide
Solution:

If x = 1, y = 4^1 - 3 = 1.

If x = 2, y = 4^2 - 3 = 13.

If x = 3, y = 4^3 - 3 = 61.

If x = 4, y = 4^4 - 3 = 253.

We see that if x is an integer > 4, then y > 253. Therefore, y can’t be 7 if x is a positive integer.

Answer: B

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