Digital PSAT Math Practice Question 318: Answer and Explanation

Question: 318

Given that x and n are numbers greater than 1, which of the following expressions would have the greatest overall increase in y values between x values from 2 to 100?

• A. y = nx + 3
• B. y = –nx + 3
• C. y = xⁿ + 3
• D. y = x^–n + 3

Correct Answer: C

Explanation:

(C) Try plugging in some sample values for x, like 2 and 100, and assume n is a constant, like 3, to see how the equations behave: Choice (C) clearly has the greatest overall increase, going from 11 to 1,000,003. Alternatively, you can simply realize that a number greater than 1 to a power more than 1 will be greater than the other possibilities.

Equation	Substitute $x=2$ and $n=3$	Value when $x=2$ and $n=3$	Substitute $x=100$ and $n=3$	Value when $x=100$ and $n=3$
$\mathrm{A}.y=nx+3$	$y=3\times 2+3$	9	$y=3\times 100+3$	303
$\mathrm{B}.y=-nx+3$	$y=-3\times 2+3$	-3	$y=-3\times 100+3$	-297
$\mathrm{C}.y=x^n+3$	$y=2^3+3$	11	$y={100}^3+3$	1,000,003
$\mathrm{D}.y=x^{-n}+3$	$y=2^{-3}+3$	$3\frac{1}{8}$	$y={100}^{-3}+3$	3.000001