PSAT Math Multiple-Choice Question 834: Answer and Explanation

Question: 834

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, like 2 and 100, for x and assume n is a constant like 3 to see how the equations behave:

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
A. y = nx + 3	y = 3 × 2 + 3	9	y = 3 × 100 + 3	303
B. y = -nx + 3	y = -3 × 2 + 3	-3	y = -3 × 100 + 3	-297
C. y = xn + 3	y = 23 + 3	11	y = 1003 + 3	1,000,003
D. y = x-n + 3	y = 2-3 + 3		y = 100-3 + 3	3.000001

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.