Question

Set m contains the values {-12, -7, 4, 11} and set n contains the values {-3,2,8}. What is the greatest possible difference of m^2 - n^2 ?

A. 76
B. 117
C. 140
D. 153

Answer 1

C. 140

Explanation:

We want m^2 to be the largest value it can be, so ignoring the sign of m the largest value of |m| is 12

(-12)^2 = 144 which is the largest value of m^2

We want n^2 to be the smallest it can be, so ignoring the sign of n the smallest value of |n| is 2

(2)^2 =4

m^2 -n^2

144-4 = 140