Question

In the expression (2a4b−1)+2c,


a, b, and c are positive integers. Select all the actions that cause the expression’s value to increase.
A. Increase a by 1.
B. Increase b by 1.
C. Increase c by 1.
D. Decrease a by 1.
E. Decrease b by 1.
F. Decrease c by 1.

Answer 1

Interpret 2a4b and 2c as the numbers with digits 2,a,4,b and 2,c. Then
(2a4b − 1) + 2c = (2000 + 100a + 40 + b − 1) + (20 + c) = 2059 + 100a + b + c.

So increasing a by 1 increases the value by 100, increasing b by 1 by 1, and increasing c by 1 by 1. Decreasing any variable by 1 decreases the value.

Answer: A, B, C.