ACT practice 2020-2021 Math #50

Question

The sum of 2 positive numbers is 151. The lesser number is 19 more than the square root of the greater number. What is the value of the greater number minus the lesser number?

A. 18 B. 121 C. 81 D. 91. 101

How to solve it in less than 60 seconds?

Strategies for solving as a multiple choice question.

Answer 1

g = greater number, l = lesser number

Given:

g , l >0; g + l = 151; l = g^0.5+ 19

Solve g - m = ?

1. g , l are all integers and g is a square number.
2. Answer choices are values of (g - m), (g + m) + (g - m) =2g
3. D gives g = 121 = 11². This is the correct answer.

20-60 seconds for this question.

Answer 2