Problem 8 - Entrance Test

If $12 is removed from the sum of the two numbers, the result is 4 times the smaller number, what are the two numbers?

A. A) 2 and 4B. B) 2 and 6C. C) 4 and 8D. D) 5 and 11E. E) 4 and 12

Correct: D

Let x and y be the two numbers where x < y. Then the given condition becomes x + y - 12 = 4x. This simplifies to y - 12 = 3x, and further to y = 3x + 12. Since y = 3x + 12 and x + y - 12 = 4x, by checking each choice we see that only choice (D) satisfies the equation.