Question

The next test will be a hundred points total, but only forty questions will be asked. Some questions are worth two points each and the rest are four points each. How many of each questions is there?

Answer 1

• 10 questions that are 4-point
• 30 questions that are 2-point

Explanation:

Numerical reasoning

If all questions were 2-point, the total score would be 80. It is 20 more than that. Each 4-point question that replaces a 2-point question will add 2 points to the score, so there must be 20/2 = 10 of them.

There are 10 4-point questions and 30 2-point questions.

_____

With an equation

Let x represent the number of 4-point questions. Then 40-x is the number of 2-point questions. The total number of points is ...

... 2(40-x) +4x = 100

... 2x +80 = 100 . . . . simplify

... 2x = 20 . . . . . . . . .subtract 80

... x = 10 . . . . . . . . . . divide by 2.

There are 10 4-point questions and 40-10=30 2-point questions.