There are 8 true/false questions and 32 multiple choice questions.
To find out how many true/false and multiple choice questions are on a test worth 144 points with 40 questions, in which true/false questions are worth 2 points and multiple choice questions worth 4 points, we can set up a system of equations:
Let T be the number of true/false questions.
Let M be the number of multiple choice questions.
Since each true/false question is worth 2 points and each multiple choice question is worth 4 points, the points equation will be:
2T + 4M = 144
And since there are 40 questions in total, we have another equation:
T + M = 40
Solving this system of equations will give us the number of each type of question.
First, from the second equation, expressing T in terms of M:
T = 40 - M
Substitute T in the points equation:
2(40 - M) + 4M = 144
Expand and simplify to solve for M:
80 - 2M + 4M = 144 2M = 64 M = 32
Now substitute M back into T's equation:
T = 40 - 32 T = 8
There are 8 true/false questions and 32 multiple choice questions.