Question

A math test is worth 144 points and has 40 questions. True false questions are worth 2

points each. Multiple choice questions are worth 3 points each. How many of each type


of question is there?

Answer 1

Explanation:

x = number of true/false questions

y = number of multiple choice questions

x + y = 40

2x + 3y = 144

from the first equation we get

x = -y + 40

this identity we can then use in the second equation

2(-y + 40) + 3y = 144

-2y + 80 + 3y = 144

y + 80 = 144

y = 64

and

x + 64 = 40

x = -24

that does not make any sense.

something is wrong with the problem description.

just think about it :

40 questions - if all of them would be multiple choice tests (creating the max. possible points for 40 questions), we could have only 40×3 = 120 points.

but the description says 144 points.

for 144 points we need at least 48 (144/3) questions.

that does not fit.

the described system does not have any natural number solution. therefore we are getting such crazy numbers as result, when we try.