Question

A test has twenty questions worth 100 points the test consists of true or false worth 3 points each and multiple choice ouestions worth 11 points each how many multiple choice questions are there in test

Answer 1

Answer:

5 multiple choice questions and 15 true or false questions

Answer 2

Let ' a ' be the number of True/False questions and ' b ' be the the number MCQ questions.

Total questions = 30.

It means,

a + b = 20 _____________ ( ! )

It is also given that the true/false questions are worth 3 points. So  the number of points we could score on these questions :

• 3 × a  

The Multiple Choice questions are worth 11 points each. So  the number of points we could score on these questions :

• 11 × b

Now,

if we add up the total number of points possible, the result will be

100 points.

That is,

3a + 11b = 100 ________ ( !! )

Now,

Observe ( ! )  and subtract a  from both sides. After the subtraction ,

b  will be canceled from the left side and the equation formed will be :

⇒ a = 20 - b

Now,

substitute the value of ' a ' in question ( !! ).

We get,

3(20 - b) + 11b = 100

⇒ 60 - 3b + 11 b = 100

⇒ 60 + 8b = 100

⇒  8b = 100 - 60

⇒ 8b = 40

⇒ b = 40/8

∴ b = 5

Hence,

There were total 5 MCQ questions in the test.

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