## 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 p

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

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4 days 2021-10-10T21:30:50+00:00 2 Answers 0 views 0

5 multiple choice questions and 15 true or false questions

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. 