## 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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2021-10-10T21:30:50+00:00
2021-10-10T21:30:50+00:00 2 Answers
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## Answers ( )

Answer:5 multiple choice questions and 15 true or false questions

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 :

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

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 subtractafrom both sides. After the subtraction,

bwill be canceled from the left side and the equation formed will be :⇒

a = 20 – bNow,

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 = 5Hence,

There were total

5MCQ questions in the test.