Question

There are 20 questions in a mathematics test. 7 marks are awarded for each questions
answered correctly; 4 marks are deducted for each question answered wrong; and no
marks is given for each question left unanswered. If a student scores 100 marks, what
is the number of questions he left unanswered?​

Answer 1

Answer:

5

Step-by-step explanation:

The answer is 5.

There are three variables in the question.

x = Number of questions the boy got correct

y = Number of questions the boy got wrong

z = Number of questions the boy omitted.

There are two equations according to the given conditions:

x + y + z = 20

7x - 2y = 87

Let us look at the second equation first. We can easily guess that since x and y are whole numbers, the value of x has to be odd to meet the equation. Also, x should be greater than 12. So, let’s start putting odd whole number values, greater than 12 for x and try to corresponding values for y. We will have the following combinations:

x = 13 ; y = 2

x = 15 ; y = 9

x = 17 ; y = 16

Since, the sum of x and y cannot exceed 20, only the first case is possible according to the question. Putting these values of x and y in the first equation, we have z = 5