Question

In a quiz, you receive 7 points for a correct answer and –4 points for an incorrect answer.You receive 0 points if you do not answer the question.There are 20 questions in total.Is it possible to get a score of –11 in this quiz?

Answer 1

Yes it is possible

Explanation:

Given

`n = 20`

`x= 7` --- correct

`y = -4` --- wrong

`z = 0` --- empty answer

Required

Is a total of -11 possible?

To do this, we apply trial by error method.

After so many approaches, I found the following solution

`x \to 3` -- Got 3 correctly

`y \to 8` --- Failed 8

`z \to 9` ---- Didn't answer 9

The above will give a score of -11.

We have:

`3x+8y+9z`

`3x+8y+9z = 3 * 7 + 8 * -4 + 9 * 0`

`3x+8y+9z = 21-32 + 0`

`3x+8y+9z = -11`

Hence, a score of -11 is possible