Question

There are 30 questions in a multiple choice test. A student will get 1 mark for each unattempted question, 0 marks for each wrong answer and 4 marks for each correct answer.A student answered x questions correctly and scored 60. Then the number of possible values of x are
A.15
B.10
C.6
D.5

Answer 1

Hint: This is a problem of linear inequalities. We have to form an inequation and find the possible values using the hit and trial method. We can assume the number of questions answered or left unattempted as a variable and form the inequations.

Complete Step-by-Step solution:
The number of questions answered correctly is x. Let the number of unattempted questions be y.So the number of questions answered wrong will be the total number of questions minus the number of questions answered correctly or left unattempted.
The number of questions answered wrongly are (30-x-y).

It is given that the total marks are 60. Marks obtained from correct answers are 4x and unattempted questions are y. Marks obtained from wrong answers will be 0 so they won’t be counted.
4x + y + 0 = 60
Also, we know that x and y will be less than the total number of questions. So.
x <= 30 and y <=30

Also, the sum of x and y will be less than the total number of questions. So,
x + y <= 30

Now, we will use the hit and trial method, and the cases which satisfy all the equations will be the possible values of x.

x	y	4x + y	x + y < =30?
15	0	60	Yes
14	4	60	Yes
13	8	60	Yes
12	12	60	Yes
11	16	60	Yes
10	20	60	Yes
9	24	60	No

Only six cases satisfy all the conditions, hence the possible values of x are 6.
The correct option is C.

Note:These types of questions can be solved by forming the required inequalities, and putting all the possible values to find the cases. If the number of cases are very large and cannot be written, then look for trends in the values of the variables. For example, in the above question, when the value of x reduces by 1, y increases by a value of 4.