ANSWER: There are 2 blank answers
EXPLANATION
Let
The number of right answers be ‘r’
The number of wrong answers be ‘w’
The number of blank answers be ‘b’
r + w + b = 50
This means r + w ≤ 50
Then we know,
Right answers = 2 marks
Wrong answers = -0.5 mark
Blank Answers = 0 marks
2r – 0.5w = 88.5
2r = 88.5 + 0.5w … (Equation I)
Since the score as .5, we know that there is at least one wrong answer, and the number of wrong answers is an odd number.
Since the score is 88.5, and each right answer gives 2 marks
There are at more than 44 (i.e. 88/2) right answers
Since r + w ≤ 50, and possible values of w are odd numbers
If r = 45, Possible values of w are 1, 3, and 5
If r = 46, Possible values of w are 1, 3
If r = 47, Possible values of w are 1, 3
If r = 48, The only possible value of w is 1
If r = 49,The only possible value of w is 1
Since 2r = 88.5 + 0.5w (Equation I)
We test for possible values:
If r = 45
2r = 88.5 + 0.5w
2(45) = 88.5 + 0.5w
90 = 88.5 + 0.5w
0.5w = 90 – 88.5
0.5w = 1.5
w = 3
So,
If there are 45 right answers
There are 3 wrong answers
r + w + b = 50
45 + 3 + b = 50
48 + b = 50
b = 50 – 48
b = 2
Then, there are 2 blank answers.
If r = 46
2r = 88.5 + 0.5w
2(46) = 88.5 + 0.5w
92 = 88.5 + 0.5w
0.5w = 92 – 88.5
0.5w = 3.5
w = 7
So,
If there are 46 right answers
There are 7 wrong answers
We know that r + w ≤ 50
46 + 7 = 53
So 46 and higher numbers are not possible solutions.
The only possible solution is:
There are 45 right answers
There are 3 wrong answers
There are 2 blank answers