Question

A test contains of 120 questions. Each correct answer carries 1 point, each
incorrect answer carries -0.5 point and each attempted question carries -0.25
point. Find the maximum number of wrong answers that the student could have
given if the student scored 50 points.​

Answer 1

Answer:

Let’s assume, X= no of questions attempted correctly

Y = no of questions attempted incorrectly

Z = no of unattempted questions

As per given conditions, total no of questions is 120. Hence, X+Y+Z=120

Total marks obtained = 228. Hence, 4X-2Y-Z=228

Adding equation 1 and 2,

5X-Y=348

Using above equation we need to find maximum value of Y such that X+Y should not exceed 120.

So, if we put value of X as 70 then we get y =2

If we put X as 80, we get Y as 52, but this will violate condition that X + Y less than or equal to 120

So put X as 79, we get Y as 47, again this will violate condition that X + Y less than or equal to 120

Put X as 78, we will get Y as 42 which satisfies our constraint also( X+Y=120).

Hence Max value of X that is= attempted questions is 78 and max wrong questions = y= 42.

Answer 2

Given: A test contains of 120 questions. Each correct answer carries 1 point, each incorrect answer carries -0.5 point and each attempted question carries -0.25 point.

To find: The maximum number of wrong answers that the student could have given if the student scored 50 points.​

Solution:

There were 120 total questions of 1 point each so the maximum marks that could be obtained by a student is 120. But the marks obtained by the student is 50. Hence, the marks lost is calculated as

$120 - 50 = 70$

For each wrong question, 0.5 points are deducted and each answer carries 1 point. This means that every wrong answer would carry -1.5 points. Thus, the maximum number of wrong answers can be calculated as follows.

$\frac{70}{1.5} = 46.67$

Therefore, the maximum number of wrong answers that the student could have given if the student scored 50 points is 46.