Exam Parameters Calculation

The examination initially had $100$ questions, each worth $1$ mark, totaling $100$ marks.

After evaluation, $20$ questions were deleted, leaving $80$ questions.

These $80$ questions are scaled to contribute a total of $100$ marks.

Therefore, the marks awarded per evaluated question are calculated as:

Marks per evaluated question = $ \frac{\text{Total Marks}}{\text{Evaluated Questions}} = \frac{100}{80} = 1.25 $ marks.

Student Score Impact Analysis

We calculate the impact of deleted questions on Student A and Student B by comparing their hypothetical original scores with their final evaluated scores.

Student A Score Change

• Student A's final score: $40$ marks.
• Number of questions A answered correctly from the evaluated $80$: $ \frac{40}{1.25} = 32 $.
• Number of questions A answered correctly from the deleted $20$: $4$.
• Total correct answers by Student A: $ 32 + 4 = 36 $.
• Hypothetical original score (assuming $1$ mark per question): $36$ marks.
• Change in score for A: Final Score - Original Score = $ 40 - 36 = +4 $ marks.
• Outcome: Student A gained $4$ marks.

Student B Score Change

• Student B's final score: $35$ marks.
• Number of questions B answered correctly from the evaluated $80$: $ \frac{35}{1.25} = 28 $.
• Number of questions B answered correctly from the deleted $20$: $10$.
• Total correct answers by Student B: $ 28 + 10 = 38 $.
• Hypothetical original score: $38$ marks.
• Change in score for B: Final Score - Original Score = $ 35 - 38 = -3 $ marks.
• Outcome: Student B lost $3$ marks.

Score Comparison Final Result

Student A's score changed by $+4$ marks (a gain).

Student B's score changed by $-3$ marks (a loss).

Comparing the outcomes:

• Student A gained marks.
• Student B lost marks.

Since Student B incurred a loss of $3$ marks while Student A had a gain of $4$ marks, Student B lost more marks relative to their potential score than Student A did.