Question

In an examination, the maximum possible score is N while the pass mark is 45% of N. A candidate obtains 36 marks, but falls short of the pass mark by 68%. Which one of the following is then correct?

• A. N ≤ 200
• B. 243 ≤ N ≤ 252.
• C. N ≥ 253
• D. 201 ≤ N ≤ 242

Answer 1

The Correct Option is B

We are told:

• Pass mark \( P \) is 45% of \( N \)
• The candidate scored 36, which is 68% less than the pass mark

 

Step 1: Express \( P \) in terms of \( N \)

\[ P = 0.45N \]

Step 2: Relating the score to the pass mark

The score is 68% less than the pass mark: \[ 36 = P - 0.68P = 0.32P \]

Step 3: Solve for \( P \)

\[ P = \frac{36}{0.32} = 112.5 \]

Step 4: Relate \( P \) to \( N \)

Since \( P = 0.45N \): \[ 0.45N = 112.5 \] \[ N = \frac{112.5}{0.45} = 250 \]

Step 5: Verify the range

\[ 243 \le 250 \le 252 \] This is true.

✅ Final Answer: \( \mathbf{243 \le N \le 252} \)