Question

A test has 50 questions. A student scores 1 mark for a correct answer, $-1/3$ mark for a wrong answer, and $-1/6$ mark for not attempting a question.
If the net score of Ananyaa who is a student who attempted the test is 32, then the number of questions answered wrongly by Ananyaa cannot be less than how much of the following?

• A. 6
• B. 4
• C. 3
• D. 12
• E. 9

Hint:

Look for arithmetic or geometric patterns, or operations between adjacent numbers.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Model the score using linear equations with three variables representing correct, wrong, and unattempted questions.
Step 2: Key Formula or Approach:
Let \(x\) = correct, \(y\) = wrong, \(z\) = unattempted. 1. \(x + y + z = 50\) 2. \(1x - \frac{1}{3}y - \frac{1}{6}z = 32\)
Step 3: Detailed Explanation:
From eq (1), \(z = 50 - x - y\). Substitute into eq (2): \[ x - \frac{y}{3} - \frac{50 - x - y}{6} = 32 \] Multiply by 6: \[ 6x - 2y - (50 - x - y) = 192 \] \[ 6x - 2y - 50 + x + y = 192 \] \[ 7x - y = 242 \] \[ y = 7x - 242 \] Since \(x + y \le 50\) (attempted questions): \(x + (7x - 242) \le 50 \implies 8x \le 292 \implies x \le 36.5\). Also, \(y \ge 0 \implies 7x \ge 242 \implies x \ge 34.57\). Possible values for \(x\): 35, 36. - If \(x = 35\), \(y = 7(35) - 242 = 245 - 242 = 3\). - If \(x = 36\), \(y = 7(36) - 242 = 252 - 242 = 10\). The minimum number of wrong answers is 3.
Step 4: Final Answer:
The number of wrongly answered questions cannot be less than 3.