A test has twenty questions worth 100 marks in total. There are two types of questions. Multiple choice questions are worth 3 marks each and essay questions are worth 11 marks each. How many multiple choice questions does the exam have? A. 12 B. 15 C. 18 D. 19

GATE 2017 · General Aptitude · Numerical Computation · medium

Answer: m = 15 multiple choice questions

  1. Set up the system of equations: Let m = number of MCQs, e = number of essay questions. Equation 1: m + e = 20. Equation 2: 3m + 11e = 100.
  2. Express e from Equation 1 and substitute: e = 20 - m. Substitute into Equation 2: 3m + 11(20 - m) = 100 => 3m + 220 - 11m = 100 => -8m = -120 => m = 15.
  3. Verify: e = 5. Check: 3*15 + 11*5 = 45 + 55 = 100. Correct. Answer is B. 15.