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GATE CS 2017 Set 2 · General Aptitude

Question 59

MCQPrinted as GA Q.41 markWrong answer: −1/3Easy (estimate)

Question

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?

Choose one option
Official answer and solution
Official answer
B
From
Official GATE 2017 answer key

Solution

Formulate a system of two linear equations in two variables representing the question count and total marks.

Let mm be the number of multiple choice questions (3 marks each) and ee be the number of essay questions (11 marks each).
We are given:

  1. Total questions: m+e=20  ⟹  e=20−mm + e = 20 \implies e = 20 - m
  2. Total marks: 3m+11e=1003m + 11e = 100

Substitute e=20−me = 20 - m into the marks equation:

3m+11(20−m)=1003m + 11(20 - m) = 100
3m+220−11m=1003m + 220 - 11m = 100
220−8m=100220 - 8m = 100
8m=120  ⟹  m=158m = 120 \implies m = 15

Thus, the exam has 15 multiple choice questions (and 20−15=520 - 15 = 5 essay questions, giving 15×3+5×11=45+55=10015 \times 3 + 5 \times 11 = 45 + 55 = 100 marks).

This corresponds to option B.

Final answer

B

Common trap

Solving for the number of essay questions (5) instead of multiple choice questions (15).

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2017 Computer Science and Information Technology (CS) Session 2
Question
59 of 65, printed as GA Q.4
Section
General Aptitude

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