XAT 2017 — QA & DI Question 9
In a True/False quiz, 4 marks are awarded for each correct answer and 1 mark is deducted for each wrong answer. Amit, Benn and Chitra answered the same 10 questions, and their answers are given below in the same sequential order.
AMIT T T F F T T F T T F
BENN T T T F F T F T T F
CHITRA T T T T F F T F T T
If Amit and Benn both score 35 marks each then Chitra’s score will be:
Answer & solution
10
- B
15
- C
20
- D
25
- E
None of the above
The correct answer fetches 4 marks whereas the wrong answer fetches -1 marks.
Amit scored 35 marks each in these 10 questions.
Let the number of correct answers be ‘c’ and wrong answers be ‘w’
4c – w = 35
c + w = 10
⇒ c = 9, w = 1, which means 9 correct answers and 1 wrong.
∴ Both Amit and Ben gave 1 wrong answer each.
Amit and Ben marked different answers for 3rd and 5th questions.
⇒ Amit and Ben would’ve answered 3rd or 5th question wrong in any order.
∴ They marked all other answers correctly.
⇒ Chitra marked correct answers for 3 questions (i.e., 1st, 2nd and 9th)
Out of 3rd and 5th questions marked by Chitra one would be correct and the other wrong.
Hence, Chitra marks 4 answers correctly and remaining 6 were wrong.
∴ Chitra’s score = 4 × 4 – 6 × 1 = 10.
Hence, option (a).