CAT 2004 — QA Question 36
Answer the following question based on the information given below.
In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
Tarak is standing 2 steps to the left of a red mark and 3 steps to the right of a blue mark. He tosses a coin. If it comes up heads, he moves one step to the right; otherwise he moves one step to the left. He keeps doing this until he reaches one of the two marks, and then he stops. At which mark does he stop?
A. He stops after 21 coin tosses.
B. He obtains three more tails than heads.
Answer & solution
- A
1
2
- C
3
- D
4
Let Tarak get h heads and t tails.
Let Tarak be at 0 on the number line.
Then the blue mark is at –3 and the red mark is at 2.
Consider statement A: h + t = 21 and
h – t = 2 (if he stops at the red mark) or
h – t = –3 (if he stops at the blue mark)
Solving, 2h = 23 (however, this is not possible)
or 2h = 18
∴ h = 9 and t = 12
∴ Tarak stops at the blue mark.
∴ Statement A is sufficient.
Consider statement B: h = t – 3 and h – t = 2 or h – t = –3
∴ He stops at the blue mark.
∴ Statement B is also sufficient.
Hence, option (b).