CAT 2004 — QA Question 24
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.
If group B contains 23 questions, then how many questions are there in group C?
Answer & solution
1
- B
2
- C
3
- D
Cannot be determined
Let there be a, b and c questions in groups A, B and C respectively.
Then, a + b + c =100
Total marks = a + 2b + 3c
Also,
b = 23
⇒ a + c = 77
⇒ a = 77 – c
⇒
⇒ a ≥ 0.6a + 27.6 + 1.8c
⇒ 4a ≥ 276 + 18c
⇒ a ≥ 69 + 4.5c
⇒ a – 4.5c ≥ 69
⇒ 77 – c – 4.5c ≥ 69
⇒ 77 ≥ 69 + 5.5c
⇒ c ≤ 8/5.5
⇒ c = 1
Hence, option (a).
Alternatively,
Evaluating options,
If C has 1 question then B and A have 23 and 76 questions respectively.
The total number of marks = 125
⇒ Group A has 60.8% marks.
⇒ Option (a) is possible.
If C has 2 questions then B and A have 23 and 75 questions respectively.
The total number of marks = 127
⇒ Group A has 59.05% marks.
⇒ Option (b) is not possible.
If C has 3 questions then B and A have 23 and 74 questions respectively.
The total number of marks = 129
⇒ Group A has 57.36% marks.
⇒ Option (c) is not possible.
Hence, option (a).