CAT 2004 — QA Question 39
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.
In a class of 30 students, Rashmi secured the third rank among the girls, while her brother Kumar studying in the same class secured the sixth rank in the whole class. Between the two, who had a better overall rank?
A. Kumar was among the top 25% of the boys merit list in the class in which 60% were boys.
B. There were three boys among the top five rank holders, and three girls among the top ten rank holders.
Answer & solution
1
- B
2
- C
3
- D
4
Consider statement A: There were 60% of 30 = 18 boys in the class.
Kumar’s rank among boys ≤ |0.25 × 18| or 4
If Kumar’s rank among boys = 4, there are 2 girls in the first 6 rankers.
∴ Rashmi’s rank is seven.
If Kumar’s rank among boys is 3, 2 or 1, there are 3, 4 or 5 girls in the first 6 rankers.
∴ Rashmi’s rank is three.
∴ Statement A is insufficient.
Consider statement B: There were three boys in the top 5 and Kumar was 6th.
∴ There were 4 boys and 2 girls in the top 6.
∴ Rashmi was not in the top six.
∴ Kumar had a better overall rank.
Statement B is sufficient.
Hence, option (a).