CAT 2004 — QA Question 35
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.
Ravi spent less than Rs.75 to buy one kilogram each of potato, onion, and gourd. Which one of the three vegetables bought was the costliest?
A. 2 kg potato and 1 kg gourd cost less than 1 kg potato and 2 kg gourd.
B. 1 kg potato and 2 kg onion together cost the same as 1 kg onion and 2 kg gourd.
Answer & solution
- A
1
- B
2
3
- D
4
Let one kilogram of potatoes, onions and gourd cost Rs. p, Rs. o and Rs. g respectively. Then p + o + g < 75.
Consider statement A: 2p + g < p + 2g
∴ p < g
But, nothing is known about o.
∴ Statement A is insufficient.
Consider statement B: p + 2o = o + 2g
∴ o + p = 2g
∴ The cost of 1 kg of gourd is the average of the costs of 1 kg potatoes and 1 kg onions.
∴ g is neither the costliest nor the cheapest.
But the costliest vegetable cannot be found.
∴ Statement B is insufficient.
Considering both statements together: p < g and g is the average of p and o
∴ o > g
∴ Onions are the costliest.
Hence, option (c).