CAT 2004 — QA Question 37
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.
Nandini paid for an article using currency notes of denominations Re. l, Rs. 2, Rs. 5, and Rs. 10 using at least one note of each denomination. The total number of five and ten rupee notes used was one more than the total number of one and two rupee notes used. What was the price of the article?
A. Nandini used a total of 13 currency notes.
B. The price of the article was a multiple of Rs. 10.
Answer & solution
- A
1
- B
2
- C
3
4
Let Nandini use a, b, c and d notes of denominations 1, 2, 5 and 10 respectively.
Then c + d = a + b + 1 and price of the article = a + 2b + 5c + 10d
Consider statement A: a + b + c + d = 13
∴ 2(a + b) + 1 = 13
∴ a + b = 6, c + d = 7
Price of the article cannot be found from this data.
∴ Statement A is insufficient.
Consider statement B: a + 2b + 5c + 10d = 10k
As a, b, c, d ≥ 1, 10k ≥ 18
∴ k ≥ 2
But, statement B is also insufficient.
Considering both statements together: We know that a + b = 6, c + d = 7 and Price = 10k
When c = 2 and d = 5, Price = a + 2b + 60
When c = 4 and d = 3, Price = a + 2b + 50
Even if we assume that there is only one value of (a, b) such that a + 2b is a multiple of 10, we will still get at least 2 values for the price of the article.
Hence, data is insufficient.
Hence, option (d).