CAT 2002 — QA Question 55
Answer the following question based on the information given below.
A boy is supposed to put a mango into a basket if ordered 1, an orange if ordered 2 and an apple if ordered 3. He took out 1 mango and 1 orange if ordered 4. He was given the following sequence of orders.
12332142314223314113234
Each question is followed by two statements A and B. Answer each question using the following instructions:
Answer (1) if the question can be solved by any one of the statements, but not the other one.
Answer (2) if the question can be solved by using either of the two statements.
Answer (3) if the question can be solved by using both the statements together and not by any one of them.
Answer (4) if the question cannot be solved with the help of the given data and more data is required.
Is |x − 2| < 1?
A. |x| > 1
B. |x − 1| < 2
Answer & solution
- A
1
- B
2
3
- D
4
|x − 2| < 1
Consider statement A:
|x| > 1
x < −1 or x > 1
For x = 1.5, |x − 2| < 1 is true.
For x = 4, |x − 2| < 1 is false.
∴ Statement A alone is not sufficient.
Consider statement B:
|x − 1| < 2
−2 < x − 1 < 2
−1 < x < 3
For −1 < x < 1, |x − 2| < 1 is false.
For 1 < x < 3, |x − 2| < 1 is true.
∴ Statement B alone is not sufficient.
Consider both the statements:
We have, 1 < x < 3
For this range, |x − 2| < 1 is true.
∴ Both the statements combined together are sufficient to answer the question.
Hence, option (c).