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
Explanation:
|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).
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.