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CAT 2002 — QA Question 55

Number TheoryEasy

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

Correct answer: 3

  • A

    1

  • B

    2

  • 3

  • D

    4

Solution

|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).

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CAT 2002 QA Q55: Each question is followed by two statements A and B. Answer each question using the following instructions: An — Solution | TheCATExam