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CAT 2000 — QA Question 57

Number TheoryEasy

Choose 1; if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Choose 2; if the question can be answered by using either statement alone.
Choose 3; if the question can be answered by using both statements together, but cannot be answered using either statement alone.
Choose 4; if the question cannot be answered even by using both statements together.

Let X be a real number. Is the modulus of X necessarily less than 3?

  1. X(X + 3) < 0
  2. X(X – 3) > 0

Answer & solution

Correct answer: 1

  • 1

  • B

    2

  • C

    3

  • D

    4

Solution

From statement A

X (X + 3) < 0

∴ –3 < X  < 0

∴ |X| < 3

∴ Statement A alone is sufficient.

From statement B

X(X – 3) > 0

X < 0 or X > 3

This statement does not give a unique answer.

Hence, option (a).

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CAT 2000 QA Q57: Choose 1 ; if the question can be answered by using one of the statements alone, but cannot be answered using — Solution | TheCATExam