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CAT 1993 — QA Question 40

Number TheoryEasy
Passage / Data

The following functions have been defined for three numbers A, B and C:

@ (A, B) = average of A and B
*(A, B) = product of A and B
/(A, B) = A divided by B

Answer these questions with the above data.

Let x < 0, 0 < y < 1, z > 1. Which of the following may be false?

Answer & solution

  • (x2 – z2) has to be positive.

  • B

    yz can be less than one.

  • C

    xy can never be zero.

  • D

    (y2 – z2) is always negative.

Solution

Let us evaluate each option.

Option (a): As x < 0 and z > 1, let x = – 1 and z = 3, then (x2 –z2) = – 8. Hence, this option is not true.

Option (b): As 0 < y < 1 and z > 1, let y = 14 and z = 2, then yz = 14×2=12.
Therefore, yz can be less than 1.

Option (c): Since, none of the x and y is equal to zero, therefore xy can never be zero.

Option (d): 0 < y < 1 and z > 1, therefore (y2 – z2) is always negative.

Hence, option (a).

CAT 1993 QA Q40: Let x < 0, 0 < y < 1, z > 1. Which of the following may be false? — Solution | TheCATExam