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CAT 2000 — QA Question 21

Basics (Functions)Easy
Passage / Data

Answer the following question based on the information given below.

For real numbers x, y, let

f(x, y) = Positive square-root of (x + y), if (x + y)0.5 is real

= (x + y)2,    otherwise

g(x, y) = (x + y)2, if (x + y)0.5 is real

= –(x + y), otherwise

Under which of the following conditions is f(x, y) necessarily greater than g(x, y)?

Answer & solution

Correct answer: Both x and y are less than –1

  • Both x and y are less than –1

  • B

    Both x and y are positive

  • C

    Both x and y are negative

  • D

    y > x

Solution

If 1 > (x + y) > 0; f(x, y) > g(x, y) and if (x + y) < –1; f(x, y) > g(x, y).

If both x and y are less than –1, (x + y) will also be less than –1.

Hence, option (a).

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CAT 2000 QA Q21: Under which of the following conditions is f(x, y) necessarily greater than g(x, y)? — Solution | TheCATExam