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CAT 2000 — QA Question 20

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

Which of the following expressions yields a positive value for every pair of non-zero real number (x, y)?

Answer & solution

Correct answer: f(x, y) + g(x, y)

  • A

    f(x, y) – g(x, y)

  • B

    f(x, y) – (g(x, y))2

  • C

    g(x, y) – (f(x, y))2

  • f(x, y) + g(x, y)

Solution

If (x + y) > 0, (x + y)0.5 is real.

∴ For (x + y) > 0;

f(x, y) = Positive square-root of (x + y) > 0

g(x, y) = (x + y)2 > 0

Otherwise,(i.e. for (x + y) < 0);

f(x, y) = (x + y)2 > 0

g(x, y) = –(x + y) > 0

Now it is clear that f(x, y) + g(x, y) will always be positive.

Hence, option (d).

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CAT 2000 QA Q20: Which of the following expressions yields a positive value for every pair of non-zero real number (x, y)? — Solution | TheCATExam