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CAT 1997 — QA Question 33

Surds & IndicesEasy
Passage / Data

Direction: Answer the questions based on the following information.

For these questions the following functions have been defined.

la(x, y, z) = min(x + y, y + z)

le(x, y, z) = max (x − y, y − z)

ma(x, y, z) = 12 [le(x, y, z) + la(x, y, z)]

A, B and C are defined as follows.

A = 2.000004 ÷ [(2.000004)2 + (4.000008)]

B = 3.000003 ÷ [(3.000003)2 + (9.000009)]

C = 4.000002 ÷ [(4.000002)2 + (8.000004)]

Which of the following is true about the values of the above three expressions?

Answer & solution

  • A

    All of them lie between 0.18 and 0.2

  • B

    A is twice of C

  • C

    C is the smallest

  • B is the smallest

Solution

A=2.000004[(2.000004)2+2(2.000004)]

=2.0000042.000004[(2.000004)+2]

= 1[(2.000004)+2]

=14.000004

= 14=0.25 (Approximately)

B=3.000003[(3.000003)3+3(3.000003)]

=3.0000033.000003[(3.000003)+3]

=1[(3.000003)+3]=16.000003

C=4.000002[(4.000002)2+2(4.000002)]

=4.0000024.000002[(4.000002)+2]

=1[(4.000002)+2]=16.000002

Looking at the answer choices, we can see that the only (d) satisfies the relationship, viz. B is the smallest.

CAT 1997 QA Q33: A, B and C are defined as follows. A = 2.000004 ÷ [(2.000004) 2 + (4.000008)] B = 3.000003 ÷ [(3 — Solution | TheCATExam