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CAT 1991 — QA Question 11

Basics (Functions)Easy
Passage / Data

Use the following information:

Prakash has to decide whether or not to test a batch of 1000 widgets before sending them to the buyer. In case he decides to test, he has two options: (a) Use test I ; (b) Use test II. Test I cost Rs. 2 per widget. However, the test is not perfect. It sends 20% of the bad ones to the buyer as good. Test II costs Rs. 3 per widget. It brings out all the bad ones. A defective widget identified before sending can be corrected at a cost of Rs. 25 per widget. All defective widgets are identified at the buyer’s end and penalty of Rs. 50 per defective widget has to be paid by Prakash.

A function can sometimes reflect on itself, i.e. if y = f(x), then x = f(y). Both of them retain the same structure and form. Which of the following functions has this property?  

Answer & solution

  • A

    y = 2x+33x+4

  • y = 2x+33x-2

  • C

    y = 3x+44x-5

  • D

    None of the above

Solution

For each of the given expressions, you may have to simplify and express x in terms of y and hence verify for which one does the form & structure remain the same.

In general, any function of the form y = ax+bbx-a reflects on to itself as we can rearrange it as

x = ay+bby-a

Let us check option (b).

y = f(x)

⇒ y = 2x+33x-2

⇒ 3xy - 2y = 2x + 3

⇒ 3xy - 2x = 2y + 3

⇒ x(3y - 2) = (2y + 3)

⇒ x = 2y+33y-2

∴ x = f(y)

Hence, the answer is (b).

CAT 1991 QA Q11: A function can sometimes reflect on itself, i.e. if y = f(x), then x = f(y). Both of them retain the same stru — Solution | TheCATExam