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CAT 1991 — QA Question 12

Simple EquationsEasy
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.

What is the value of k for which the following system of equations has no solution:

2x – 8y = 3 and kx +4y = 10

Answer & solution

  • A

    -2

  • B

    1

  • -1

  • D

    2

Solution

For two lines a1x + b1y = c1 and a2x + b2y = c2 to be parallel, the condition is

a1a2 = b1b2 ≠ c1c2

For no solution, lines must be parallel and not over lapping

⇒ 2k=-84≠310

∴ k = − 1.

Hence, option (c).

CAT 1991 QA Q12: What is the value of k for which the following system of equations has no solution: 2x – 8y = 3 and kx + — Solution | TheCATExam