CAT 1991 — QA Question 13
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.
How many 3-digit even numbers can you form such that if one of the digits is 5 then the following digit must be 7?
Answer & solution
- A
5
- B
405
365
- D
495
Case 1: The number has 5 as one of the digits
Three digit number such that 7 follows 5 could be of the form 57_ or _57
Since, the number is an even number
Therefore possible numbers are 570,572,574,576 or 578.
Hence, 5 such numbers are possible.
Case 2: The number does not have 5 as one of the digits
First digit can be fille din 8 ways, second in 9 ways and third in 5 ways (even digits only).
∴ Number of ways = 8 × 9 × 5 = 360
∴ Total number of ways = 5 + 360 = 365
Hence, option (c).