CAT 2000 — QA Question 17
Sam has forgotten his friend’s seven-digit telephone number. He remembers the following: the first three digits are either 635 or 674, the number is odd, and the number nine appears once. If Sam were to use a trial and error process to reach his friend, what is the minimum number of trials he has to make before he can be certain to succeed?
Answer & solution
- A
1000
- B
2430
3402
- D
3006
Case i: The last digit is 9.
∴ The remaining 3 digits can be filled by any of the 9 digits (i.e., 0 to 8) in 93 ways.
∴ Total number of ways = 729
Case ii: The last digit is not 9.
∴ The last digit can be filled in 4 ways.
Let any of the other 3 digits be 9. This can happen in 3 ways.
∴ The remaining two digits can be filled in 92, i.e. 81 ways.
∴ The total number of ways = 92 × 3 × 4 = 972
∴ Number of trials for last four digits = 729 + 972 = 1701
Also, for the first three digits he has two options.
The minimum number of trials he has to make before he can be certain to succeed = 2 × 1701 = 3402
Hence, option (c).