CAT 1993 — QA Question 10
Numbers (P&C)Easy
An intelligence agency decides on a code of 2 digits selected from 0, 1, 2, …. , 9. But the slip on which the code is hand–written allows confusion between top and bottom, because these are indistinguishable. Thus, for example, the code 91 could be confused with 16. How many codes are there such that there is no possibility of any confusion?
Answer & solution
- A
25
- B
75
80
- D
None of these
Solution
Total number of two digit codes that can be formed is 10 × 10 = 100
Out of them 0,1,6,8,9 can create confusion.
Using these five digits, total number of two digit numbers that can be made is 5 × 5 = 25.
But out of these 25 numbers 00,11,88,69 and 96 will not make any confusion.
Hence, the required answer is 100 – 25 + 5 = 80.
Hence, option (c).