CAT 1993 — QA Question 26
Answer the next 2 questions based on the information given below:
A function f(x) is said to be even if f(–x) = f(x), and odd if f(–x) = –f(x). Thus, for example, the function given by f(x) = x2 is even, while the function given by f(x) = x3 is odd. Using this definition, answer the following questions.
A five digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them. What is the sum of all such possible numbers?
Answer & solution
6666600
- B
6666660
- C
6666666
- D
None
If we assume that any digit is in a fixed position, then the remaining four digits can be arranged in 4! = 24 ways. So each of the 5 digits will appear in each of the five places 24 times. So the sum of the digits in each position is 24(1 + 3 + 5 + 7 + 9) = 600.
Hence, the sum of all such numbers will be 600(1 + 10 + 100 + 1000 + 10000) = 6666600.
Hence, option (a).