The mean of all 4-digit even natural numbers of the form ‘aabb’, where a > 0, is
Explanation:
‘aabb’ is an even number hence, b can be either 0 or 2 or 4 or 6 or 8.
∴ ‘aabb’ can be:
1100, 1122, 1144, 1166, 1188
2200, 2222, 2244, 2266, 2288
…
9900, 9999, 9944, 9966, 9988
Adding all these number
= 5 × (1100 + ... + 9900) + 9 × (22 + 44 + 66 + 88)
= (5 × 1100 × 45) + 9 × 22 × 10 = 5500 × 45 + 44 × 45 = 5544 × 45
∴ Average of all such numbers = (5544 × 45)/45 = 5544.
Hence, option (d).
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.