ardz24 wrote:Find the sum of all the four digit numbers which are formed by digits 1, 2, 5, 6
A. 933510
B. 93324
C. 65120
D. 8400
From the four digits, the total number of possible arrangements = 4! = 24.
Thus, the number of integers that can be formed from the four digits = 24.
Given a set of values that is symmetrical about the median:
Sum = (number of values)(median of the values).
The set of 4-digit integers that can be formed from the digits 1, 2, 5 and 6 is symmetrical about the median:
...2516, 2561, 2615,
2651, 5126, 5162, 5216, 5261...
In the set above, the integers in green constitute the two middle numbers.
Working from the center out, we get the following differences:
2651-2615 = 36 and 5162-5126 = 36.
2615-2561 = 54 and 5216-5162 = 54.
2561-2516 = 45 and 5261-5216 = 45.
Since the differences to the left of center are the same as those to the right of center, the set is symmetrical about the median.
Thus, the sum can be calculated as follows:
Median = (average of the two middle numbers) = (2651+5126)/2 = 7777/2.
Sum = (number of values)(median of the values) = (24)(7777/2) = (12)(7777) = integer with a units digit of 4.
The correct answer is
B.
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