Question

A 4 digit number when squared, the last 4 digits of the square are same as that of the original number. Find the sum of digits of this number.

• A. 16
• B. 19
• C. 23
• D. 25
• E. None of these

Answer 1

The correct option is D 25

We done this question by back tracking rule we start from single digits such as 1, 2, 3, 4, 5, 6, 7, 8, 9 and we got square of 1, 5 and 6 last digit as same as original digit.
Such as square of 1 is 1, square of 5 is 25 and square of 6 is 36
after that we start with two digit series that end by 1,5 and 6.
Such that 11, 21, 31....., 91
And 15, 25, 35....., 95
and 16, 26, 36......, 96
And we got a square of 25 and 76 last digit is same as original digit.
After that we start with three digits series that end by 35 and 76
such as 125, 225, 325...., 325
And 176, 276, 376,.........976
And again we got a square of 625 and 376 last digit is same as original digit.
After that we start with three digits series that end by 25 and 76
such as 1625, 2625, 3625,......, 9625
And 1376, 2376, 3376,..........., 9376
And we got a square of 9376 last digit is same as original digit. So number is 9367
And its sum is 25.