SOLUTION: The number n is divisible by 3. The number n^2 is 3641A5. What digit does A represent?

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Question 1012933: The number n is divisible by 3. The number n^2 is 3641A5. What digit does A represent?
Found 2 solutions by macston, MathLover1:
Answer by macston(5194) About Me  (Show Source):
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.
No integers fulfill the requirements.
603%5E2=363609 . too low
604%5E2=364816 . too high
The number that would give 3641A5 as a square is between
603 and 604, thus is not evenly divisible by 3.
.
If it does not have to be evenly divisible,
replace A with any digit,and find the square root to find "n".
"A" will be your digit of choice.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Since the number n is divisible by 3, the number n%5E2 is divisible by 9.
By the divisibility rules, a number is divisible by 9 if the sum of its digits is divisible by 9.
Therefore, 3+%2B+6+%2B+4+%2B+1+%2B+A+%2B+5+=+A+%2B+19 must be divisible by 9.
Now, since A+is a 1-digit number, the only possible value for A+=+8 since 19+%2B+8+=+27+ and 27 is divisible by 9. Therefore, +A+=+8.