X and Y are the digits at the unit's place of the numbers (408X) and (789Y) where X ≠ Y. However, the digits at the unit's place of the numbers (408X)63 and (789Y)85 are the same. What will be the possible value(s) of (X + Y)?
Example: If M = 3 then the digit at unit's place of the number (2M) is 3 (as the number is 23) and the digit at unit's place of the number (2M)2 is 9 (as 232 is 529).
Explanation:
For various powers the units digit of a number always a cycle of 4 terms.
We need unit’s digits of (X)63 and (Y)85 to be same
Unit’s digit of X63 will be same as unit’s digit of X3 Similarly, unit’s digit of Y85 is same as unit’s digit of Y1.
∴ unit’s digits of (X)3 should be same as units digit of Y.
This is possible (from the table) when (X, Y) = (2, 8) or (8, 2) or (7, 3) or (3, 7).
In any of these cases X + Y = 10.
Hence, option (b).
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