If n is a three digit number and last two digits of square of n are 54 (n2 = 54), then how many values of n are possible?
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Simple answer is None.
For the square of a given number to end in 4, unit place of the given number should end in 2 or 8.
In general, for all 3 digit numbers ending in 2 or 8, the last 2 digits of its square would be 04, 24, 44, 64 and 84
Therefore, there are no numbers exist meeting the given criteria.
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