Question

How many two-digit numbers satisfy this property.: the last digit (unit's digit) of the square of the two-digit number is 8 ? 1 2 3 none of these?

Answer 1

Heya user,

Let the two digit no. be [ 10x + y ]

Then, [ 10x + y ]² = 100x² + 20xy + y² = 10 [ 10x² + 2xy ] + y²

.'. The unit digit of square of the no. depends on the unit's digit of original no.

Now, how many no. satisfy the above property...

Clearly, we know: 
1² = 1;
2² = 4;
3² = 9;
4² = 6(mod 10);
5² = 5(mod 10);
6² = 6(mod 10);
7² = 9(mod 10);
8² = 4(mod 10);
and 9² = 1(mod 10)

Therefore, there is no. unit digit y for which y² = 8;
Hence the correct option is .. none of these...