Question

Find the value of A and B.

$AB\times B\underset{–}{}8A\underset{–}{}$

• A. A = 5, B = 1
• B. A = 4, B = 2
• C. A = 6, B = 3
• D. A = 5, B = 5

Answer 1

The correct option is B A = 4, B = 2

B x B = A or B x B = number with units digit A and
A x B = 8 or A x B + (carryover) = 8

(i) B x B = A or number with units digit A.

1 x 1 = 1 (so B cannot be 1 as A and B are different digits)
So, B $\ne$ 1
Similarly, B $\ne$ 5, 6
2 x 2 = 4
So if B = 2, A = 4
and 4 x 2 = 8.
Therefore, the values of A and B can be 4 and 2 respectively.

If B = 3,
3 x 3 = 9
B = 3 and A = 9,
and 9 x 3 = 27 which is cannot be equal to C8.

We can observe that for the values B = 3, 4, 7, 8 and 9, we end up with a three digit number but our result 8A is a two digit number.

Therefore the values of A and B is be 4 and 2 respectively.