Question

Find the digit A
$\begin{array}{c}BA\\ \times B3\\ 57A\end{array}$

• A. 2
• B. 3
• C. 5
• D. None of These

Answer 1

The correct option is C

5

This has two letters A and B whose values are to be found.

Since the ones digit of $3\times A$ is A, it must be that A = 0 or A = 5.

Now look at B. If B = 1, then $BA\times B3$ would at most be equal to either $10\times 13$ which is equal to 130 or $15\times 13$ = 195 since A can take either the value of 0 or 5 But the product here is 57A, which is more than 500. So we cannot have B =1.

If B = 3, then $BA\times B3$ would be more than $30\times 33$ = 990 or $35\times 33$ = 1155 which is more than 600

But 57A is less than 600. So, B can not be equal to 3.

Putting these two facts together, we see that B = 2 only. So the multiplication is either $20\times 23$, or $25\times 23$.

The first possibility fails, since $20\times 23=460$. But, the second one works out correctly, since $25\times 23=575$. So the answer is A = 5, B = 2.
$\begin{array}{c}25\\ \times 23\\ 575\end{array}$