Question

In the following multiplication, each of the letters denote a different integer. Each letter stands for the same integer throughout where 'A' stands for '2' and 'E' stands for 6.
A B A
$\times$ C A
D A D
E C E x
E F G D

What is the value of F?

• A. $9$
• B. $8$
• C. $3$
• D. $7$

Answer 1

The correct option is D $7$

As A=2 & E=6.
2 B 2
x C 2
D 2 D
6 C 6 x
6 F G D
In first multiplication
2x2=D=4 and 2xB=2 (unit digit) so B can be either 1 or 6, if it is 6, then the product is 2x6=12, where 1 is a carry over but, at the hundred's place also 2x2=4. Thus 2xB=2 and not 12 where B=1.

In second multiplication.
Cx2=6 so C is either 3 or 8, if it C=8, then the Ten's place multiplication would have become BxC+1=1xC+1, but it remains 1xC=C, thus C=3.
Therefore,
2 1 2
x 3 2
4 2 4
6 3 6 x
6 7 8 4

Hence, F = 7