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

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D A D

E C E X

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E F G D

Which of the following numbers stand for C A B ?

• A. 467
• B. 324
• C. 627
• D. 321

Answer 1

The correct option is D 321

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,
22=D=4 and 2$\times$B=2 (unit digit)

So B can be either 1 or 6, if it is 6, then the product is 2$\times$6=12, where 1 is a carry over but, at the Hundred's place also 2$\times$2=4. Thus 2$\times$B=2 and not 12 where B=1.

In the second multiplication.
C$\times$2 = 6 so C is either 3 or 8, if it C=8, then the Ten's place multiplication would have become B$\times$C+1=1C+1, but it remains 1C=C, thus C=3.
Therefore,
2 1 2
x 3 2
4 2 4
6 3 6 x
6 7 8 4
So, C,A,B take the value 3, 2 and 1 respectively.

321 stands for CAB (option D)