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Question
Find the value of the letter in the following and give reasons for the steps involved.
1 A
x A
------
9 A
------
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Solution
The multiplication of A with A itself gives a number whose ones digit is A again. This happens only when A = 1, 5, or 6.
If A = 1, then the multiplication will be 11 × 1 = 11. However, here the tens digit is given as 9. Therefore, A = 1 is not possible. Similarly, if A = 5, then the multiplication will be 15 × 5 = 75. Thus, A = 5 is also not possible.
If we take A = 6, then 16 × 6 = 96. Therefore, A should be 6.
The multiplication is as follows
1 6
x 6
------
9 6
------
Hence, the value of A is 6.
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