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Question
Find the values of the letters in the following and give reasons for the steps involved.
A B
x 6
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B B B
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Solution
The multiplication of 6 and B gives a number whose one’s digit is B again.
It is possible only when B = 0, 2, 4, 6, or 8
If B = 0, then the product will be 0. Therefore, this value of B is not possible.
If B = 2, then B × 6 = 12 and 1 will be a carry for the next step.
6A + 1 = BB = 22 ⇒ 6A = 21 and hence, any integer value of A is not possible.
If B = 6, then B × 6 = 36 and 3 will be a carry for the next step.
6A + 3 = BB = 66 ⇒ 6A = 63 and hence, any integer value of A is not possible.
If B = 8, then B × 6 = 48 and 4 will be a carry for the next step.
6A + 4 = BB = 88 ⇒ 6A = 84 and hence, A = 14. However, A is a single digit number. Therefore, this value of A is not possible.
If B = 4, then B × 6 = 24 and 2 will be a carry for the next step.
6A + 2 = BB = 44 ⇒ 6A = 42 and hence, A = 7
The multiplication is as follows.
7 4
x 6
-----
444
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Hence, the values of A and B are 7 and 4 respectively.
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