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Question
212 × 5 is a multiple of 3 and 11. Find the value of x.
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Solution
Since, 212 × 5 is a multiple of 3,
2 + 1 + 2 + x + 5 = 0, 3, 6, 9, 12, 15, 18,
⇒ 10 + x = 0, 3, 6,...........
⇒ x = 2, 5, 8 ...(i)
Again, 212 × 5 is a multiple of 11, (2 + 2 + 5) – (1 + x) = 0, 11, 22, 33
⇒ 8 – x = 0, 11, 22,....
⇒ x = 8 ...(ii)
From equations (i) and (ii), we have
x = 8
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