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A number is multiplied by 11 and 11 is added to the product. If the resulting number is divisible by 13, the smallest original number is = ?
Answer & Solution
Correct Answer:
Option
A
Let the required number be x.
Then, $$\frac{11x + 11}{13}$$ = a whole number.
So, (11x + 11) must be divisible by 13
By hit and trial, we get x = 12
Hence, the smallest original number is 12
Then, $$\frac{11x + 11}{13}$$ = a whole number.
So, (11x + 11) must be divisible by 13
By hit and trial, we get x = 12
Hence, the smallest original number is 12
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Loginthe number is multiplied by 11. 11*x=y
11 is added to the product. 11*x= y+11
Now, the product is divisible by 13. 11*x= (y+11)/13
By hit and trial, apply x=12,
11*12= 132+11= 143 which is divisible by 13.
So the answer is 12.