Question

By which of the following numbers, $N = 0.abccbaabccba……$ must be multiplied so that the product is an integer?

• A. 990909
• B. 90909
• C. 9990
• D. 99099

Answer 1

Answer: (B)

90909

Answer 2

Given, $N = 0.abccbaabccb.................$
$⇒N = 0\ \overline {abccba}$
It is clear that, $N$ is divisible by $11$,
$⇒ (a+b+c) - (a + b+ c) = 0$
Now, $N =\frac {abccba}{999999}$
By cancelling common factor $11$ from numerator and denominator,
We get $90909$ in denominator.
Therefore, we should multiply N by $90909$ so that product is an integer

So, the correct option is (B): $90909$