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

The Correct Option is B

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): \(90909\)