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Question

During his explorations on Earth 2, Bill happened to visit “Numerus Linum”. Bill was excited to visit this place because he had heard a lot of stories about this place. Legend has it that this place is said to have a note of EVERY occupant of the “House of Rational Numbers, Q”. It was also rumored that this place is essentially a huge line which extends forever on both sides and never ends. It is on this line that all these occupants of the house are marked – each occupant has a unique place.

Bill wanted to see if this rumor was actually true, he decided to see the marking for the occupant “12.456”. He knew that this occupant would be between “12” and “13” and so he navigated to the mark 12. What could be his next step to identify “12.456”?


A

Navigate to the occupant which lies immediately next to 12

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B

He would be able to identify “12.456” if he could identify 12.4 and 12.5

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C

He would be able to identify “12.456” if he could identify 12.45 and 12.46

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D

None of the above

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Solution

The correct options are
B

He would be able to identify “12.456” if he could identify 12.4 and 12.5


C

He would be able to identify “12.456” if he could identify 12.45 and 12.46


He needs to divide the space between 12 and 13 into 10 parts and cover 4 parts to get to 12.4, as 12.456 would lie between 12.4 and 12.5. Similarly, having reached 12.4, he has to get to 12.45 by dividing the region between 12.4 and 12.5 into 10 equal parts and moving to 12.45. As the number lies between 12.45 and 12.46, he has to repeat the operation one more time. Now, he can get to 12.457

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