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”?

Navigate to the occupant which lies immediately next to 12

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

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

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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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Similar questions

Bill noticed that it was easy to find occupants of the “House of Rational Numbers, Q” if they “dressed up” in their decimal form. He wanted to understand if he could locate the occupants of the house on Numerus Linum if they were in their “ $\frac{p}{q}$ ” form. Bill remembered interacting once with the occupant “ $\frac{2}{9}$ ” before. He thought of locating this on the line. Bill knew that this occupant lived between occupants “0” and “1” – both of which had markings on the line. To locate “ $\frac{2}{9}$ ”, Bill first mentally divided the part on Numerus Linum between 0 and 1 with required number of markings – which was “x”. Then he navigated to division number “y” after 0 to reach “ $\frac{2}{9}$ ”.

What is the numerical value of (x+y)?

___

Bill thought of giving “The Hall of Operations” a visit, after listening to these interesting behaviors of the halls towards occupants from different rooms and houses.

He happened to visit the Hall from the back door entry and he saw 4 huge stones, one against each of the 4 halls (Addition, Subtraction, Multiplication and Division). Each stone had engravings on it describing the hall against which it is erected.

On one such stone, the following was engraved

“This hall has been and forever will be commutative for EVERY occupant of the “House of Rational Numbers, Q””.

This stone could correspond to which of the four halls?

Bill heard that the two entries of the “Hall of Division” had special names – Numerator and Denominator. A special detector is installed at the entry “Denominator” so that it does not allow one specific occupant (referred to as “The Oblivion”) from the “House of Rational Numbers, Q”. When Bill enquired as to why the entry “Denominator” shows such strict regulations towards this particular occupant, he was told that the presence of The Oblivion at the “Denominator” entry could erase the entire Earth 2 from existence and that life on Earth 2 would become undefined.

Choose the correct inference made by Bill:

Bill understood the meaning of the engravings. He had a better idea of the nature of the occupants of “The House of Rational Numbers, Q”. He saw another stone which had the following message engraved:

"This hall would always be associative for any occupants of the "House of Rational Numbers, Q""

This stone could correspond to which of the four halls?

Having left the “House of Rational Numbers, Q”, Bill wandered off to a playground where a group of occupants (numbers) of Earth 2 were playing. He observed that a team consisted only of the occupants from one room or a house.

The captain of one such team was " $\frac{2}{3}$ " an occupant of “House of Rational Numbers, Q”. He needs to pick players who are part of his house only. Select all the possible players given in the options below that the captain could pick.

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