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)?

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Solution

Bill needs to divide 0 to 1 into 9 equal parts. To divide the region between 0 and 1 into 9 equal parts he would have to make 8 markings and select 2 parts of it.
Thus, x = 8, and y = 2
so that, (x + y) = 8 +2 = 10

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Similar questions

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”?

During his initial days of stay in Earth 2, Bill had got his accommodation with “1/5” and “1/2” in “House of Rational Numbers, Q”. Having located these occupants, he wanted to locate other occupants satisfying the following conditions:

1. They lie between 1/5 and 1/2.

2. They have a denominator 10.

Which of the following occupants satisfy these properties?

Bill met a couple of friends from the “House of Rational Numbers, Q”. They claimed to be unharmed by The Reciprocus. Bill challenged both of them to prove their claim. These occupants went to the temple, entered and exited the temple,with no effect on them! The Reciprocus had no effect on these occupants!

How many occupants could be in that group? (Enter the numerical value)

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Bill took his time to admire the “House of Rational Numbers, Q”. He observed an interesting feature of the occupants on Earth 2.

The physical size of the occupants depends on their numerical value, i.e. if “a” and “b” are two occupants of the house, the sizes of “a” and “b” depend on the numerical values“a” and “b”. If a $>$ b, then “a” would appear larger and if a $<$ b, “a” would appear smaller compared to “b”

Bill noticed TWO occupants of the house which were equal in size. Who could these occupants be? Choose all the correct possible pairs.

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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Bill needs to divide 0 to 1 into 9 equal parts. To divide the region between 0 and 1 into 9 equal parts he would have to make 8 markings and select 2 parts of it. Thus, x = 8, and y = 2 so that, (x + y) = 8 +2 = 10

Bill needs to divide 0 to 1 into 9 equal parts. To divide the region between 0 and 1 into 9 equal parts he would have to make 8 markings and select 2 parts of it.
Thus, x = 8, and y = 2
so that, (x + y) = 8 +2 = 10