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.

(1/2) and (5/10)

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(4/7) and (6/9)

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(6/11) and (60/110)

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(5/7) and (10/12)

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Solution

The correct options are
A
(1/2) and (5/10)

C
(6/11) and (60/110)

$\frac{1}{2}$ and $\frac{5}{10}$ are both equal, as dividing one apple into two parts or dividing 5 apples into 10 parts would both give us apples of equal sizes. Similarly, $\frac{6}{11}$ and $\frac{60}{110}$ are equal.

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Similar questions

Bill wanted to confirm his observation regarding the physical sizes of occupants of the “House of Rational Numbers, Q”. He observed two such occupants – " $\frac{2}{3}$ " and " $\frac{3}{5}$ "

Bill told himself – " $\frac{3}{5}$ " has physically a larger size. Say whether Bill’s inference is True or False.

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)

___

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.

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 heard that in “The Hall of Operations”, there was another ancient temple, named “The Reciprocus”.

Legend says that when an occupant, say “a”, of the “House of Rational Numbers, Q” enters the temple, it exits the temple as a different occupant, “b”,belonging to the same house. Bill observed that, these occupants “a” and “b”, when they enter the hall of multiplication, they exit the hall as “1”.

Bill realized that the numerical counterparts of a and b (Earth 1) are ___________ of each other.

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The correct options are A (1/2) and (5/10) C (6/11) and (60/110) 12 and 510 are both equal, as dividing one apple into two parts or dividing 5 apples into 10 parts would both give us apples of equal sizes. Similarly, 611 and 60110 are equal.

The correct options are
A
(1/2) and (5/10)

C
(6/11) and (60/110)

$\frac{1}{2}$ and $\frac{5}{10}$ are both equal, as dividing one apple into two parts or dividing 5 apples into 10 parts would both give us apples of equal sizes. Similarly, $\frac{6}{11}$ and $\frac{60}{110}$ are equal.