Missing Numbers - 6

Logic Level 1

5 : 24 : : 6 : 35 : : 7 : 48 : : 8 : □ \large 5 : 24 ~::~ 6 : 35 ~::~ 7 : 48 ~::~ 8 : \square Find what number should replace the square.

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The answer is 63.

Ram Mohith by Ram Mohith , 18, India

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1 solution

Ram Mohith
Jan 18, 2019

Each term in the given analogy is of the form n : n 2 − 1 n : n^2 - 1 . So,

5 : 5 2 − 1 : : 6 : 6 2 − 1 : : 7 : 7 2 − 1 : : 8 : 8 2 − 1 5 : 24 : : 6 : 35 : : 7 : 48 : : 8 : 63 \begin{aligned} 5 : 5^2 - 1 ~::~ 6 : 6^2 - 1 ~:&:~ 7 : 7^2 - 1 ~::~ 8 : 8^2 - 1 \\ 5 : 24 ~::~ 6 : 35 ~:&:~ 7 : 48 ~::~ 8 : \boxed{63} \\ \end{aligned}

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You should give more terms to give people a clearer idea.

X X - 2 years, 4 months ago

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I didn't understand what you said. In analogy we will use only two terms. Or did you mean like this : 2 : 3 : : 3 : 8 : : 4 : 15 : : 5 : 24 : : 6 : 35.... 2 : 3 :: 3 : 8 :: 4 : 15 :: 5 : 24 :: 6 : 35 ....

Ram Mohith - 2 years, 4 months ago

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Something like that. Because if you don't give more terms, then I can say it is in the form of n : ( n − 1 ) ! n:(n-1)!

X X - 2 years, 4 months ago

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@X X – This is a good point @X X . I will update it. In this type of problems we must be very careful as there may be two different answers for two different valid approches for the same question.

Ram Mohith - 2 years, 4 months ago

Also worth noting is n^2 - 1 = (n+1)(n-1), so it can also be the product of the term's immediate neighbours.

Marcopolo Chan - 2 years, 4 months ago

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