In the following question, two numbers given on the left of the sign (: :) are related in some way. Find the numbers having the same relationship with the number given to the right of the sign (: :)
729 : 7 :: 9261 : ?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 19
Note: It seems that there is a mistake in the original NTA paper, which prints the number on the right as 9621, which is not a perfect cube (\(21^3=9261\) and \(22^3=10648\)). To arrive at the NTA answer, it should read 9261, as shown in the question here and explained below. NTA’s printer swapped two digits, and 9261 stopped being a cube.
729 is a perfect cube, and the number paired with it comes from its cube root minus 2.
\(729=9^3\), and \(9-2=7\)
\(9261=21^3\) (since \(21^2=441\) and \(441\times21=9261\)), and \(21-2=19\)