Choose one number which is similar to numbers in the given set:
8, 1331, 4913
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2197
All three numbers of the set are cubes of prime numbers:
\(8=2^3\), \(1331=11^3\), \(4913=17^3\), and 2, 11 and 17 are primes
\(2197=13^3\), and 13 is a prime, so 2197 belongs to the set
Why the other options are incorrect
Option (1) 121 — Incorrect. \(121=11^2\) is the square of a prime, not a cube.
Option (3) 49 — Incorrect. \(49=7^2\) is also the square of a prime, not a cube.
Option (4) 81 — Incorrect. \(81=3^4=9^2\) is a fourth power and a square, not a cube.
Note: The original NTA paper printed Option (3) as 64. NTA’s answer key accepted it as well as Option (2), because \(64=4^3\) is also a perfect cube, which fits the set if one looks only at cubes and not at their prime roots. For the benefit of students and to ensure a single answer, Option (3) has been changed to 49, a square and not a cube. Two cubes walked into the options, and NTA’s key let both of them in.