64 is related to 4 following a certain logic. Following the same logic, 216 is related to 6. To which of the following is 729 related, following the same logic? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /deleting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)

Correct — C. The second number is the cube root of the first.

Rule: ∛n
64 → ∛64 = 4
216 → ∛216 = 6
729 → ∛729 = 9

Check it forwards if roots are slow: 9 × 9 = 81, and 81 × 9 = 729. So 729 is related to 9 — option (c).

Why the others are wrong

• (a)
  11 — 11³ = 1331, well past 729. The cube is fixed by both worked pairs, so the answer must be the number whose cube is exactly 729.
• (b)
  7 — 7³ = 343, not 729. The pairs also rule out a square root, since √64 would give 8 while the paper gives 4.
• (d)
  13 — 13³ = 2197. The three numbers in play, 64, 216 and 729, are the cubes of 4, 6 and 9, and 13 belongs to none of them.

The pair 64 → 4 has more than one reading. 64 is 4 cubed, and it is also 8 squared, so the first pair alone leaves a square root open.

The second pair settles it. 216 is 6³, and 216 is not a perfect square at all, so no square-root rule can survive. That is why SSC gives two worked pairs before asking anything.

Once the operation is fixed, the work is recall: 729 is the cube of 9.

Key facts

• 4³ = 64, 6³ = 216 and 9³ = 729.
• 216 is not a perfect square, which is what rules out a square-root reading of the first pair.
• The cubes worth knowing on sight run 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000.

Common traps

• Reading 64 → 4 as a square root and then being stranded on 216
• Taking √729 = 27 instead of ∛729 = 9, since 729 is both a square and a cube
• Settling on a number-times-itself rule without checking which power the second pair demands

No directly related past PYQ was found.