Select the set in which the numbers are related in the same way as are the numbers of the given sets. (3, 9, 27) (4, 16, 64) (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. Each printed set is a number followed by its square and its cube.

Rule: (n, n², n³).

(3, 9, 27): 3² = 9 and 3³ = 27
(4, 16, 64): 4² = 16 and 4³ = 64

Testing option (c): 7² = 49 and 7³ = 343

Both worked sets and (7, 49, 343) obey the same rule, so it is the set.

Why the others are wrong

• (a)
  (6, 36, 84) — 6² = 36 is right, but 6³ = 216, not 84. The cube step fails.
• (b)
  (9, 81, 731) — 9² = 81 is right, and 9³ = 729 — two short of the printed 731. A deliberate near miss.
• (d)
  (5, 25, 120) — 5² = 25 is right, but 5³ = 125, not 120. Five short of the cube.

Set-analogy items give two worked sets and ask which option obeys the same rule. Derive the rule from both sets before looking at the options; a rule that fits only one is usually the wrong one.

Here every option gets its square right, so the square carries no information. The cube is the entire question, and the wrong options miss it by 132, 2 and 5.

The bracketed NOTE is routine on these: operations run on the whole number, so 27 is twenty-seven and never a 2 beside a 7.

Key facts

• Cubes to know here: 3³=27, 4³=64, 5³=125, 6³=216, 7³=343, 9³=729.
• Knowing cubes to 12 (12³ = 1,728) removes the arithmetic from most of these items.
• The NOTE forbids digit-splitting, so a rule needing the 4 and the 9 of 49 read apart is out of bounds.

Common traps

• Reading the rule off the first set alone
• Checking the middle number of each option, which is correct in all four
• Splitting a number into digits despite the NOTE forbidding it

No directly related past PYQ was found.