189 is related to 21 following a certain logic. Following the same logic, 234 is related to 26. To which of the following is 468 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.
Rule: divide by 9.

189 ÷ 9 = 21
234 ÷ 9 = 26
468 ÷ 9 = 52

The stem's note bars splitting a number into its digits, so you are looking for one operation on the whole number — and a single constant divisor fits both given pairs.

468 ÷ 9 = 52, which is option (c).

Why the others are wrong

• (a)
  58 — 58 × 9 = 522, not 468, so 58 cannot be 468 divided by the same constant.
• (b)
  48 — 468 ÷ 9 is 52, so 48 falls four short. Landing on 48 would need a divisor of 9.75.
• (d)
  54 — 54 is the ninth of 486, not of 468. The two numbers are a digit swap apart, which is the whole trap.

Number analogies give you two solved pairs and one to finish. The discipline is to find a rule that fits both solved pairs before touching the third.

Run through the usual candidates on the first pair — a constant added or subtracted, a constant multiplier or divisor, a square, a cube, a digit-sum — then test the survivor on the second pair. Here 189 to 21 and 234 to 26 are both a division by 9, and nothing else fits both.

The whole-number rider in the stem is a real constraint: it removes every rule that works on individual digits.

Key facts

• 189 = 9 × 21 and 234 = 9 × 26, so the constant is a divisor of 9.
• 468 = 9 × 52.
• The stem's note bars digit-level operations, so the relation acts on the whole number.

Common traps

• Fitting a rule to the first pair and never testing it on the second
• Confusing 468 with 486, whose ninth is 54

No directly related past PYQ was found.