21 is related to 220 by certain logic. Following the same logic, 72 is related to 781. To which of the following is 27 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 — B. The bracketed rider says to work on the whole number, so look for one operation applied to 21 and to 72 as they stand.

Rule: 11 × (n − 1) — multiply by 11, then subtract 11.

21 → 11 × 21 = 231 → 231 − 11 = 220, which matches
72 → 11 × 72 = 792 → 792 − 11 = 781, which matches
27 → 11 × 27 = 297 → 297 − 11 = 286

286 is also the single value among the four options that divides by 11, so the arithmetic can be confirmed in a second → option (b).

Why the others are wrong

• (a)
  340 — 340 is not a multiple of 11 — 11 × 30 is 330 and 11 × 31 is 341 — and the rule 11 × (n − 1) only ever produces multiples of 11.
• (c)
  290 — 290 is the near miss for anyone who reaches 27 × 11 = 297 and then subtracts the wrong constant. Only a subtraction of 11 fits both worked pairs.
• (d)
  316 — 316 would need the constant to change between the two given pairs. Both 21 and 72 lose exactly 11 after multiplication, and 297 − 11 is 286.

A number-analogy item gives two worked pairs and one to complete. The efficient method is to find a single arithmetic relation that holds for both given pairs, never one that merely fits the first.

Start by testing a plain multiple. 220 ÷ 21 is not a whole number, so that is out.

Next test a multiple with a constant adjustment. 220 = 231 − 11 suggests the shape 11n − 11, and 11 × 72 − 11 = 781 confirms it on the second pair. Only then is it safe to apply the rule to 27.

Key facts

• The relation here is 11n − 11, which is the same as 11 × (n − 1).
• A candidate rule must satisfy both given pairs before it is applied to the third number.
• Divisibility by 11 uses the alternating digit sum, so for 286 it is 2 − 8 + 6 = 0, a multiple of 11.
• The bracketed rider forbids splitting a number into its digits, so 21 may not be read as 2 and 1.

Common traps

• Fitting a rule to the first pair alone. 21 × 10 + 10 also gives 220, but 72 × 10 + 10 is 730, not 781.
• Ignoring the rider and splitting 21 into the digits 2 and 1.
• Slipping on 11 × 27. It is 297, not 287, and the wrong product lands you near 276.

No directly related past PYQ was found.