19 is related to 209 following a certain logic. Following the same logic, 27 is related to 297. To which of the following is 61 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 — D. The note bars digit-level tricks, so test the pairs for one operation on the whole number.

209 divided by 19 = 11
297 divided by 27 = 11

Rule: multiply by 11. It fits both given pairs, which is the test a rule has to pass.

61 times 11 = 610 + 61 = 671 — option (d).

Why the others are wrong

• (a)
  653 — 653 is not a multiple of 11. The nearest multiples are 11 times 59 = 649 and 11 times 60 = 660, so no whole-number multiplier lands here.
• (b)
  600 — 600 comes from multiplying by roughly 10, but the first pair kills that rule outright: 19 times 10 is 190, not 209.
• (c)
  571 — 571 is not a multiple of 11 either, since 11 times 51 is 561 and 11 times 52 is 572. It is also below 61 times 10, so no multiplier reaches it.

A number-analogy item gives two worked pairs and asks you to apply the same rule to a third number. The point of giving two pairs is that a single pair can be explained several ways.

The note printed with this question tells you the operation acts on the whole number, so rules built from the digits are excluded before you start.

That leaves a small search: try dividing the output by the input, then subtracting, then squaring. Division settles this one on the first try.

Key facts

• 19 times 11 is 209 and 27 times 11 is 297, so the multiplier is the same in both pairs.
• Multiplying a two-digit number by 11 quickly: add a zero and then add the number, so 61 gives 610 plus 61.
• The question's note rules out breaking a number into its digits, which removes digit-sum and digit-swap rules from the search.

Common traps

• Fitting a rule to the first pair alone, since 19 plus 190 also gives 209 but 27 plus 190 gives 217
• Trying digit-level rules that the printed note has already excluded
• Computing 61 times 11 as 671 and then second-guessing it because the option list contains three near numbers

No directly related past PYQ was found.