19 is related to 76 following a certain logic. Following the same logic, 27 is related to 108. To which of the following is 49 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 — A. Rule: the second number is four times the first.

19 × 4 = 76
27 × 4 = 108

Apply it to 49.
49 × 4 = 196 — option (a)

The same pairs also read as 'add three times the number', since 19 + 57 = 76 and 27 + 81 = 108. That reading gives 49 + 147 = 196 as well, so both routes agree.

Why the others are wrong

• (b)
  190 — 190 is six short of 4 × 49. It is 19 × 10 — a product built from the sample pair rather than from 49.
• (c)
  202 — 202 needs a spare +6 on top of 4 × 49. Neither sample pair carries a remainder: 19 × 4 hits 76 exactly and 27 × 4 hits 108 exactly.
• (d)
  198 — 198 exceeds 4 × 49 by two. A rule of the form 4n + 2 would send 19 to 78 rather than to the 76 the question prints.

A number analogy asks for one operation that fits every pair given, and the fastest first test is division: 76 divided by 19 is 4, and 108 divided by 27 is 4.

The bracketed note forbids splitting a number into its digits, which rules out tricks such as 'sum of the digits' and leaves only whole-number arithmetic.

When a single multiplier fits both pairs, stop looking. Extra terms invented to rescue one pair almost always break the other.

Key facts

• 76 = 19 × 4 and 108 = 27 × 4, so the operation is multiply by 4.
• 49 × 4 = 196.
• The stem's note bans digit-splitting, so only operations on the whole number are legal.

Common traps

• Testing the rule on one pair only and then picking the nearest option
• Applying the operation to a number from the sample pair instead of to 49

No directly related past PYQ was found.