14 is related to 42 following a certain logic. Following the same logic, 26 is related to 78. To which of the following is 47 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. Rule: the second number is three times the first.

14 × 3 = 42
26 × 3 = 78

Apply it to 47.
47 × 3 = 141 — option (d)

Division confirms it from the other side: 42 divided by 14 is 3, and 78 divided by 26 is 3.

Why the others are wrong

• (a)
  143 — 143 is two more than 3 × 47. A rule of the form 3n + 2 would send 14 to 44, not to the 42 the question prints.
• (b)
  135 — 135 is 3 × 45, not 3 × 47. It is the right rule applied to the wrong number.
• (c)
  137 — 137 is four short of 3 × 47, and it is a prime, so no whole-number multiple of 47 can land on it.

Same machinery as any fixed-multiplier analogy: divide the second number of each given pair by the first and see whether one quotient serves both.

42 divided by 14 is 3 and 78 divided by 26 is 3, so the operation is multiply by 3 and nothing further needs testing.

The bracketed note bars digit-level operations, which is what stops you reading 14 and 42 as the digits 1, 4, 4 and 2.

Key facts

• 42 = 14 × 3 and 78 = 26 × 3, so the multiplier is 3.
• 47 × 3 = 141.
• All four options sit between 135 and 143, so an estimate cannot separate them.

Common traps

• Multiplying the wrong number, which turns 3 × 45 into the tempting 135
• Adding a small constant to force one pair to fit when the other pair leaves no remainder

No directly related past PYQ was found.