17 is related to 102 following a certain logic. Following the same logic, 29 is related to 174. To which of the following is 39 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. Both given pairs return the same quotient, so the relation is a single multiplication.

102 ÷ 17 = 6
174 ÷ 29 = 6

Rule: multiply the whole number by 6.

40 × 6 = 240
240 − 6 = 234

So 39 × 6 = 234, which is option (b).

Why the others are wrong

• (a)
  228 — 228 is 38 × 6 — the right multiplier on the wrong number. Reaching 234 as 240 − 6 and subtracting the 6 twice lands here.
• (c)
  230 — 230 is not a multiple of 6: its digit sum is 5, so it is not divisible by 3, and a multiple of 6 must be.
• (d)
  238 — 238 is even but its digit sum is 13, so it fails the divisibility test for 3 and cannot be a multiple of 6. It is 34 × 7.

A number analogy with two worked pairs is a two-point fit. Take the ratio of each pair; if the two agree, the relation is multiplicative and the answer can be computed rather than hunted for among the options.

Divisibility then gives a free second check. A multiple of 6 must be even and have a digit sum divisible by 3, which throws out two of these four options before any multiplication is done.

Key facts

• 102 ÷ 17 = 6 and 174 ÷ 29 = 6, fixing the rule as multiply by 6.
• 39 × 6 = 234.
• A number is divisible by 6 only when it is even and its digit sum is a multiple of 3.

Common traps

• Computing 40 × 6 = 240 and then taking 6 off twice, which gives 228
• Assuming the multiplier is the same as in a similar item met in another shift
• Accepting an option because it is even, without checking the digit sum

No directly related past PYQ was found.