Select the option in which the numbers share the same relationship as that shared by the given pair of numbers. (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.) 40 : 123 63 : 192

Correct — D. Rule: second number = 3 × first + 3.

40 → 3 × 40 = 120, and 120 + 3 = 123 ✓
63 → 3 × 63 = 189, and 189 + 3 = 192 ✓

Now run it on each option's first number:
39 → 3 × 39 = 117, and 117 + 3 = 120 ✓ → option (d).

Why the others are wrong

• (a)
  48 : 152 — 48 gives 3 × 48 + 3 = 147, not the 152 printed beside it.
• (b)
  46 : 131 — 46 gives 3 × 46 + 3 = 141, ten more than the 131 printed beside it.
• (c)
  68 : 214 — 68 gives 3 × 68 + 3 = 207, not the 214 printed beside it.

A number-pair analogy fixes a rule from two worked examples and asks which option obeys it. Test the multiplier first — 123 divided by 40 is a little over 3, and 192 divided by 63 is a little over 3 — then find the small constant that closes both gaps.

123 − 120 = 3 and 192 − 189 = 3, so the rule is 3n + 3, which is the same as 3(n + 1). The bracketed form is quicker to run in your head across four options.

Key facts

• 40 : 123 and 63 : 192 both obey second = 3 × first + 3.
• The rule can be written 3(n + 1), which is faster to apply than 3n + 3.
• Of the four options only 39 : 120 obeys it, since 3 × 39 + 3 = 120.

Common traps

• Settling for a multiplier of 3 and dropping the constant, which lands on 117
• Splitting the numbers into digits despite the note forbidding it
• Stopping at the first option that looks close

No directly related past PYQ was found.