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.) 33 : 340 48 : 490

Correct — D. Treat each pair as one operation on the whole number, exactly as the note demands.

Rule: second = (first + 1) × 10.
33 → (33 + 1) × 10 = 340
48 → (48 + 1) × 10 = 490
63 → (63 + 1) × 10 = 640 → option (d)

Why the others are wrong

• (a)
  27 : 270 — 27 : 270 is 27 × 10 with the +1 dropped; the rule needs (27 + 1) × 10 = 280.
• (b)
  31 : 279 — 31 : 279 is 31 × 9, a different operation altogether — (31 + 1) × 10 would give 320.
• (c)
  44 : 460 — 44 : 460 adds 2 before multiplying, since (44 + 2) × 10 = 460. The rule adds 1, giving 450.

A number analogy hands you two worked pairs so that a rule fitting only one of them can be thrown out.

33 → 340 on its own is satisfied by ×10 then +10, by (n + 1) × 10 and by several near misses. Testing 48 → 490 keeps the first two, and those two are the same rule written differently.

The bracketed note is doing real work: it bars digit-level play, so you may not split 33 into 3 and 3. Every candidate rule has to survive on the whole number.

Key facts

• (33 + 1) × 10 = 340 and (48 + 1) × 10 = 490.
• The keyed pair follows the same step: (63 + 1) × 10 = 640.
• The note in the question forbids breaking a number into its digits.

Common traps

• Fitting a rule to the first pair and never checking it against the second.
• Settling for a near miss such as 27 × 10 = 270 because it looks like the same family.
• Splitting numbers into digits despite the note that forbids it.

No directly related past PYQ was found.