Select the option in which the numbers share the same relationship as that shared by the given pair of numbers. (317, 202) (438, 323) (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 — C. Rule: second number = first number − 115.

317 − 202 = 115
438 − 323 = 115

Now subtract inside each option, on the whole numbers as the printed note demands:

(a) 415 − 295 = 120
(b) 391 − 270 = 121
(c) 402 − 287 = 115
(d) 424 − 315 = 109

Only option (c) reproduces the gap of 115.

Why the others are wrong

• (a)
  (415, 295) — 415 − 295 = 120, five more than the required 115 — a near miss aimed at anyone who eyeballs the size of the numbers instead of subtracting.
• (b)
  (391, 270) — 391 − 270 = 121, so this pair shares no relation with the two given pairs.
• (d)
  (424, 315) — 424 − 315 = 109. Subtraction is the whole job here, and 109 is not 115.

Number-pair items are worked by testing the basic relations in a fixed order: difference, then ratio, then square or cube, then a mix such as n² + k.

Start with the difference, because it is the cheapest test. Here 317 − 202 and 438 − 323 both give 115, one constant explains both given pairs, and there is no reason to go further.

The note attached to the stem forbids splitting a number into its digits, which removes digit-sum and digit-reversal answers before you begin.

Key facts

• 317 − 202 = 115 and 438 − 323 = 115.
• 402 − 287 = 115, which matches both given pairs.
• The printed note bars breaking a number into its constituent digits.

Common traps

• Trying a ratio first and burning time when a plain difference works
• Subtracting in the wrong order and then hunting for +115
• Rejecting the right option after a careless 402 − 287

No directly related past PYQ was found.