Select the option in which the numbers share the same relationship as that shared by the given pair of numbers. (149, 213) (168, 232) (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. Work out the gap inside each given pair first.

Rule: second = first + 64.

213 − 149 = 64
232 − 168 = 64

Now test the four candidates:

(a) 222 − 162 = 60
(b) 217 − 153 = 64
(c) 211 − 137 = 74
(d) 198 − 144 = 54

Only (153, 217) keeps the gap of 64 → option (b)

Why the others are wrong

• (a)
  (162, 222) — (162, 222) gaps by 60, four short. Both sample pairs gap by exactly 64 and the rule is not allowed to drift.
• (c)
  (137, 211) — (137, 211) gaps by 74. 137 + 64 would be 201, not 211.
• (d)
  (144, 198) — (144, 198) gaps by 54. 144 + 64 would be 208, so this pair fails the same test.

Two sample pairs are given rather than one, and that is the gift: whatever rule you propose must hold for both before you take it to the options.

Difference is the cheapest test, so run it first. Only if the two differences disagree do you move on to ratios or to power-plus-offset rules.

The NOTE bars digit-level operations, so 149 is one number, not a 1, a 4 and a 9.

Key facts

• 213 − 149 = 64 and 232 − 168 = 64.
• 153 + 64 = 217.
• The other three options gap by 60, 74 and 54 respectively.

Common traps

• Comparing 149 with 168 instead of comparing inside each pair
• Accepting an option after checking only its first number against the samples
• Splitting 149 into digits, which the NOTE forbids

No directly related past PYQ was found.