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.) 17 : 67 21 : 79

Correct — A. Both given pairs obey one linear rule.

Rule: second = first × 3 + 16.

17 × 3 = 51 → 51 + 16 = 67
21 × 3 = 63 → 63 + 16 = 79

Apply it to option (a): 34 × 3 = 102 → 102 + 16 = 118, which is the number printed beside 34. Option (a) is the pair that shares the relationship.

Why the others are wrong

• (b)
  23 : 69 — 23 × 3 = 69 exactly, so this pair is a plain tripling with nothing added. Both given pairs add 16 after tripling, and 23 × 3 + 16 is 85.
• (c)
  33 : 110 — 33 × 3 + 16 = 115, not 110. The printed 110 is 33 × 3 + 11, so the added constant is wrong even though the multiplier is right.
• (d)
  42 : 100 — 42 × 3 + 16 = 142, nowhere near 100. The printed 100 is 42 × 2 + 16, so the multiplier here is 2 rather than 3.

A number-pair analogy asks you to fit one rule to two given pairs, then test the options against it.

Run the checks in order. Constant difference first, then constant ratio, then the two-step form ax + b.

Here the differences are 50 and 58, so addition alone is out. The ratios, 3.94 and 3.76, are close but not equal, which is the signature of ax + b with a small a and a positive b.

Key facts

• 67 = 17 × 3 + 16 and 79 = 21 × 3 + 16 — a single rule covers both given pairs.
• The differences 67 − 17 = 50 and 79 − 21 = 58 are unequal, which rules out constant addition.
• The printed NOTE bars splitting a number into digits, so 17 must be handled as 17.

Common traps

• Testing only constant addition and guessing once 50 and 58 disagree.
• Fitting a rule to a single given pair, which is how 23 : 69 survives as plain tripling.
• Accepting an option whose multiplier is right without checking the added constant.

No directly related past PYQ was found.