16 is related to 63 following a certain logic. Following the same logic, 28 is…
2026
16 is related to 63 following a certain logic. Following the same logic, 28 is related to 99. To which of the following is 12 related to, following the same logic? (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 / subtracting / 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.)
Answer: D. 51 — Concept: In a number analogy the two whole numbers of every given pair are joined by one single arithmetic rule that must hold for all the pairs. When that…
- A.
73
- B.
77
- C.
76
- D.
51
Attempted by 18 students.
Show answer & explanation
Correct answer: D
Concept: In a number analogy the two whole numbers of every given pair are joined by one single arithmetic rule that must hold for all the pairs. When that rule has the linear form (number × a) + b, two given pairs are enough to fix it completely: the multiplier a equals the change in the second numbers divided by the change in the first numbers, and the constant b is whatever remains after the multiplication is subtracted.
Application:
The given pairs are 16 → 63 and 28 → 99.
Change in the second numbers: 99 − 63 = 36. Change in the first numbers: 28 − 16 = 12.
Multiplier: a = 36 ÷ 12 = 3.
Constant: b = 63 − (3 × 16) = 63 − 48 = 15.
So the rule is (number × 3) + 15, which is the same as 3 × (number + 5).
Apply the rule to 12: (12 × 3) + 15 = 36 + 15 = 51.
Cross-check:
First pair: (16 × 3) + 15 = 48 + 15 = 63, which matches the given 63.
Second pair: (28 × 3) + 15 = 84 + 15 = 99, which matches the given 99.
The equivalent form 3 × (number + 5) gives 3 × 21 = 63 and 3 × 33 = 99, so both readings of the rule agree, and it gives 3 × 17 = 51 for 12.
Every step multiplies or adds to the whole number itself, so the note's restriction against splitting a number into its constituent digits is respected.
Hence, following the same logic, 12 is related to 51.