Below are given two sets of numbers. In each set of numbers, a certain…
2026
Below are given two sets of numbers. In each set of numbers, a certain mathematical operation on the first number results in the second number. Similarly, a certain mathematical operation on the second number results in the third number, and so on. Which of the given options follows the same set of operations as in the question?
(NOTE: Operations should be performed on the whole numbers, without breaking the numbers down into their 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.)
44 - 308 - 307 - 317
28 - 196 - 195 - 205
Answer: B. 16 - 112 - 111 - 121 — Concept: In a number-analogy chain, every arrow stands for one fixed arithmetic operation applied to the whole preceding number, and the same ordered sequence…
- A.
38 - 304 - 298 - 308
- B.
16 - 112 - 111 - 121
- C.
41 - 287 - 279 - 289
- D.
50 - 300 - 294 - 303
Attempted by 28 students.
Show answer & explanation
Correct answer: B
Concept: In a number-analogy chain, every arrow stands for one fixed arithmetic operation applied to the whole preceding number, and the same ordered sequence of operations must govern every chain of the family. The rule is therefore recovered by testing consecutive terms first as a ratio (which exposes a multiplication) and then as a difference (which exposes an addition or a subtraction), and it is accepted only when both sample chains obey that identical ordered rule.
Application — recover the rule from the two given chains:
First arrow of 44 - 308 - 307 - 317: 308 ÷ 44 = 7, so the operation is × 7.
Second arrow: 308 − 307 = 1, so the operation is − 1.
Third arrow: 317 − 307 = 10, so the operation is + 10.
Test the same ordered rule on 28 - 196 - 195 - 205: 28 × 7 = 196, 196 − 1 = 195, 195 + 10 = 205. Both sample chains obey × 7, then − 1, then + 10.
Application — generate the chain that each candidate first term must produce under × 7, − 1, + 10:
First term | × 7 | − 1 | + 10 |
|---|---|---|---|
38 | 266 | 265 | 275 |
16 | 112 | 111 | 121 |
41 | 287 | 286 | 296 |
50 | 350 | 349 | 359 |
Cross-check — where the other printed chains depart from the recovered rule:
38 - 304 - 298 - 308 multiplies by 8 at the first step (38 × 8 = 304) and subtracts 6 at the second, so both the multiplier and the subtractor differ.
41 - 287 - 279 - 289 begins correctly with × 7 (41 × 7 = 287) but then subtracts 8 rather than 1, so the chain breaks at the second arrow.
50 - 300 - 294 - 303 multiplies by 6 (50 × 6 = 300), subtracts 6 and adds 9, so none of its three operations match.
Result: the printed chain 16 - 112 - 111 - 121 is exactly the chain generated by × 7, then − 1, then + 10, so it is the required answer.