Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) 8 – 33 – 66 – 81; 11 – 36 – 72– 87
- (a)21 – 46 – 82 – 107
- (b)18 – 43 – 86 – 100
- (c)15 – 40 – 80 – 95
- (d)6 – 31 – 62 – 97
Answer
Why
Correct — C. Pull the chain of operations out of both given sets, then run it on each option.
8 – 33 – 66 – 81 is +25, then ×2, then +15.
11 – 36 – 72 – 87 is +25, then ×2, then +15.
Rule: +25, then ×2, then +15, applied to the whole number each time.
15 + 25 = 40
40 × 2 = 80
80 + 15 = 95
The chain 15 – 40 – 80 – 95 holds at every step, so option (c) follows the same operations.
Why the others are wrong
- (a)21 – 46 – 82 – 107 — The first step works, 21 + 25 = 46, but 46 × 2 = 92, not 82. The chain breaks at the doubling.
- (b)18 – 43 – 86 – 100 — Two steps hold, 18 + 25 = 43 and 43 × 2 = 86, and then the last one fails: 86 + 15 = 101, not 100.
- (d)6 – 31 – 62 – 97 — 6 + 25 = 31 and 31 × 2 = 62 both hold, but the jump from 62 to 97 is +35, not the +15 the given sets fix.
Concept
These items give two worked examples of one hidden chain. Derive the chain from both, never from one: 8 → 33 on its own also fits multiply by 4 and add 1, and that reading dies the moment 11 → 36 has to satisfy it too.
The bracketed NOTE is doing real work. Operations act on the whole number, so splitting 33 into 3 and 3 is not allowed, and digit-sum or digit-reversal readings are ruled out before you start.
Every option here survives the first step, so the item is decided at the second and third — check an option all the way through before accepting it.
Key facts
- Both given sets follow +25, then ×2, then +15.
- 8 + 25 = 33, 33 × 2 = 66 and 66 + 15 = 81, which is the first given set.
- 15 + 25 = 40, 40 × 2 = 80 and 80 + 15 = 95, so all three steps hold for the keyed chain.
Study next
Common traps
- Reading the chain off the first set alone, after which two options appear to fit
- Abandoning an option halfway once the first two steps look right
- Breaking a number into digits despite the NOTE forbidding it
The stem is fixed word for word and only the chain changes — 18 Sep 2024, 12:30, Reasoning Q.9 and 12 Sep 2024, 12:30, Reasoning Q.2 both carry it, NOTE about whole numbers included.
Related PYQs
No directly related past PYQ was found.