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.) 11 – 14 – 8 – 17; 12 – 15 – 9 – 18
- (a)5 – 8 – 3 – 10
- (b)6 – 9 – 3 – 12
- (c)3 – 6 – 2 – 8
- (d)4 – 7 – 12 – 18
Answer
Why
Correct — B. Read the differences along each given set.
11 - 14 - 8 - 17: 14 = 11 + 3, 8 = 14 − 6, 17 = 8 + 9
12 - 15 - 9 - 18: 15 = 12 + 3, 9 = 15 − 6, 18 = 9 + 9
Rule: +3, then −6, then +9, applied to the whole number each time.
Test it on 6:
6 + 3 = 9
9 − 6 = 3
3 + 9 = 12
That is 6 - 9 - 3 - 12 -> option (b).
Why the others are wrong
- (a)5 – 8 – 3 – 10 — 5 - 8 - 3 - 10 passes the first step, 5 + 3 = 8, but then needs 8 − 6 = 3, and 8 − 6 is 2. Its own steps are +3, −5, +7.
- (c)3 – 6 – 2 – 8 — 3 - 6 - 2 - 8 also opens with +3, but 6 − 6 = 0, not 2. Its steps are +3, −4, +6, so the fall is too shallow.
- (d)4 – 7 – 12 – 18 — 4 - 7 - 12 - 18 opens with +3 and then rises to 12 where the rule falls by 6. Its steps are +3, +5, +6.
Concept
A number-chain analogy asks for a fixed sequence of operations applied in the same order to every set. Find the differences first — here they are enough.
The differences are +3, −6, +9: a rise, then a fall, then a rise, each three larger than the last.
Test every step of a candidate, not the first one. A chain is only right if all three steps match, and options are built so that the early steps agree.
All four options open with +3, so the first step separates nothing. The second step, the fall of 6, is what decides the item.
Key facts
- The operation chain is +3, then −6, then +9.
- Both given sets obey it: 11 - 14 - 8 - 17 and 12 - 15 - 9 - 18.
- The stem's note bars breaking a number into its digits before operating on it.
Study next
Common traps
- Stopping after the first step, which every option here passes.
- Reading the differences correctly but applying them in the wrong order.
- Splitting a two-digit number into its digits, which the stem's note forbids.
The note about operating on whole numbers is printed in the stem itself, so digit-level tricks are off the table — operate on 11, never on 1 and 1.
A different kind of number pattern sits at Reasoning Q.7 in this shift (19 Sep 2024, 09:00), where the operators themselves are interchanged.
Related PYQs
No directly related past PYQ was found.