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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.) 16 – 17 – 21 – 30; 13 – 14 – 18 – 27
24 – 25 – 29 – 42
15 – 16 – 20 – 26
11 – 12 – 16 – 18
22 – 23 – 27 – 36
22 – 23 – 27 – 36
Look at the differences between consecutive numbers in each set. If the differences form a consistent increasing arithmetic sequence (e.g., +1, +4, +9 or +1, +4, +9 or similar patterns), find the matching option immediately without testing every arithmetic combination.
Look at the differences between consecutive numbers in each set. If the differences form a consistent increasing arithmetic sequence (e.g., +1, +4, +9 or +1, +4, +9 or similar patterns), find the matching option immediately without testing every arithmetic combination.
Analyze Set 1 Differences
For the first set (16, 17, 21, 30), find the difference between consecutive terms: 17 - 16 = 1 (+1), 21 - 17 = 4 (+4), 30 - 21 = 9 (+9). The differences are +1, +4, +9, which correspond to the squares of consecutive integers (1 squared, 2 squared, 3 squared).
Verify Set 2 Differences
For the second set (13, 14, 18, 27), check consecutive differences: 14 - 13 = 1 (+1), 18 - 14 = 4 (+4), 27 - 18 = 9 (+9). This confirms the underlying rule is adding consecutive squares (+1², +2², +3²).
Test Option D
For Option D (22, 23, 27, 36), calculate consecutive differences: 23 - 22 = 1 (+1), 27 - 23 = 4 (+4), 36 - 27 = 9 (+9). Since the differences are exactly +1, +4, +9, it perfectly matches the given sets' pattern.
A: Differences are +1, +4, +13 (incorrect pattern). B: Differences are +1, +4, +6 (incorrect pattern). C: Differences are +1, +4, +2 (incorrect pattern).
D is correct because the given number sets follow a progressive addition of consecutive squares (+1², +2², +3²), and Option D (22 – 23 – 27 – 36) exhibits the exact same difference sequence: 23-22=+1, 27-23=+4, and 36-27=+9.
When analyzing multi-term number sequences, always compute first-order differences (and second-order if necessary) before attempting complex multiplication or division rules.
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