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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 to/subtracting from/multiplying with 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
6 – 36 – 72 – 144; 7 – 49 – 98 – 196
15 – 225 – 625 – 676
5 – 25 – 50 – 110
8 – 64 – 128 – 226
12 – 144 – 288 – 576
12 – 144 – 288 – 576
Identify the pattern: (N) → (N * N) → (N² * 2) → (N² * 4). Every set follows X, X², 2X², 4X².
Identify the pattern: (N) → (N * N) → (N² * 2) → (N² * 4). Every set follows X, X², 2X², 4X².
Analyze the pattern
In both given sets (6-36-72-144 and 7-49-98-196), the relation is: Second number = (First)2. Third number = (Second) * 2. Fourth number = (Third) * 2.
Apply to Options
Checking Option D: 12. 12² = 144. 144 * 2 = 288. 288 * 2 = 576. This perfectly matches the sequence 12 - 144 - 288 - 576.
A: 15² is 225, but 2252 is 450, not 625. B: 5² is 25, 252 is 50, but 502 is 100, not 110. C: 8² is 64, 642 is 128, but 128*2 is 256, not 226.
D is correct because the series follows the mathematical progression of N, N squared, 2 times N squared, and 4 times N squared (12, 144, 288, 576).
When encountering these sets, always test for square relations first as they are the most common foundation for rapid arithmetic progressions.
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