Number series (2^n − 1 pattern): 15, 31, 63, 127, 255, (…) Determine the next Mersenne-type number in the sequence.
Aptitude
Odd Man Out and Series
Difficulty: Easy
Choose an option
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A513
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B511
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C517
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D523
Answer
Correct Answer: 511
Explanation
Introduction / Context:The sequence resembles Mersenne numbers of the form 2^n − 1. Recognizing powers of two and subtracting one is a staple pattern in number series problems.
Given Data / Assumptions:
- Given terms: 15, 31, 63, 127, 255.
- Test whether each equals 2^n − 1 for increasing n.
Concept / Approach:Check: 2^4 − 1 = 15, 2^5 − 1 = 31, 2^6 − 1 = 63, 2^7 − 1 = 127, 2^8 − 1 = 255. The next would be 2^9 − 1.
Step-by-Step Solution:
2^4 − 1 = 16 − 1 = 15.2^5 − 1 = 32 − 1 = 31.2^6 − 1 = 64 − 1 = 63.2^7 − 1 = 128 − 1 = 127.2^8 − 1 = 256 − 1 = 255.Next: 2^9 − 1 = 512 − 1 = 511.Verification / Alternative check:Observe the near-doubling between terms, consistent with powers of two less one.
Why Other Options Are Wrong:
- 513, 517, 523: Not equal to 2^n − 1 for n = 9; 2^9 − 1 is 511.
Common Pitfalls:Assuming exact doubling; the sequence grows approximately doubling minus one, not pure geometric progression.
Final Answer:511