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Complete the analogy. 8128 : 496 :: 496 : ?
28
30
24
31
28
Recognize the sequence of perfect numbers (a positive integer that is equal to the sum of its proper divisors). The sequence goes 6, 28, 496, 8128.
Recognize the sequence of perfect numbers (a positive integer that is equal to the sum of its proper divisors). The sequence goes 6, 28, 496, 8128.
Identify the number property
The given numbers 8128 and 496 are consecutive terms in the sequence of perfect numbers. A perfect number equals the sum of its proper positive divisors.
Verify the sequence
The sequence of perfect numbers is 6, 28, 496, 8128. In the given analogy 8128 : 496, the relationship is (Term N) : (Term N-1).
Apply to the next pair
Given the pattern 8128 : 496, applying the same logic to 496, we look for the number that precedes 496 in the perfect number sequence, which is 28.
B: 30 is not a perfect number, C: 24 is not a perfect number, D: 31 is a prime number, not a perfect number.
A is correct because the series represents consecutive perfect numbers in descending order: 8128, 496, 28.
Always keep a mental list of special number types like perfect numbers, Fibonacci sequence, and prime numbers, as they frequently appear in SSC and Banking exams.
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