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Which of the following options should come in place of the question mark (?) in the given series to make it logically complete? 429, 534, 452, 557, 475,?
574
555
580
592
580
Observe the two alternating series: 429, 452, 475 (+23 each step) and 534, 557, ? (+23 each step).
Observe the two alternating series: 429, 452, 475 (+23 each step) and 534, 557, ? (+23 each step).
Analyze the series structure
The series 429, 534, 452, 557, 475, ? consists of two alternating sub-series.
Identify Sub-Series 1
The terms at odd positions are 429, 452, 475. The differences are: 452 - 429 = 23 and 475 - 452 = 23. This is an arithmetic progression with a common difference of +23.
Identify Sub-Series 2
The terms at even positions are 534, 557, ?. The difference is: 557 - 534 = 23. To find the next term, add 23 to 557: 557 + 23 = 580.
A: 574 is incorrect, B: 555 is incorrect, D: 592 is incorrect; 580 is the only value obtained by continuing the +23 addition pattern in the alternating sequence.
C is correct because the series follows an alternating pattern where +23 is added to every second term, and 557 + 23 equals 580.
In numeric series, if values don't grow monotonically, always test for alternating sub-series (interleaved sequences) as the first step.
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