If the series 4, 5, 8, 13, 14, 17, 22, .... is continued in the same pattern, which one of the following is not a term of this series?
33
Begin as always with the differences between consecutive terms, because a repeating cycle in the gaps is the commonest structure in series of this kind.
The differences are 5 - 4 = 1, 8 - 5 = 3, 13 - 8 = 5, 14 - 13 = 1, 17 - 14 = 3, 22 - 17 = 5. So the pattern of gaps is 1, 3, 5 repeating in a cycle of three.
Continuing from 22 with the same cycle: 22 + 1 = 23, 23 + 3 = 26, 26 + 5 = 31, 31 + 1 = 32, 32 + 3 = 35, 35 + 5 = 40.
The full series is therefore 4, 5, 8, 13, 14, 17, 22, 23, 26, 31, 32, 35, 40, and so on.
Checking the options against it: 31 appears, 32 appears, 35 appears, but 33 does not. Between 32 and 35 the series jumps by 3, skipping 33 and 34 entirely.
The trap is that 31, 32 and 35 are clustered close together, which makes it tempting to assume the series covers that whole stretch of numbers. It does not - the cycle 1, 3, 5 means the terms come in tight pairs separated by a gap of 5, and 33 falls inside one of those gaps. A useful safeguard is to extend the series far enough past the largest option before checking any of them, rather than testing each option in isolation.
Hence 33 is not a term of this series.
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Important Questions from Number Series
- In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 676 :: 17 : Y - Which of the following options should come in place of the question mark (?) in the given series to make it logically complete?
125, 128, 133, 140, 149,? - What should come in place of the question mark (?) in the given series?
801 800 792 765 701 ? - What should come in place of the question mark (?) in the given series?
101 110 121 134 149 ? - What should come in place of the question mark (?) in the given series?
40, 48, 58, 66, 76, ?
