Interleaved series almost always come up in the IPAT and are one of the easiest to recognize and solve. Lets try to explain this series type with an example:
1, 2, 5, 3, 9, 4, ?
If we split this series into two series –
1, 5, 9 (consists of the 1st 3rd and 5th numbers – all odd numbered terms)
2, 3, 4 (consists of the 2nd 4th and 6th numbers –all even numbered terms)
We see a simple difference based pattern in both series. The first series has a constant difference of 4 while the second series has a constant difference of 1. The next number in the parent series (which is the 7th term- an odd number) is the next number in the 1st sub series (1,5,9) and hence is equal to 9 + 4 = 13.
The rule of 1, 2, 3
The rule of 1,2,3 gives us a simple framework to approach this type of series. The rule goes as follows: form subseries in the series by first leaving 1 term in between, then 2 terms in between and then 3 terms in between to see which interleaved difference gives a legitimate difference series.
For example, the series above had a subseries gap of 1 term. Here is an example of 2 term subseries
1, 7, 11, 2, 9, 14, 3, 11, 17
Breaking the series into subseries based on 2 term difference
1, 2, 3 (1st, 4th, 7th terms : simple difference series with constant difference of 1)
7, 9, 11 (2nd, 5th, 8th terms : simple difference series with constant difference of 2)
11, 14, 17 (3rd, 6th and 9th terms: simple difference series with constant difference of 3)
Now let’s practice with some IPAT like questions
Q) 7, 6, 14, 12, 21, 18, ?
A] 32
B] 28
C] 14
D] 17
E] 21
Solution
Solution – B] 28. Breaking the series into subseries based on 1 term difference we observe-
7, 14, 21, ? (This is 7×1, 7×2, 7×3)
6, 12, 18 (This is 6×1, 6×2, 6×3)
It is seen that terms in each subseries are multiple of the first number in the subseries. Hence the solution is 7×4 = 28
Q) 2, 3, 4, 4, 9, 16, 16, 81, ?
A] 169
B] 144
C] 256
D] 250
E] 181
Solution
Solution – C] 256. Breaking the series into three subseries with a 2 term (as 1 term does not yield any solution) interleave difference we see.
2, 4, 16
3, 9, 81
4, 16, ?
We observe the next term in each subseries in the square of the previous term in the same subseries.
Hence the solution is 16×16 = 256
Q) 1, 2, 3, 4, 1.1, 3, 6, 4, 1.21, 4.5, 12, 4, 1.331, ?
A] 6.75
B] 1.441
C] 14.11
D] 7.25
E] 8.25
Solution
Solution – A] 6.75. Here is a more complex series, breaking the series into subseries with a 3 term interleave difference we see –
1, 1.1, 1.21, 1.331 ( each next term is formed by multiplying previous term by 1.1)
2, 3, 4.5, ? (each next term is formed by multiplying previous term by 1.5)
3, 6, 12 (each next term is formed by multiplying previous term by 2)
4, 4, 4 (each next term is formed by multiplying previous term by 1)
Consequently, the next term in the series is 4.5×1.5 = 6.75
Want more practice? Get the most comprehensive IPAT numeric series practice guide here