# Pairs based series

As the name suggests this type of series are formed with a common rule between pairs, triplets or quadruplets in the series. Let’s start with a simple example

1, 2, 4, 5, 9, 10, 37, ?

Notice the following:

(1, 2), (4, 5), (9, 10) have the second number in the pair as the mathematical increment (+1) of the first number. Consequently the next number in the series is 37 + 1 = 38.

Now, let’s practice with a few more examples

Q) 3, 9, 2, 4, 5, 25, 11, ?

A] 121

B] 14

C] 69

D] 49

E] 4

Solution

Solution – A] 121. As we observe in (3,9), (2,4), (5,25) the second number in the pair is the square of the first number, consequently the next number in the series is 11×11 = 121

Q) 1, 1, 2, 2, 11, 13, 6, 4, 10, 5, 2, ?

A] 10

B] 9

C] 8

D] 7

E] 4

Solution

Solution – D] 7. A slightly more tricky example, here we see a triplet pairing in action

(1,1,2), (2,11,13), (6,4,10) we observe that the third number in each triplet is the sum of the first two numbers. Consequently, the next number in the series would be 5 + 2 = 7.

Q) 1, 7, 9, 1, 6, 2, 1, 4, 3, ?

A] 3

B] 0

C] -1

D] 11

E] 1

Solution

Solution – E] 1. We see a recurrent 1 in the series, using that as a hint, lets try to split the series in triplets form.

(1,7,9) (1,6,2) (1,4,3), we observe that the first number in each triplet is 1 and hence the first digit (and the next number in the series) in the next triplet will be 1.

Q) 4, 3, 6, 2, 2, 8, 4, 4, 5, 6, 3, ?

A] 11

B] 10

C] 4.5

D] -4

E] 10.5

Solution

Solution – B] 10. A more complicated example, not seeing a clear patterns by splitting into doubles or triplets, lets try splitting the series into quadruplets.

(4,3,6,2) (4×3 = 6×2)

(2,8,4,4) (2×8 = 4×4)

We notice that the product of the first two digits in the quadruplet is equal to the product of the last two numbers in the quadruplet.

(5,6,3,?)

Hence the solution is 10

We can’t stress enough the importance of this solution method. If you want to get quick on these types of questions do check out our IPAT practice guide here. Let’s next move on to another very important type of the IPAT numeric series question – the interleaved series.