Logical Reasoning - Number Series - Discussion

Hi all,

I believe there is another explanation to this series, and I'd like to share it here.

If you look at the official answer, it seems like we have two series of numbers that are kind of randomly chosen. One series is an incrementation of 16 by 10, the other one is an incrementation of 56 by 12, and the two series are not connected.

I can prove to you that there actually is a connection between the two series that can be explained with 3 simple patterns.

To understand the patterns, try not to look at the numbers of the series, but at the difference from one to the next:

10, 30, -20, 10, 22, -12, 10

Obviously, 10 is what you need to get from 16 to 26, and so on.

I propose that the patterns are based on groups of 3 numbers each. So, the first group is {10, 30, -20}, and so on.

Pattern 1: The third number in a group can be received by subtracting the second from the first number, i.e. 10 - 30 = -20

Pattern 2: Every first number in a group is calculated by adding the numbers 2 and 3 from the previous group, i.e. 30 + (-20) = 10

Pattern 3: This is where it gets interesting because this is the pattern that removes the randomness out of the two series. Every second number in the group is received by subtracting 8 from the second number in the previous group, i.e. 30-8=22.

Using these patterns, you will correctly find the missing numbers:

Pattern 2 tells us that the difference between 56 and the next (unknown) number equals 22+(-12), which is 10, so the number we're looking for is 66.

Pattern 3 tells us that the difference between 66 and the next (unknown) number equals 22 -8 = 14, so the following number is 80.

We could now easily take it further, the difference to the next unknown number would be, according to pattern 1, equal to 10-14 which is -4, so the third unknown would be 76.

As you can see, 76 equals to 66 + 10 which is what we would expect anyway from the original solution.

I assume this explanation will be interesting especially to those who don't understand the choice of the number 56 and were explained that it's just a random starting point which, according to my patterns, it's not.

Enjoy :)

Let's assume the two unknown numbers be x and y respectively.
16 26 56 36 46 68 56 x y.

Let (in sequence)
[ 16 26 56 ] be series (a)
[36 46 68 ] be series (b) and
[56 x y ] be series (c).

Now substrate (b-a)
36 46 68 ------> (b)
16 26 56 -------> (a)
i.e = 20 20 12 ------> (i)
{These are the difference between a and b series}

Now, add the difference (i) with (b)
36 46 68 ------> (b)
20 20 12-------> (i)
=56 66 80 (answer)

x = 66,
y = 80.

In this number series, note
16 26 56, 36 46 68, 56...

Let's break it from every 3rd number as :
Series 1:- 16 26 36 46 56 and so on
Series 2:- 56 68...

Now, if we note that
Series 1:- 16+10= 26,
26+10= 36,
36+10= 46,
46+10= 56 and so on.
So next one will be:- 56+10= 66.
Now series 2:- 56+12= 68,
So next one will be:- 68+12= 80.

Hence our series is like this:-
16, 26, 56, 36, 46, 68, 56, 68, 80.

This is simple, take 16, 26, 56 as series 1.

36, 46, 68 series 2,

56, 68, 80 series 3 now check all one positions in every series is added with 20, all second positions in every series is added with 20 and finally, all third positions in every series is added with 12. Hence we got the series 16, 26, 56, 36, 46, 68, 56, 68, 80.

Given Series 16 26 56 36 46 68 56.

There are two series merged.
1) 16 26 36 46 56...
2) 56 68...

16+10=26.
26+10=36.
36+10=46.
46+10=56.
56+10=66....

In second series, which is appearing at every third position in the given pattern(- - 56 - - 68 - - ?).

It's simple addition.

56+12= 68.
68+12= 80.

So the Ans is 66 80.

First of all 3rd number is different (56, 68). But 1st and 2nd at difference of 10. And also 4th and 5th difference of 10.

So next will become at place 8th is (56+10=66) and 9th will become according to addition 3rd place of 12 such as (56+12=68) at 6th place and 9th will be (68+12=80). Last one is ( (66 80).

1st & 2nd numbers = 16, 26.

Then
4th & 5th numbes = 36, 46.
Then as per the series repeated,
7th & 8th = 56,[ 66].

Now,
After the first 2 numbers = 56.
Again after 2 numbers = 56 + 12 = 68.
As per series = 68 + 12 = [80].

According to logic answer is,
[66,80].

Hope this is helpful.

In the given series,

First second---- fourth fifth---- seventh eighth....... are one series which is +10 for next reach like 26, 36, 46, 56, (66),76 ...
Similarly, third---- sixth---- ninth... are the second series which is +12 for next reach like 56, 68, (80), 92...

So the answer is 66, 80.

Again as question 13, you consider two separate series ..
1st series..(starting wid 16)
16 ,26,36 ,46, 56, 66 ....They are increasing by 10

and the 2nd series (starting with 56) i.e
56 ,68, 80.. They are increasing by 12 !

that way you get 16 ,26 ,56 ,36, 46 ,68 ,56, 66,80....

It is Simple.

To get the second number you should add 10 to the first number and every third number added with 12.

16 + 10 = 26
36 + 10 = 46
56 + 10 = 66
Here, the third number is 56, 68,
From the given, 56 + 12=68,
Similarly 68 + 12 = 80,
Our answer is 66, 80.