Logical Reasoning - Number Series - Discussion
Discussion Forum : Number Series - Type 3 (Q.No. 15)
Directions to Solve
Look carefully for the pattern, and then choose which pair of numbers comes next.
15.
16 26 56 36 46 68 56
Answer: Option
Explanation:
Here, every third number follows a different pattern from the main series. In the main series, beginning with 16, 10 is added to each number to arrive at the next. In the alternating series, beginning with 56, 12 is added to each number to arrive at the next.
Discussion:
45 comments Page 4 of 5.
Prakash said:
1 decade ago
I can't understand your logic.
RAUANK SINGH said:
1 decade ago
16 26 [56]36 46 [68]56 66 [80]
after two no there will be adition of 12 and remaining series will continue like this.
after two no there will be adition of 12 and remaining series will continue like this.
Udit said:
1 decade ago
Raunak I did not understand please explain.
Vikash said:
1 decade ago
Raunak is absolutely correct and clear
Mrudula said:
1 decade ago
@Raunak thanks.
Rajju said:
1 decade ago
How it is explan briefly?
Sakshi said:
7 years ago
I can't understand this question. After 26 why 56 has came? Please explain it.
Almira said:
1 decade ago
The first time I've read the calculations, using numbers then finally I get it. It is just a simple logic. But difficult to understand if it is explained in words.
Anurag tripathi said:
1 decade ago
16 26 [56]36 46 [68]56 ...
Series 1: 16, 26, 36, 46, 56, 66, ...
Series 2: 56+12, 68+12, 80+12, ...
Series 1: 16, 26, 36, 46, 56, 66, ...
Series 2: 56+12, 68+12, 80+12, ...
Viktor said:
1 decade ago
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 :)
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 :)
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