Transcript for:
Logical Reasoning: Series Lecture

welcome to a logical reasoning video on series from Korea right calm this is an important topic of placement test job interviews and entrance exams wherein many candidates struggle they are not able to quickly find the relation in the series and hence they waste a lot of time on the question many even at the end leave the question and some of them don't even attempt the question but today we will see some approaches and tips to quickly solve the questions on theories along with this you can check out latest job offerings in the market on Korea right calm the profile which you submit will be shared directly by us with the employers you will also get to know of interview experiences shared by other candidate so now let's start with series first let us take a look regarding types and tips the off series okay now over here type means series can be of three major types ok 99% sums are related to this only one is numeric that is related to number second is alphabet that is letters and the third one is alpha numerics that is letters plus numbers combination of letters a number and the fourth type is generally as that is symbols we are not going to deal with it because generally symbol has no logic whatever logic is needed for solving symbol series it is already given in the question okay so no need to consider symbols over here here will focus on the most important topic where 99% sums are asked that is numbers letters and letter numbers or alphanumeric right now series sums can be asked in three formats okay these are three types there are three formats of sums one is find the next number in the series or find the next group of letters or makes later in the series next then is find the missing numbers or the missing alphabet or the missing group of alphabets the third one is find the odd man out or find the odd number or the odd alphabet or the or group within the given series right now we have seen the type we have scenes of the format of questions over here in the type these types need three types have many subcategories okay these subcategories are you have already seen these subcategories it is nothing big in it we are going to see each and every subcategory so that you will be able to understand what kind of sums are are and how to approach them okay now let's move on to some tips regarding series while approaching the series some please understand the first thing you have to do is to find the relation between the given element okay and second sum is using the relation solve the question and get the answer now how to find a relation okay or what kind of relation we should search now whenever you are talking about finding a relation let us assume that this is a series 3 4 5 6 this is a series now in it say if we take this element we have to find the relation of this element with the previous element and the next element then if you move on to this element find the relation between previous element and next element if we move on to this element find the relation between previous element and next element then you will get a pattern okay this pattern is what we need and using this pattern we can solve the question so now how to go on or how to approach in finding the relation very easy what you need to do is I'd say this is a series okay this is a series 1 2 3 4 5 6 and we have to find the pattern in it what you need to do first is let us find the difference between two elements okay in this is for only for the number series okay I'm not talking about letters and alphanumeric for that I am going to tell you a different strategy for but form numbers it is important please pay attention over here because this will help you get the series pattern very very quickly okay or easily now over here let us find the difference between two numbers 2 minus 1 is 1 3 minus 2 is 1 4 minus 3 is 1 here you are seeing that there is a steady difference or a constant difference if the difference is not constant okay if the difference is like first there is a difference of 1 there between the second and third element the differences of say seventh then third and fourth the difference is suddenly 25 and fourth and fifth differences say 215 six differences say five thousand five hundred so this difference is increasing arbitrarily and it is very very huge it is not going steadily something like that it is increasing very well it is going very high if there is a very steep rise in the difference in such cases always remember that the series must be related to square of number cube of number or multiplication okay or simple multiplications right if this is the case if the difference between the numbers or element is very very high it is increasing very highly or very quickly that means the series is related to squares of numbers cubes of numbers multiplication of numbers okay now we tell you what exactly we mean by square tube multiplication but just remember this I am going to repeat it afterwards also but still remember it if the difference is constant like this 1 1 1 or if the differences are increasing very slowly like you know the difference is 1 then here the difference is instead of 1 it becomes 3 then your the difference becomes page 7 then here the difference becomes say 10 your difference becomes say 50 so it is increasing but it is slowly increasing it is not increasing very arbitrarily and all that stuff so over here in this scenario the series must be related to addition okay addition subtraction multiplication division multiplication division okay or the series might be of of prime numbers or it might be of Fibonacci sequence I tell you what all these things are given a sequence for n numbers addition subtraction okay but just listen to what I am saying so these might be three types there are many more okay miscellaneous types also are there or combinations is also there so these these two rules which are there they are very very important while approaching was some related to see is always keep these rules in mind that is the reason I've told you right at the start okay now what we will do is now we will first see what are the type of series okay okay we will see what is numeric series what is letters what is alphanumeric and then we will try while solving the sums we will try to understand how to approach the stands are related to series okay of more detailed approach as to how to identify what kind of series it might be okay moving on to the first type that is a numeric series number series numeric series or number series has a lot of subcategories okay we will denote a few prominent ones or the basic ones which are extremely important and most on the related to that okay first one is related to addition or the addition series take a look at this example 19 25 30 to 40 question mark and we have 59 now in this series what we have learned first always showing the difference 25-19 is 6 this is 6 32 minus 25 is 7 40 - 30 breezy that means that 19 plus 6 you will get 25 25 plus 7 universe 32 32 + 8 unit 40 so here we are finding difference so here our pattern is emerging that 4 6 is added then in the second element 7 is added in the third element it is added that is one more so in fourth element how much should we added plus 9 okay then you will get some answer over here and in that you will add 10 and you will get 59 so let's see whether we are right or not 19 plus 625 + 7 32 + 8 is 40 plus 9 is 49 and 49 + 10 is 15 9 so this series looks complete it is following a pattern so 6 is added then 7 then it such kind of tedious addition series where things just are just added ok to the previous number you add something to get the next number again you add something over here to get the next number now here there is plus 6 plus 7 plus 8 plus 9 plus 10 okay they might even have add a plus 1 plus 1 plus one or plus 2 plus 2 plus 2 or they might even add say odd numbers right so force they'll add 1 then they'll add they're 83 then they'll add 5 then they'll add 7 then they'll add 9 only odd numbers my divided or only even numbers might get addition can be of anything so when you determine that it is an addition series you just need to find out the pattern as to what exactly is being added same way you have the subtraction series okay in subtraction series instead of addition it is subtraction for example 1 0 2 it is 568 question mark 34 what is the difference 1 0 to minus 85 is 1785 minus 68 is 70 so 1 0 to minus 17 is 85 85 minus 17 is 68 so here also it should be subtracting minus 17 subtracting 1730 68 minus 17 you get 51 again from here you subtract 17 and you get 34 so you're a constant value has been subtracted okay so whenever a series is increasing it is addition or multiplication okay next number is greater than previous number okay so 32 is also greater than 1940 greater than 1949 greater than 1925 so it is increasing like this so it is addition or multiplication series in subtraction the numbers will decrease like this okay even individual the numbers will decrease right now next like addition subtraction like we have talked about right now multiplication series in multiplication series the number is multiplied by some number to get the next number like I will give you an example take a look at this series 1 2 6 24 1 21 2 2 okay what is the difference the difference is 1 6 difference is 4 24 here difference is 18 20 minus 24 120 minus 24 different 96 see the difference is increasing very very quickly that means this must to multiplication okay so let's try to think of some multiplication like one in two what is the relation 1 into 2 is 2 okay so we found this relation 1 into 2 is 2 2 & 6 what might be the relation we know 2 into 3 is 6 correct now 6 and 24 what can be the relation 6 into 4 is 24 so what is happening is that the next number which is there it is taken over here and it is multiplied by something it is first it is multiplied by the first is multiplied by 2 then 3 then 4 so this must be multiplied by 5 right this should come over here and this must be multiplied by 5 so 24 into 5 we can 120 right so what will be the next number right it's 120 over here here it is 5 2 3 4 5 6 120 into 6 will give you 720 this is the answer this is multiplication it might also happen that each of these each of the number is multiplied by a constant number okay let's say 6 12 24 48 96 6 is multiplied by 2 you get 12 12 is again multiplied by 2 you get 24 24 is multiplied by 2 you get 48 48 is multiplied by 2 you get 96 okay such multiplication can also be there same way there is division there is nothing to it okay this is the division series take a look at it okay - 1 672 36 12 question mark - ok here the difference which is there it is falling okay here we saw if it is rising very quickly it is multiplication if it is falling very quickly exactly opposite that is this will be division okay let us see what division 216 when it is divided by 3 you will get 72 72 when you divide by 2 you get 36 36 again when you divide by 3 with 12 so divided by 3/2 divided by 3/2 answer here it will be 6 again divided by 3 3 2 3 2 3 you will get stress too so our answer is correct the year it will come near the answer will be six this is division we are going to see examples of all of these so don't worry don't panic there is nothing to it it is very very easy now after these basic numeric series let us move on to some special numeric series now special numeric series I mean they are not that special I just said it for like if X purpose and all that sub but over here see there are some numeric series which you should know for sure because many a times sums are asked on then the first one is regarding okay square the square of a number Square cubes and the series which are nearer to it I'll explain what it means near to it and all that stuff okay you you must know squares of numbers square up to 30 and you must know cubes of numbers up to 10 it is very very useful to Desa for other series also it would be useful for your quant right so first of all let us see an example of square series or sour numbers near it say take a look at this series zero okay not this 0 3 8 15 24 35 question mark 63 now if you observe closely if what do we see over your differences 3 minus 0 is how much 3 8 minus 3 difference is 5 you hear difference is 7 here the difference is 911 okay question we don't know where so it is increasing okay it is steadily increasing right so this must be related to addition subtraction multiplication something like that now over here we have taken smaller values okay if we go on if you go on increasing over here you will realize that it is increasing more and more the difference is increasing more and more okay over here if you observe very closely this is 0 0 is nothing but 1 minus 1 3 is nothing but 4 minus 1 it is nothing but 9 minus 1 15 is 16 minus 1 this is 25 minus 1 this is the 6-1 question mark we don't know this is 64 minus one and this is nothing but 1 squared 2 squared 3 squared 4 squared 5 squared 6 square so by default here it should be 7 square this is H square so 7 square minus 1 now you'll see that by looking directly at this how will we guess that it is a square series or something like that that is the thing of series whenever you get a series if you are not able to think about what series it might be you have to apply some tricks like okay is this mirror to school some square is this mirror to some square is it a square of some number like that okay here it is 4 square minus 1 nice study it is 4 2 square minus 1 3 square minus 1 4 square minus 1 all that stuff is given over here this is what we mean by square series or a series which is nearer to square if you talk about cubes what you can have this is a cube series 64 125 to 1 6 3 4 3 okay observe carefully these this is for cube this is 5 cube this is 6 cube and this is 7 Q okay these are the cubes so this is a series now after this take let us take a look at another very important special series and that is nothing but prime and number series okay you know what are prime numbers random numbers are those numbers which are divisible by themselves and one apart from that no other number okay so we know 1 is not a prime number with prime number start with 2 2 3 5 7 11 13 17 19 and so on these are crimes of us this is the prime number theory it might happen that they might give you an addition series okay and in that while adding first they'll add two then July 3 then there are five then they'll add seven okay so such kind of you need to find out what the addition is and then you need to see okay this is like prime numbers are getting added so after 7-eleven is the next prime number so in the next element I have to add 11 after 11 13 is the next prime number so I add 13 in the next element to get the next element okay this is prime number series the numbers which are not prime are called as composite numbers okay the rest of them are numbers like four six eight okay nine ten all twelve all these numbers are composite numbers because they are not prime now after prime number series a very important series I am going to talk about that is the Fibonacci series now what do we mean by the Fibonacci series over here in Fibonacci series the best part about Fibonacci series is that state this is for second third fourth fifth sixth element okay addition of this element and this element will give you this element if you want this element then add this and this you will get this element okay if you want this element you will have to add this element to this element and then you will get this element so Fibonacci series always starts with two one that is this C I'll draw over here one and one Fibonacci sequence starts with this and it goes on up to infinity so this is the first element this is the second element so what is the next element and this end is what you will get one plus one is two what is the next element at the previous two elements two plus one is three next three plus two is five next Phi plus three is eight 8 plus 5 is 13 13 plus eight is 21 21 plus 13 is 34 34 plus 21 is 55 plus is 89 89 plus 55 is 144 and so on okay this is the Fibonacci sequence or the Fibonacci series so in exact okay or in paper they might give you the series right from here to here like that in between only so you just need to check whether addition of these two numbers is this these two numbers is this these two numbers is this if that is the case that means that it is a Fibonacci sequence and you just need to add these two numbers to get the next number okay after privelage a sequence I am going to tell you a very important point please pay attention okay it is really very important sometimes it might happen that a series is given like say one say two three four five eight seven six five four okay this series is given now here you observe it increases the difference here from one to eight there is an increase it to two there is a decrease to two seven three seven two three three degrees so if the research increase decrease increase decrease that means that there are two possibilities one is there are two different series just like I wrote over here one two three four five and other series I wrote eight seven six five four there might be two different series or there is another possibility that is that two different operations are going on that means once it is getting a here some addition is there and your subtraction is that your addition is there your subtraction is that something like that is going on okay so two different operations are going on or they are two different series everything in these ways we are going to see example of it but still I am telling you right now I will explain it again during the example also apart from this say if you are not able to understand how to solve a sum what you need to do is you just need to break the number and analyze each number individually that also we are going to see it might also happen that say for synthesis a b c d e if so instead of given directly ABC they might write c ba they might reverse it okay if e d okay they might reverse it and give the series even that is the possibility of to check that also okay so we have seen some of the theories right now let's move on to we have seen numeric series let us move on to the alphabet series or the letter series alphabet series are bit easier than number series or the numeric series and the thing that is going to help you a lot when it comes to alphabets agrees and alphanumeric series is this A to Z you have to write always whenever you go to the exam always write a to z and their position that is a comes first v ii z is 26 okay and reverse position this is another very important concept that you should know reverse position of the letters that means even read is considered as one y will be two x will be three and a will be 26 how to find reverse positions we have checked that out in the previous logical reasoning videos okay but again I also tell you over here total number of letters are 26 okay so what is 26 plus 127 so if you want the reverse position of any alphabet just subtract the original position from 27 let us take an example B over your original position is 4 I want the reverse position of d 27 - 427 - for what is the answer 23 this is the reverse position of D this will become 24 this will become 25 and a will be gone 26 okay see how easy it is remember subtract from the original position from 27 and you will get the reverse position when you go in the exam always write this down right the reverse positions also so it becomes very easier to calculate okay now we will see how this chart of A to Z helps in alphabet series later on while solving the sum but over your in alphabet series okay I draw lines over here okay there are two type of sums which means early are as 99% x so these two types are there one is regarding vowels and consonants okay wobbles and consonants what are the words AEIOU okay a I owe you these are the vowels and relate it to this the question might be asked or this omit the vowels and they just keep on Sun and that is the rest of the letters and the question would be asked on that and the second would be the position of the alphabet okay Val which we have like a-to-z their position question might be on their position like first is there okay then this gets two letters and directly right Adele skip B and C B and C is skipped and they'll write D again E and s two letters are stripped and they'll write G like that so it is based on position right so there are many types in this we are going to sing it in examples but remember that there are only two types muesli and the best way to tackle tackle the sums related to alphabet series is discharge a-to-z now here also you should see the position of the first alphabet C the position of the next alphabet then the third alphabet there are two type of two type of sunset media's it might be like this a b c d that is a each element is just one letter and sometimes there may be groups instead of letters like a b c d e f g h i j k l and we have to find the next three letters okay so here what we have to do take the first letter find relation with the second letter take the second find relation with the fourth and also we have to find the relation of this group with this okay so such things are there it is very easy actually once you draw the chart you will very easily be able to get the answer or the pattern let us take a look at you example so that it would become more and more clear now look at this example c e h question marks then you have Oh Q T then we have u W Z we have to find what comes in place of question mark see this is the first letter okay C is over here e1 position second position so plus two you will get e e f g h okay plus two again what you let us know I can see de only one one over here only one skip is e and from E to H one skip second step okay so two skips are there and then the third letter is written over here for oqt four against one skip oh is over here one skip you get P okay one skip Q and T one skip second skip there are two skips over here again here also one skip you are also two skips between W and Z so whatever answer will come over here okay whatever options would be given a b c d e whatever options are there we have to see that in that option the whatever is given like for example they give say m o-- r we have to as a then we have to see if between m no.1 skip is there and onr two scripts are there if that is the case that will be our answer okay see how easy it is using this table or this whatever rough mode you have written over of A to Z and the positions let us take another example B D is if H e then question mark then in p m now over here B and D what is the difference here B is over here B and E difference is 1 so there is only one skip OKC has been skipped be skipping C then we get B okay then B and a now the a comes before D so 1 1 before D is c2 before D is V and 3 before D is a so what we can say between D and a the differences minus 3 ok 1 2 & 3 this is the third so minus 3 d 2h when we go three places back we will get a same way over here F G G has been skipped so plus 1 and derivative H now H 2 e again 1 over here look at the table over here E and H 1 2 & 3 again minus 3 skips here also into P 1 skip and P 2 m we have to go backwards three times is right is minus three the third letter backwards would be in so whatever would be the answer over here we have to see that that group has this pattern right plus 1 and minus 3 now over here we have DD we have fhe we have NPN there must be some relation between this group and this group let us find out what the relation is you can there are two ways to think about it what you can think is that after a they have given directly s okay a to AK what is the distance one two three four okay four is the distance between a and F is the fifth distances fourth and fifth is f so distances for now e to the next later now this group has one two and three letters so distance between E and this first letter would be how much again for right what is it one two three and four it will be J so it has to be J over here also we have learned that from J okay when we skip one the next one will be the second letter J skip one don't write k it would be l l comes over here again from L we have to skip three in the opposite direction that is with to go rivers we have to go back three one two and three what we get is i okay from i now let us check this for okay whether it is for or not from i 1 2 3 & 4 we get NS v so we are exactly right on track and we have s recorded properly this is how you identify now there is another logic to identify the connection between these two elements or these two elements let us see what over here what do we have we have V da okay now we know a comes before B so what we can write we can write this as a is a then becomes and then becomes we skip C and then D comes over here is this then F comes then we skip G and H comes just like this over here I over here let's not go over here will go over here M is there then n comes then we skip oh and then T comes correct this is also logic also you can see D a then B then D and this after this V what comes out ready E is over here at the last correct e if H H is over here what comes up wretch I I should be also here at the last then from I what comes with J we skip K and we get L after L what comes in comes so n much we are at the last which is already there after M in comes in hippo and we get P this is also a logic you can use any logic just get the right answer ok moving on to another series let us see H F D okay n l j question mark question mark o X V T now let us see whether we can find some relation okay now H F D so H is over here F is over here d is over here oh we are going in the opposite direction H then f then e in the reverse direction we are going so let us now say let us see or we can what we can say is that 1 1 skipping is there H is a script G then F there script E and then D okay in opposite direction so J is it where is jay jay is over here l okay J is over here L L is over here n is over here J there script 1 k then I am going to L this script 1 then n right over here so here what is happening is that H FB we are going in opposite direction like this in LJ okay first first is n then L again over here in opposite direction jl & n jl n or n LJ right n LJ again we are going in this direction this we do not know we have to go in this direction only let us check from your TV and x-force to be or XV and T first we have X then we have V then we have T again we are going in this direction right so here also we will go in the opposite direction oh okay we don't know what is over here but we know Oh as the last element so we have to skip one since we are going in this direction this is the last element so we have to now go in this or direction-- to find the answer okay what comes before oh we have to skip the will get Q over here okay again keep our we'll get it over your so answer is SQ o if you try to Marcus Q you will get S then we skip our Q then steep R and oh that is again we are going in this direction so our answer this correct answer is s Q sort of question mark s Q will come see how easy it becomes using the table of A to Z now let us take a look at some of the alphanumeric series alphanumeric series has alphabets and numbers in it okay now again in alphanumeric series the most important part is this chart a to Z and the position of the alphabet as well as the reverse positions okay and how to find reverse positions that we have seen subtract everything for how subtract the original position from 27 you will get the reverse positions right now in alphanumeric series generally how to find out the relation I give you an example of alphanumeric series right now over here so you will understand what exactly we mean by alphanumeric series to e 2 1 h 9 1 k-6 then we will have 1 n 3 or find the next one this is one okay not I this is one now over here this is an alphanumeric series where we have alphabets and numbers what to do whenever you find an alphanumeric series the first thing that you have to do is whatever number is there in the group or element you have to see if they are related to the position of the alphabet okay position or reverse position of the alphabet right so 2 n 2 if they are related to position of e or not or a reverse position of a or not that we have to check now after that say if it is not related to position you have to find whether these numbers are related to each other like if there is each other okay I'll write it over here each other so we will not forget make a note of this now 2 & 2 we know 2 is equal to 2 1 n 9 we don't know what relation it is there 1 & 6 again don't know what relation 1 & 3 don't know what relation so over here we have to we try I should try to find if they have any kind with each other okay now if that is not the case then try to find relation with numbers of other groups with numbers of numbers of other groups like for example here we have - n - ok - n - is it related to 1 in mine is it relative to 1 + 6 or 1 + 3 or is this - related to 1 or this - related to 9 like that we have to try to find or what you can do is take this as 22 take this as 90 something like that we have to find the relation okay now even if that is not possible then actually parallel to this we also should check out if the letters are connected to each other same thing we have to do for letters also right so whatever alphabets are there we have to find out the relation for those also and in this trial and error you will get the for a pattern I am now will see an example we will solve this example also as well as we will see another example as to what we are talking about now this sum which we are saying or the question which we are seeing over here it can be solved in two ways there are two logics you can use any logic okay i listening both the logic over here - is there - is there what we have to check whether it is related to position of the letter so 2 & 2 no e position of E is 5 so 2 n 2 is not related what is the reverse position of each 27 - 5 22 okay this to this to this to this - let's check over here 1/9 okay what is the reverse position of H 27 - 819 yes we are finding a pattern 1 9 mins 1 9 over here so one six one three these must be the reverse positions of the letters right so whatever option is there we have to check there we have to see if whatever the option is given it has there for example if the option is like this P and 2009 or 9 0 if this is the reverse position of P then we can select it as a correct option okay so check out the options now what is the second logic over here - n 2 is 22 1 + 9 is 19 1 + 6 16 1 & 3 is 30 if you observe closely what is happening is that - three - three - three so by default next one will be minus 3 this will be 10 so that means the three positions which are there this is 1 this is 0 we have to find the letter e and H is over here H is over here there is a gap of 2 ok they skipped two letters H and K 1 letter skip second letter script k k + n1 letter script second letter script n n and next what is it one letter scripts second later scripts q so answer is Q so answer is one Q oh so this was the second way to solve the same sum you can use any number of ways just get the right answer let's take another example h 8 l 12 Oh 15 H 19 and next one okay here HH l - L Oh 15 s 19 is given what is number check if it is related to position each position is 8 yes so 8th position is of H so H a 12th position is of L so L - L o 15 oh is 15 s is 19 what will be next now how to find XA is no options are given what you will do or a fine option say options I'll give you four options so you will understand what I am talking about you 21v 22 are 18 and X 24 ok now if all the four options the letter which is there and position is correctly on you is 21 V is 22 r is 18 X is 20 volts so what will be the correct answer how you will write now comes that the number has to be connected to the other numbers or the numbers of the other group this is one group this is second group third group so eight relation of eight and twelve months we found out twelve and fifteen modules out of 8 plus 4 is 12 12 plus 3 is 15 15 plus four days - okay now here we are senior relation plus four plus three plus four so here it will be plus 319 plus three is 22 what is 22 we answer is v-22 see how easy it is with the chart which is given okay so moving on we'll see some of the sums related to series we will solve them and we will see how we are approaching the sum in exam also please do not forget to log in to career write comp to check out the latest jobs in the market go on to the job forum of courier is calm question number one to five cents 17:28 question mark let us try to find out what exactly is the next element in this series now first I will tell you what to do now whenever if you are not able to find the series directly or if you are not able to tell what series it is by direct observation what you can do is first try addition okay additions if you start to see if it is an addition series then try if it isn't subtraction series then try if it is a multiplication series then division series then see if there are prime numbers involved okay if all of them are prime numbers of prime numbers are being added or subtracted multiplied something like that after that after prime numbers still you're not getting try for Fibonacci okay Fibonacci sequence if it is a Fibonacci sequence right and even after this if you are not getting whenever what you can try is that even try a combination of all these methods right you will get the answer for sure most of 99 percent times you will always get the answer from these methods now sometimes what will happen is that the series would be really huge like see I will give an example for eight nine five four eight nine seven four eight nine nine okay now I know how they I am just adding two to two but let us assume that this is a series and in this I am NOT able to decipher and the numbers are also looking big so what to do what you can do over here is you can break this number into two parts 4895 same way you can analyze this 48 you can analyze this 95 again divided 4890 you can see that 48 gets repeated okay 95 to 97 plus two is there okay over here also 48 rated 97 to 99 plus two is there so like this you can break this you can even break this 4 is 9 5 into 4 parts this this this and check ok 4 gets acquitted a you get separated 9 your turbid X 5 plus 2 is 7 you can try to analyze this way also sometimes that if you see the series might be like this 5 a 9 5 then 6 8 9 5 so over here they might what they are just adding 1 1000 or them are what they might be doing is that 4 8 9 5 if you reverse it you will get nine five nine eight four five nine eight five five nine eight six so this is also series just like ABC they can write it as C VA just to confuse you they might do it with numbers also so please pay attention let us solve the first two and five difference what we have learnt firstly what the difference is two to five difference is 3 5 to 10 it is 5 10 to 7 7 7 to 11 so what will be next over here is if we see observe carefully these are nothing but odd numbers but what are the odd numbers 3 5 7 9 is also odd number but 9 is not included then these must be some special kind of odd numbers or some special numbers if you observe is carefully you will know that these are prime numbers 3 5 7 11 so what is the next prime number 13 so 28 plus 13 will be how much 41 okay it's plus 3 1 2 ok so 41 so next number which is there is 41 41 is our answer see how easy it is moving to the next question question number 2 let us see here you have to find the missing element what is the difference 34 and 21 the difference is 30 34 and 55 21 okay 55 and 80 34 okay now can you observe ok this also difference 55 can you observe something in the difference you get 21 34 55 which are massive at these numbers when such a thing happens direct you should know that it is a Fibonacci sequence okay please remember very important right it is a Fibonacci sequence how let's see 21 and 34 34 plus 21 is 55 55 plus 34 age 89 89 plus 55 144 so this will be what 144 plus 18 in what it will be 144 80 minus 9 plus 4 13 1 for 1213 233 is the answer 233 this will be the next number in the series moving on now next is L o JQ h and we have to find the other one okay I purposefully written this A to Z because in exam you'll always be having this in rough space okay and you can refer what is the first one it is ill then is o then is J then is Q then is H so it is like we are going this way going this way again coming this way this way again coming this way this is like what we have seen in number series there is an increase there is a decrease there is an increase there is in degree so that means that two different operations might be happening over here or there are two different series okay so how the series might be it might be like this and this my dear series let us see l j h l where is J and H so we are going in this direction LLL skip one J skip one H okay this is the sort of a pattern let's see the other one Oh Q question mark we have o skip one Q and the other one no two it will be as per this pattern we are going in this direction what will be the next one skip this s so answer is s see how easy it became even if there are two series they've combined it you try to make it difficult using this chart it becomes very easy to pinpoint or find the pattern and solve the question moving to question number four you sp question mark okay where is you you s P l g okay over here can you see this much get this much get this much gap this much gap so you skip one okay s then skip one and two then P then one two three three our script and then is one two three four four accident so skipping which is there we are going in opposite direction like this and skipping which is their first one is skipped then two are six then three letters are steps and four letters escape so now five letters must be skipped one two three four five Oersted answer is a moving to question number five okay now we are here with question number five the wrong term question okay the third kind of sum which can be are sincerely find the wrong term in the following series 10 14 28 34 64 68 136 ten and four differences four four and twenty eight differences 14 28 and 34 differences 634 and sixty-four differences what what is the difference earlier thirty 64 and 68 difference is what for 68 and 136 difference is what this is about 68 so now over here if you see two times you get a difference of four over here only there is a difference of six you have to find the wrong term in the series okay what happens over here 14 and 28 differences 14 that means it is like sort of being doubled right it is being doubled over here also 68 136 difference is 68 so it is being doubled so say here it is 4 and then doubling is there here it is 4 and doubling is there here it is 4 and doubling is it so there must be some problem over here here also it should be 4 and then doubling must be there ok so here what happens is that 6 is getting added then we get 34 say if we add 4 over here what we will get over here 32 and difference between thirty twos double is 64 so we are getting a very correct series that means the wrong term over here 34 okay because of 34 what is happening we are finding that six is getting added and only 13 is getting added we are not we are not getting this kind of relation 4n double for and double okay so a common relation should be there we found what kind of relation might be there evil doubtful so what we did instead of after 28 instead of adding 6 we added 4 what we got as 32 double of 22 is 64 so what we have over here is the correct series will be 10 14 14 mm ta 28 plus 4 is 32 32 twos are 64 64 plus 4 is 68 68 - Zac 136 so we have add a poor and then multiplied by 2 okay moving to next question again find the wrong term okay fifteen sixteen twenty thirty forty five seventy now we don't know how to start so let's see the difference here the differences one 16 minus 15 one 20-16 for 30 minus 20 10 45 minus 30 16 okay 70 minus 25 is how much this is 25 so over here okay difference is steadily little by little increasing it is not going too fast or something like that but if you see there are some common numbers which when you see the first thing that you get to know is there is a specific thing that comes to mind like for example whenever you see four you say okay to square is force whenever you say nice you say okay three square is nice whenever you see 25 you say Phi square is 25 or if you say 27 will immediately say three nines are or nine threes are expedition or 3 cubed is 27 like over here it comes it can be 1 square this can be 2 square this can be 5 square so there is problem between these two numbers only in this pattern ok there is a problem between these two numbers so this difference if it would have been nice then this would have been 3 square okay and if this if the difference is 9 that means this number has to be 29 then difference between 20 and 45 would be 16 what is between 16 16 is nothing but 4 square then the pattern is correct that means this number which is there it is not healthy it has to be 29 then only we can get a nice series of 1 square to square Z square 4 square Y square so the answer is 30 30 is the wrong term correct term should be 15 16 20 29 45 and 70 so the difference here becomes 1 your differences for your difference is 9 your differences 16 here differences 25 this is 1 squared 2 squared 3 squared 4 squared v square moving to question number 7 find the wrong term in the following series 1 3 10 20 163 129 now over your different 3 minus 1 is 2 10 minus 3 7 21 here it is 11 63 minus 21 is 52-42 okay 129 minus 63 is to use 9 minus 3 is 6 12 minus 6 66 ok so here again the difference which is there it is increasing too much so this must be like the other see how it is 2 7 directly 11 direct 42 direct 16 is so it is increasing at a steady rate and quickie so this must be somehow related to multiplication but what multiplication 1 into 3 is 3 ok 1 is here 3 is here 10 is here 2163 129 1 into 3 is 3 but 3 into methods 10 is not a multiple of 3 we add Mexican right 3 into 3 is 9 and 9 plus 1 but then over here again staying in to what - uh 10 into 3 30 30 minus 9 we left to do ok 30 minus 9 10 into 3 minus 9 then 21 into 3 is 63 so there is no direct relation when it comes to multiplication also but so the reason I have taken this example is to show you how complex or how combination works ok let's see what is 3 say if we write 1 into 2 plus one what you will get 1 - Z - 2 plus 1 is 3 now after that now we have to come near 10 so 3 into 3 is 9 9 plus 1 is 10 we have to come to 21 we have 10 into say 2 plus 1 is 21 so over here it so happen is that this is multiplied by 2 this is by 3 again it is 2 let's see over here 21 x 3 directly we are getting 63 okay so here x 2 plus 1 is there x 3 plus 1 is there x 2 plus 1 is there so this should be multiplied by 3 plus 1 so answer should be 64 over here but still will check will check ok 64 2 3 2 3 2 64 into 2 plus 1 64 into 2 is 128 plus 1 is 129 so answer has to be 64 this is the wrong number ok see how when you see certified and 2 3 tools like that such when such pattern is seen by you even if you don't have much enough evidence to prove it what you can do is you can trick your hunch and you can try it just like I did what I assume that ok this 63 might be wrong let us assume this pattern only and right 64 and let us see if the next number checks out ok such trial and error method is always needed in series otherwise you won't get the answer quickly moving to question number 8 here we have 3 2 8 12 13 24 18 ok so again up the up down little bit up down is it so we can assume that there are two series or two operations are being done okay so let us assume there are two series how the thing is might be it might be like this okay like this can you see 3 plus 5 is 8 plus 5 is 13 plus 5 is okay okay so here we have plus five plus five plus five next theory is what we left to 12 12 24 24 32 32 42 2 and 12 different sense 12 and 24 difference to n okay it can be 10 adult well added 14 added 24 and 32 difference is Oh while different let's see two at 32 and 42 difference 10 so here we have two tens so here it might be there might be some problem over here if this dish is shifted over here you will get ten and ten generators proper or what we say proper series so say if this is twelve and if we add 10 to it what you will get will get 22 and 22 again when we alder send to it what you will get we will get 32 so that means the problem is over here okay correct series has to be 3 2 8 12 13 and 22 then 1832 23 they will follow so what will happen 2 plus 10 is 12 12 plus 10 is 20 2 plus 10 is 32 plus 10 is 40 to answer is 22 so correct answer is 24 24 is the wrong term moving to next question so here we have 111 34 75 139 question mark okay let us find the difference 11 minus 1 is 10 34 minus 11 is 23 okay 75 minus 7 75 minus 34 is 41 139 minus 75 is 9 minus 5 is 4 13 minus 7 is 6 so this is 10 so your I am NOT able to find any relation directly so what I will do is I'll use an other methods that I am going to teach you know that is triangular method you can try to solve the sums by this way also try to find a pattern using this way also if you are not getting a pattern in the immediately in the second night what you can do is you can try to find the difference again 23 minus 10 13:41 minus 23 1864 minus 41 23 okay again over here 13 and 18 difference is 5 18 23 cents if I see now here we have a pattern that 5 5 is there so 13 plus 5 is 18 18 plus 5 is 23 then 10 plus 13 is 23 23 plus 18 is 41 41 plus 23 is 64 so how to find the next one very very easy this is Phi this is Phi this will also five so 23 plus y will be how much 20 is okay then 64 plus 28 will be how much 8 + or - 6 + 1 7 8 9 92 okay and 139 plus 92 would be how much 9 plus 2 is 11 1 3 4 4 plus 9 is thirty two hundred and thirty one so 231 would be the next number this is known as triangular pattern if this is also a way of thinking this is not a way to solve any sum this is a way of thinking to find this is a way of finding the pattern or trying to see if you can find the pattern right just like we try square we like we try to we try the triangular pattern also moving on okay here we have 28 33 31 question mark 34:39 okay so 20 difference 28 and 30 read references 528 plus 5 is 33 33 again it has gone down oh so it is up down up down so what we can do is that we let's see let's see first we don't know this middle number so we are not sure whether it is up down up down up down or whether there is only one incident let's see 33 and 31 what is the difference - okay so this is plus 5 33 minus 2 is 31 now here we don't know anything here we don't know anything 34 and 39 is plus 5 so here we are plus y here we are plus y after plus y here minus 2 so it might be a series like this plus 5 minus 2 plus 5 minus 2 plus y ok so let's try the other this series is correct or not 28 plus 523 minus 2 is 31 plus 5 would be 36 36 minus 2 would be 34 34 plus y would be 39 so we are getting our valid series over here so 36 is the answer okay see how easy it is this is called as the combination of addition and subtraction series right series is actually very easy if you just know how to approach them just have to approach with confidence that you will get the answer try of comics after trying the basic series of addition subtraction and all that stuff like Prime and Fibonacci try the combination also okay by most of the times I tell you in 95 percent times the basic series would be enough you'll be able to deduce using the basic series and the triangular pattern which we saw right now if you know the basic series like square tubes and all that stuff 95% sums of relate which are related to series would be solved by you just practice only practice will give you the expertise when it comes to series so keep on practicing a lot this is it for series you can check other reasoning and quantitative aptitude tutorials on our channel also check the job forum on courier icon for latest jobs in the market share the video with friends and give it a like if you liked it leave your comments and suggestions for us and don't forget to subscribe to our channel for upcoming tutorials and videos