All right, guys, it's time. We have the first one for you. Since today we are going to talk about divisible rules and factoring, let's see with this one. What do you think? Remember, I am not necessarily asking you to give us answer. You can just say, sir, I would start with that step first, but I have no idea what's next. That's totally fine. Okay, give us something, please. Then I'm going to start a timer. Let's see how many seconds it's going to take for us to get a second answer, because all of our classmates already gave us some answers. Okay. I believe one of our classmates thinks that they give us some declarations. Thanks so much. Please do that, too, guys. Even you don't need to explain or give me every single step, still give us something, however you got. It's already one minute. And 10 seconds. All right. Ethan, please help me. How many of our friends says answer should be A? Do we have anyone said A? I don't have anyone saying A. OK, we just ignore that. What about B? No. Oh, interesting. What about C? No. We have just two people that just admit. Sorry, mouse. Yeah, OK. Yeah, they are good. Yeah, getting more and more people. All right. So you said no one said C. Am I right, or? No one said C. Interesting. What about D? Three people said D. OK, what about E? And no one said E. OK, others. In that case, look, guys, we have total seven people as a student, so I expect those level of fun. What do you think, guys? One thing? Or you just join? Maybe you just join? That's fine. All right. A bunch of you said answer should be D. Do any of the participants give us some sort of explanation, Ethan? Or I'm going to just start solving. Arnav said, first, there are 33 multiples of 3. And then there are 6 that are multiples of 3, but end. Wait, no, correct. There are 6 that aren't multiples of 3, but still end in 3, which are 13, 23, 43, 53, 73, and 83. OK. Then what? Then he just said that would be 33 plus 6. All right. So thanks so much, guys. So here, since you count from 100, and while saying the multiples of the number 3, let's just circle some of the keywords. While saying the numbers that are not multiples of 3, but every other last digit. How many times did we do that? OK. They say, how many times? That means there are 100, guys. Amazing. All right. So from 1 to 3, if you are looking for the multiples of 3s from 1 to 3, I assume the first thing in your mind is to divide 100 by 3. You know, this is the main one. You get 33, am I right? Because 99 is multiples of 3, which is close to 100. Then you get 33. These are all of the numbers multiples of 3. But there is another condition, if you check that, if you are on the third condition. It says, while saying the numbers that are not multiples of 3, but have 3 as the last digit. Well, think about starting 13 on the 93, I mean, if you just count 13, 23, 30, and so on, you should have 10 numbers with the last digit again. OK? 3 is 73, 83, oops, it should be 10 or 9 numbers, yeah it should be 9 numbers, my bad, 10 to 1, and 93, anyway here is the deal, I should add all of those 9 numbers and I should say 33 plus 9 is 42, there is no answer like that but we are missing something, remember, let's say that are not multiple of 3 but 3 as the last digit, that is the reason I am saying you just keep re-read the question, maybe multiple times, okay, they say it's not multiple of 3, well, if you look at 33 it's already multiple of 3, even the last digit is 3, we gotta just ignore that or cross out 63 with the same logic, 93 with the same logic, as you see we have 6 numbers left over here guys 6 numbers, alright, when you add those I believe you got the idea, so what now, is there any question here, if you have something just say yes not only say yes, please say which part is not clear to you, in the chat please or if there is no question you can just say n, represents no, then we can just move on no questions, I am gonna move on I really wanna believe that every single part which is those, all those 7 kilos says no we have 7 or couple only, 7 of them then we can go to next and you know guys, today we are gonna talk about multiples and pairings this is from last week, we just put that slide on purpose as a reminder when you have a problem guys, or some sort of word problems, you need to follow some certain rules make sure you understand them, what they are asking, underline the keywords specifically, make sure what is given and what they want us to find plan how to solve problem, are you going to use algebraic ways, are you going to create some sort of data some sort of chart, graph, whichever best works, especially geometric questions I recommend you guys to draw some sort of, it doesn't have to be perfect, but it's gonna help you get out your plan, that means, you are going to work with your calculations and please make sure check your work, couple of times, even you know everything about the question, you know something and everything if you do little tiny mistakes, well, the question is wrong and we are all upset, don't do that to yourself look back and check and reflect, especially reflect part says if you are given this much, this much cannot be negative, make sure the answer you find makes sense with what they are asking if they say, how many people are in the event, you cannot find 55.5, it's not possible, you have to have positive integers, represents number of people something like that, ok, I believe you got it, alright, next so, since we are going to talk about multiples and factors today multiples of a number are the product, when you multiply that number, the interest by an integer remember, it's not going to be only positive numbers, also we can include like negative 6, negative 15, negative 20, whatever, as a multiple of 3 as well there is a misconception with that, please be careful, all positive and negative multiples we are talking about here multiples are the numbers that are shared, multiples of 2 or more numbers, well, if you are looking for multiple of 3 and 5, of course you got to start with 15, 0, 15, 30 and so on, if I say let's just talk about common multiples of 10 and 4, I believe you got to start with 0, 10, 20, 8, like 56 and so on, ok, meanwhile, even you are not talking to me, it doesn't mean you cannot communicate guys, if something is not clear please put something on the chat and let me know, ok, factors of a number, factors of a product are the numbers that divide the freedom of reading your reminder but, I can say, one of the factors of 55 is 5 because when you divide 55 by 5 you get 11 and there is no reminder, also I should include 11 as well for that said, when you work with factors of a number, I recommend you to put them as pairs of the factors, for example, we have example here the factors of 24 are 1 and 24, as you see, we know every single number are divisible by 1 and every single number are divisible by itself, I just keep 1 and 24 first as a pair, then when I divide 24 by 2 you get 12, another pair, then when you divide 24 by 3 you get 8 and 4 and 6, so on if you put them in order, increasing order, it may not be really helpful if you just solve the question you can have like some problem solving, I mean, some examples always, determining the factors of a number can be useful tool in problem solving, exactly, some factors are shared by more than one product for example, some factors of 12 and 21 are 1 and 3 as you see, 1 and 3 is divided by 12 and 21, prime numbers are those that cannot be affected by anything except themselves and 1, as you see, 2 is the only prime number which is even number, all of the other prime numbers are odd numbers 1 is not prime, 2 is the smallest prime number, because think about that, think about the definition if you say 1 is prime, the number itself is not a problem and if divisible by 1 as well, we cannot just have overlapping rule, that rule has to be, you know, what it's afraid anyway, I still assume that there is no more questions even if there is something you can let me know, yes brother, thanks so much ok, some divisible rules, if we have any even numbers, that number is divisible by 2 think about that way, basically, once it is 0, 2, 4, 6 or 8, that means that number is exactly definitely divisible by 2, so divisible by 4 means you are going to look for last 2 digits are only divisible by 4, I mean you can think about that way if last 1 digit is divisible by 2, that is divisible by 2 if last 2 digits are divisible by 4, that number is divisible by 4 if last 3 digits are divisible by 8, that number is divisible by 8 some sort of ideas, relations here, 2, 4 and 8, you know, they are related anyway, divisible of 3 is, when you add all of those digits of the number whatever result you get has to be divisible by 3 with same logic when you look at the divisible of 9, sum of those digits has to be divisible by 9 but we all know that 72 is divisible by 9 and 7 plus 2 is 9, you know, same logic or you can think about 100 of 8 should be divisible by 9 because 1 plus 0 plus 8 giving you 9 and so on, or it can be multiple of 9 as well, anyway divisible by 5 means the last digit has to be 0, 5, similarly divisible by 10 the last digit is only being 0, when you look for divisible by 6 you have to focus divisible by 2 and 3 because 2 times 3 relative to prime numbers anyway, so in that case, when we have some even number that even number is also divisible by 3, that means that number is divisible by 6 remember, that means, that has been said, any odd number cannot be divisible by 6 it has to be here, alright, divisible by 7 is a little interesting maybe we check that we got a close of the last digit, double it and subtract from 1 and 8 and result is divisible by 7, like this, so let's just do an example 1 and 4, you are going to apply that, 2 separate digits I just take out 4, I double 4, remember, because you said you gonna double it so 4 times 2 is 8, and if I still have 1 left over, 1 minus 8 is going to give you negative 7 we both know guys, negative 7 is also multiple of 7, that means, yes, this number is divisible by 7 so you can say, but sir, what about 2, I mean, 3, 4, whatever digit numbers you can work with that too, think about, we have 133, it should be divisible by 7 I have like 133, ADC, I am gonna focus it on the last digit and multiply this digit by 2, 3 times 2 gives us 6 so when I have 13 minus 6, remember, I am not talking about, I have left over 13 I am talking about 2 separate numbers, 13 and 3, not 133 anymore anyway, 13 minus 6 also should give you 7 we all know that 7 is multiple of 7, that has been said, 133 is exactly divisible by 7 remember, there is no remainder, this is what I am saying of course you can divide every single number by 7, but you know alright guys, we are about to start with the questions so far, is there any questions about factors or divisible rules or whatever please type Y, it represents yes, and please give us what you want or what you, what you have here and please type N, it represents no, that means, I am gonna assume that everything is clear or multiple of this do we get anything eaten or I am gonna continue no questions alright, thanks so much this is the fun part, alright, are you ready for your first challenge challenge number 1, from 2005, question number 6 Thank you so much for watching, and I'll see you next time! Thank you for watching! All right, it has been one minute, Ethan, do we have any answers or I can give you like little hints, guys, if you have enough. One person has said D, no one else has answered yet. Oh, two people said D. Okay, we have two votes for D. I'll just start thinking, I believe. Guys, we are going to look for the product of four numbers. So when you multiply those four numbers, you are going to get 100. Think about, we are working about factoring. Do you think instead of thinking like randomly those four numbers, we should work with 100? Something about 100, maybe technically 100, what do you think? Please work on this, okay? Okay, after those explanations, do we have more answers, Ethan? What do you see? Just D. Okay, everyone that says D, then? In that case, it looks like we got to check with D. All right, that's okay, guys. So, you know we cannot just say any number. I mean, we cannot just get four numbers, get multiple product of those numbers, it's 100. Instead, guys, we got to start from 100. Let's just work with factors of 100. Remember from the definition and what we just found. We have 1 times 100 gives us 100, you know that. This is one of the pairs. Also, we can say 2 times 50. Remember, today we make life easier, guys. I start with the smallest number, which is 1, then continue with the smallest prime number, and so on. After we found that pair 2 and 50, we should have another one, which is 4 and 25. And the last one should be 10 times 1. Here is the trick, guys. 10 times 1, and this works too. Here is the trick, guys. If you have some sort of pair, which is 100, and you found those pair roots, you don't have to keep going. Because we already found two factors. That means we are at 1. So, after those, we are going to look for four different positive integers. Well, think about that. Let's see. We can start with 1. I'm going to do something, you know, because it's easy to do. But we still have confidence. Since we have two as well, let's just choose two as well. After we have 1 times 2, we have left over 50. Well, what else numbers I can use? Do you think I can just choose 5? I mean, 5 times 10 gives us 50. Because if you just forget those numbers, 1 times 2 is 2, 2 times 5 is 10, 10 times 10 is 100. The question is, can we use these numbers? Well, we can either use these numbers, or we can try to use, you know, 1 times 2 times 2 and 25 maybe. But it says, here is the catch, remember. It says it's not for four different numbers. Remember, even if you just try to add 1 plus 2 plus 2 plus 25, it wouldn't give you those, any of those answer choices. Well, when we add those numbers, if it gives us one of the answer choices, we can assume that it's going to be right. Let's see. 1 plus 2 plus 5 plus 10 should give us 17 and 18. As you see guys, answer was B, alright? Remember, we can still find different combinations, but each time you are going to get some of the numbers are same, or they are going to work with the condition. We are looking for four different integers. Remember from our problem solving strategies, re-read the problem, make sure you get it right. And they are asking us, there is some, remember, some means you will add those numbers. When you get them, make sure you add them as well, okay? Alright, any questions about this one? This is time for you to say, why represents yes and why represents no. If there is anything I need to miss some address, I'm going to call you with the next question. Are we good? Yep, no questions. All right. Thank you so much. Then we can just move on. Next please. All right, Klaus. This is your second challenge. Number two from 2013. Have fun. Let's start. Thank you for watching! Alright, we just had 1 minute before. I'm going to give you a little hint, guys. So here, Ravastelkanger number with the product of its digits equal to 24. You are going to have, like, 2-digit numbers. I assume it's going to be 2, because the product is going to be 24. So next, you have 98. And when you think about that 98, the product of those 2-digits is going to give you 72. Something like that. You are looking here. It says, what's the sum of the digits of the smallest number? Well, well, well. You are looking for the smallest number, remember. Okay, after this hint, we have some answers. And which one, people, says which one? I have a couple for E and D. Okay, so others, no one says A, B, or C? No. Okay, good. In this case, we are going to find out if it is either D or E. So guys, if you think the answer is D, please type your answer, which 2-digit number you find in the checkbox, please. And if you find the answer is E, which 2-digit number you find? So we can just compare those. Look, I really want to interact with you. You know what? You don't say that I cannot. No, please give us something on your VHF, please. Okay, Ethan, do we get some numbers for you? 46, 64, and 38. Okay, if people says 4 to 6, it should be part D, you know, because 4 plus 6 is 10, you know. And 64 works in that case, too. I'm just, you know, throwing away all of those different options. And you said for E, part E, who said what number? Someone said 38. Someone said 38, alright. So guys, think about, when I have 4 to 6, 4 times 6 is 20, yes, that works. Also 64 works. It is real. Remember, what is the sum of the digits of the smallest number? Well, okay, smallest number. If it is going to be 46 or 64, I can eliminate 4 already. Anyway, well, when we check 38, 3 times 8 is 24. Remember, you can see, you could include 3 as well, but it's still a huge number. What number? 8 is there. Anyway, I already eliminated. Anyway, so we have 4 to 6 versus 38. I believe you all know which number is smallest. Again, to those, when we have given word problems, even if it is short, not really huge paragraph, make sure you read it and make sure you get it right. Look, I am pretty sure every single of you know how to solve these type of questions. But the issue is, do you know how to solve them without making any mistake? You know, do any mistake, you will just keep solving, keep practicing, keep discussing, alright? Please discuss with me, discuss with your classmates. Then we're going to get better and better, no worries. Answer was 38, guys. I mean, the numbers were 38, but the answer was E for that case. Any question for this one, number 2? Please say Y or N. In the chat, please. Ethan, do we have anyone who says Y represents yes or we are good? No question, yes. Excellent, thanks so much. Number 3, another question from 2005, guys. It is your next challenge. Have fun. Let's just start finding. Okay. Thank you for watching! Thank you for watching! Alright guys, so It has been One minute and some seconds So we have some sort of answers guys You can continue to tell me if you have some answers, or I have one for B, two for C, and one for E Okay, oh, look at that, so You said we have B, okay Someone says B And someone says C, or a couple of people And D, am I right? E, not D Oh my god, okay Interesting And no one says either A or Neither A nor D, okay Alright kiddos, here is the deal Whoever finds 36, can you tell me your reasoning? Same thing for C and E What is your reasoning guys? Because what I'm asking, we have like Really broad thinking Someone says 7, someone says 36 It's not even close numbers Look, I just underlined and searched Here are some keywords for you He walks four consecutive days And he has Every single fifth day off So what's the pattern here, basically? In how many days That same pattern Keeps continuing What do you think? For someone who said B, they said the first working day is Monday, second is Tuesday, third is Wednesday, fourth is Thursday, and then they're off Friday, and then... So what does it mean? Do they say that we have the same cycle every five days? That was it. That's it, okay. As you see, in terms of the schedule, that schedule repeats itself every five days, am I right? And you see, look, there is no other conditions. He keeps working for four consecutive days, then the fifth day off, that's it. It doesn't say the fifth day has to be Monday, Tuesday, whatever. It's fine. Okay, we have that type of schedule. This is the first thing. Also, another thing you need to work on, how many days are there in a week? Think about those two numbers and give me something, come on. And it's interesting that no one says A or B. Okay, William says find a multiple of five that is divisible by seven and then add one. I only wonder why do you think you should add one? I mean, yeah, you said we have a the following schedule if you I mean repeat itself by five days and see each week as seven days five times seven we get a time least common multiple of those two Seven because we are relatively prime remember we talk about primes anyway, you get 35 Okay after that part is getting to be clear Remember last sunday he had a day off and on monday he started work again It says after how many days Please Will he have oil on sunday after harmony Um William says because he started on monday, which is one day after sunday, so you would add one The question you would add one of you One is my question Because think about right from monday to sunday, it should be same cycle by multiple of seven You know But after the cycle start it says after how many days Did he have a day off Almost one day Even if it's So If they were not saying after how many days After you order the third cycle You would have get right but see if it gets after you know, take out that one day guys Then you should have 35 minus that one extra day it's gonna be 34 days But I don't know if it doesn't makes it because i'm kind of sad that no one says 34 at the beginning, you know I don't know how you get 12 and 7. Maybe you just do some new mistakes Publish mistakes Is there any question We only know that, guys, these cores are a whole number. Oh, well, it's one minute already. Do we have some answers, or should I wait more? I mean, I can wait. Ethan, do we get any answers, or not yet? Not yet. Arnav, you had a question? OK. One of our friends has a question. Guys, type your question, so. They asked, are the scores out of 10? It's not necessarily. We only know that in this competition, we are just assigning a whole number. That's it. I mean, there is nothing about it has to be out of 10. It doesn't. OK. Remember class, I already underlined the keyword for you, every single judge can give all number points, they are allowed to give decimals, also the final score is the average, well well, what does it mean, how do you find average, do you remember, please use the former knowledge, your former math knowledge, to find some sort of answers here, come on, Ethan do you get some sort of answers, I have 3 people saying C, no more answers, ok that's interesting, ok guys, many of you, I mean majority of you says C, can one or couple of you tell me, why do you think it should be C, or it should be 8, how do you find 8, just a summary, tell us what do you think, I hope you don't guess, you know, if you don't guess, You can do get some answers or not yet. Let's see. Because 8 is the least number, that 5.625 can be multiplied by it to make a whole number. Oh, okay. That's a good explanation. Well, that's it. Thank you so much guys. Guys, the goal here is to make that fraction, that decimal, some type of whole number. I mean, if you like, you can just write this one. You can write it as a fraction as well. You are looking for a number. When you multiply that number by any of those answer choices, you have to get a whole number. Because, remember, average means, like the total, divided by number of items, which is going to be in the answer of choices, number of items, 5.625. So, we are going to multiply 5.625 by number of items. Number of items here represents by number of judge, as you see. And they are looking for the smallest number. You just think of what number, either 2, or 6, or 8, or 10, or 13. I need to multiply 5.625 to get a total number. You can go and keep a whole number. Remember, the score is best by a whole number. Then you will find the answer is 8. Any questions, guys? Type Y if there is a question and N if there is not. Are you good? E-team, what do you think? Can I go next one here? Ummm You have no questions Alright Then check number 5 please guys from 2014 I'm gonna start timer for you Okay, each person get the same. That's important. Thank you for watching! It's one minute, come on! If you said nothing, we don't get any answer yet? Not yet. Okay, fine. Let me give you a hint. For some questions, remember, you can work backwards. Instead of starting the sentence that I'm at the beginning, the pirate took us for a pirate took us for some gold coins. Maybe you should start from the backward. How many coins? Not this one. However, if there had been 50 coins left, each person would have received 5 coins less. What does it mean? That sentence should give you some strong ideas about to find either how much each of them get or what's the total number of pirate groups they have. I will talk more about it. Thank you for watching, and I'll see you in the next video. Thank you for watching! All right, Klaus, we have only 11 minutes left, come on, give us something. Eytan, would you like to give us something about that question? If you want to say something, you don't have to. One person said A. Okay, someone said A. That's good. Anyone else? How many coins did they pick up? All right, guys, look, let's start. I really want to go over more questions. That's the reason I might go a little bit fast. I'm sorry about that, guys. OK, let me ask you, actually, do you still think, guys, I should give you, like, 30 or, like, more seconds? Do you need that? Or I'm going to start talking? Whatever you feel like, please tell me, guys. Maybe you're almost there. I don't know. Oh, this is not the answer. Yes, thank you so much for reading my mind. Anyway, so look, think about it. If there had been 50 coins less, then each person would have received 5 coins less. But we all know that each person is supposed to get the same amount of coins because they are doing some sort of fair share. Well, and if the total was 50 less, each person would have 5 less. Means you are dividing the total to each person. Can I just say 50 divided by 5 should give me 10? In that case, we have total 10 pirates. Does it make sense to you guys? Because it's only logical to me, you know. Look, you don't necessarily worry about how many coins they had they got at the first. It's totally fine. Don't care about that. Think about if they had 50 coins less total, each person would get 5 less. Well, that means we have 10 people, you know. I hope it does make sense to you. Anyway, if we have 10 pirates, let's just keep working backward. Let's just keep working backward. The previous sentence says, if there had been 4 less pirates, OK, instead of 10, if we had 4 less pirates, basically 6 pirates, then each person would have received 10 more coins. Let's say each person gets x number of coins, you know. In that case, total number of coins would be 10 times x. Am I right? Each gets x coins. OK, let's say. So with that logic, 10 times x should be total. Also, they say, if there had been 4 less pirates, 4 less, which is 6, then each person would have received 10 more coins. That means x plus 10, as you see. Then we should get something from here. What is that? Let's just solve it by using distributive property. We get 10x. We cannot do anything here yet. 6 times x is 6x, and 6 times 10 is 16. What should be next step here? What do you remember? Please just tell us in the chat. I don't want to look at the screen and talk to the screen. Come on. It's so boring. What are we supposed to do here? How would you solve this equation for x? Ethan, are we getting something, buddy, or not yet? Subtract 6x on both sides. Look at that. Remember, because if we have variables on both sides, I always recommend that you are doing cancel the smaller ones. 4 times 6, of course, we've got to cancel 6. If you cancel the biggest one, guys, then you're going to end up negative terms. Then it's going to be confusing for you. We have 4x is equal to 60. I assume you all know that 4 times x is 60. Since optimal equation is division, you've got to divide both sides by 4. I assume you know that. It gives us x equals 15, guys. Remember what this says. x represents number of coins each pirate gets. Well, but remember what they say. How many coins did they dig up? Basically, how many coins are there total? If you only get 15 or 10, these are not the answer. Well, we've got to do 15 times 10. It was 150, guys. Our answer would be 150. Is there any question about this one? Yes or no? And please don't be shy. If you have a question that doesn't make you not smart, it just makes you more curious, it's fine. You can explain. Someone asked, how did you find 10 pirates? Oh, this one. OK, from the last sentence, it's just a logic. However, it says if there had been 50 coins less here, as you see, we don't really care about the total coins. We are just looking at that statement. Each person would have received 5 coins. Each person would have received 5 coins less. I mean, it is same as if there had been 10 coins less, that means each person would have received only 5 coins less. It is the same logic. It's the reason I just divide by 5. Or you can say 10 divided by 1, same thing. It doesn't make sense. I just read that sentence. This can give us literally how to find the number of pirates, which is 10 people we are talking about. Does it make sense, Bade? Whatever I was asking you? Or not really. Yep, they said yes. Perfect. We are good then. Any questions about this one, guys? Or can I continue? I really want to continue. Come on. Remember, Y means yes, I have a question. Y means no, I don't have a question. Ethan, do we get some yes? No questions. Alright, thanks so much. Then, this is going to be our next challenge, number 6. I can't remember. I will focus on the rules. They say add those to the others. That's the only one. Here. I put those here. You should put something. It has been 1 minute and 25 seconds, guys. I have someone saying E and someone else saying A. Okay, we have E and A. That's good, at least we get some answers. Okay, guys, let me start and go. We have the 5-digit number and this number is divisible by 4, 5, and 9. Look, since divisible by 5 represents the last digit of the first and the last digit means only there can be 0 or 5. I am going to start by 4 and 5 first because remember divisible by 9 means you are going to add those numbers. Since we have two variables x and y, x plus y can be anything. I am not going to work with that yet. Okay, first I have to make sure what y might be. Okay, y is going to be either 0 or 5. If y is 5, guys, you will get 85 as you see. Since I have only two options to test, I can just count them. Do you think 85 is divisible by 4? Yes or no, please give us y represents yes and y represents no. 85 is divisible by 4, guys. No. Ethan, do you get some answers? 85 is divisible by 4? It's not. Exactly, guys. In that case, as you see, I have to have 80 as a 1-digit. Not 85, but 80. That gives us y has to be equal to 0. That's it. There are no other chances. You see, I can just put some random numbers. Anyway, well, in that case, I'm going to have 2+, 4+, x+, 8+, 0. Equals, you still have 9 left over. You get multiple of 9, okay? Multiple of 9. Let's see. Remember, I will not just put 8 and 8 plus 2. 8 plus 2 is 10, plus 4 is 14. I just ignore 0. 14 plus x should be multiple of 9. We all know that 14 plus x cannot be 9. X cannot be negative number because this is 5-digit number. Then we just go over with the next multiple of 9, which is 18. We can work with that. I believe you all know that I cannot say 14 plus x should be 27. Because 27 minus 14 gives us 13. X is a digit. It cannot be 32-digit number. Anyway, well, it has to be something to the 18. In that case, then you take out 14 from both sides. It has to be 4. Well, then you end up 4 plus 0 is 4. This is your final answer. Any questions about this one? I hope it's over 2 minutes. I'm sorry. Any questions about number 6? No questions. Alright, guys. Thank you so much. I hope it was helpful and I hope you learned something today. I hope you enjoyed. I enjoyed a lot. I don't know about you. Alright, then see you next time. Next week, basically. Take care. Bye. Bye, everyone.

mathematical concepts

divisibility rules

factoring

problem-solving

factors and multiples

competitive exams

critical thinking

student participation

core concepts

practice