WU BBE entrance exam. Solving ACTUAL WU BBE exam tasks from 2025 (officially published by WU)

Añadido: 2026-05-25

[00:00:03]So hello and welcome everyone who is joining today's webinar to see how to solve the tasks published by VU were very kindly of them and actually I've never seen the university before ever in my life from VU because when we were doing our exams 2019 we didn't have anything basically we weren't provided with materials or nothing like that. So it's very nice that for your year they decided to well publish a bit more so that you are more or less aware of how and what to prepare for for the math part. They haven't published all the tasks there eight there should be 13 tasks in total when you will when you solve the whole thing so to say.

[00:00:46]So um some things are left out like differentiation topic or a mero probability topic. Not sure why. Maybe they just don't want to show the full thing. Just kind of still keep some element of surprise for you. But still with the eight task that are published, it's very well it's nice, right? So yeah, then to find the link to that file, I'll also into the chat and I will also publish the link after the recording has been done in the description of this video in case you're looking for it. And there's also a similar file for Visel. So they have published around I think six tasks for vis for the math part in German also in the exam section of the entrance exam for the German bachelors.

[00:01:29]So yeah and then I'll just enter in the chat in case someone couldn't find the file for the tasks themselves. It's in the entrance exam section of and I've made the solutions. They're also will be published as a file for you to check out later. So don't worry, you will not like after this is done, you will have the recording and you'll also have the PDF version of them for you to solve them yourself and then for you to look at the solutions later on.

[00:02:02]So let's start with the first one. We have a logic task first. And throughout the years they've been changing the tasks a bit. So for example in 2024 the task was still more or less one theme.

[00:02:13]So there was one big theme at the beginning let's say a party task where people are attending or not attending depending on who else is coming.

[00:02:21]Yes the session will be recorded will be posted and then I'll just close Instagram so don't disturb us.

[00:02:33]So now they have decided to switch things up a bit and make them a tiny tiny bit more challenging for you where each statement is a separate task of its own. So you have to spend time separately on them and they're not interconnected between each other. And there is actually some very nice statements honestly respect to the exam makers like like I I recognize the craft when I see it. So here we have we start off nice and easy. So if we have an implication that every mathematics student can solve equations, we say m therefore solve. So mathemat mathematician therefore solve. You can name it with any letter that you like. I use m&s just to kind of refer to the initial statement. Then is equivalent to the statement if a person cannot solve equations. Therefore he or she is not a mathematics student. So the contraositive statement would be switching them sides like you switch places and then you would have it's actually equivalent to that. The way this works is that in logic you have something called the necessary condition and the sufficient condition for each other. In an implication the first one is sufficient for the other one and for the right to left direction it's necessary.

[00:03:48]So solving equations is necessary to be a mathematician in our case. Of course like don't try to think of them like in real life scenario. Think of them with logical rule scenario because this is a math task. This is not an economics task.

[00:03:59]So here we would say that if you just say no maths therefore no salt this would be wrong. This is not correct. You cannot say this because it doesn't matter if this so being a mathematician student guarantees that you can solve equations but you can solve equations for other reasons apart from being a math student. So if the math doesn't happen this is not affected by it. But if we do the other way around where s is a necessary condition. So if you don't solve therefore not a mathematician is true because if because solving equations is necessary for being a mathematics student.

[00:04:41]So here this one guarantees this but it's not necessary. I like to do this little scheme. And here it's necessary but doesn't guarantee it and therefore if the necessary condition doesn't happen. So that's why we switch the places in the no part. So no s therefore no m would be correct because if necessary condition doesn't happen the condition that it's necessary for also doesn't happen.

[00:05:12]If you have questions as we go, please let me know in the chat or by muting yourself.

[00:05:18]Oh, it's now 70 people. Wow.

[00:05:23]71. Okay.

[00:05:25]Then here we have something called with the negation of the implication. This is a tiny bit different. So you have a statement and we say that this part is the negation of the following implication. If the sun shines we will have lunch outside.

[00:05:44]If you wanted to negate the whole implication like the whole statement together not the contraositive principle but the negation of the statement. It's slightly different. There are slightly different logical rules for this.

[00:05:56]Here you would have okay sunshines lunch outside. So the original one that we're trying to test is there is some we will have lunch and to negate it you would have okay we say this just means no it's just like a logical sign just for my notes it's a bit neater to do it this way this is a logical rule if you want to negate a statement in this form you would have the following so sun shining and we are not having side would be the negation of So sun shining and this is an n sign not having lunch.

[00:06:41]Lunch would be the negation of the original statement and this is not equivalent to the given statement. No sun, no lunch. Therefore, it's false because this doesn't match with what is written here.

[00:07:05]So, if you're new to logic and you haven't had it in school before, please look up the logical rules, how the implications work, how logical equivalences work, how negations work, and contraos principles work because this will be useful for these tasks.

[00:07:20]You can technically sometimes answer them logically as well without knowing all the rules but it definitely helps to be more confident when you know the rules.

[00:07:30]Then here we have so you immediately say okay we would have to do substitution with t. So t is equal to x^2 and is greater equal to zero because x^2 is only positive or zero cannot be negative.

[00:07:45]So here we have the fact that okay we solve the whole thing for t. So we substitute where it's going to be t ^2 then + 8 t + 15. This is our new parabola and we want to find such a part of it that will make it negative. So if it's a conc parabola and we have two roots one of them being min -5 and one of them being minus3 it is negative in between the roots and positive outside.

[00:08:13]We want the negative part and this inequality this is going to what's happen. So t has to be between minus5 and minus3. But we mustn't forget that whenever we were doing a substitution if it's x squared if t is a number squared t can be negative. It's not possible for a squared number to give you negative result.

[00:08:33]Therefore there is no real solution.

[00:08:35]There is no real like the t. Yeah. There is no real t that satisfies what we want to happen.

[00:08:41]So it actually is a case where you have a logical equivalence where both of them are false.

[00:08:49]So this is false. There is no solution here. And x^2 cannot belong to - 5 and - 3 because x^2 can belong to negative set of numbers. So when a logical equivalence is both false on the same side, it's actually true because for logical equivalence to be true, it's either you have true and true statements on either side or you have false and false statements on either side.

[00:09:13]Lovely statement. I would say a relatively niche rule in mathematics, but you know here it was necessary. But also just logically by looking at it like yeah like it's likely to like this thingy doesn't work. This thing is also weird. So they're both false and false.

[00:09:30]Therefore the overall thingy is true. So be careful here because otherwise you might just say it's false because it just doesn't work.

[00:09:37]But we're dealing with two falses on the on either side.

[00:09:45]So if an actual number x is divisible by three then it is divisible by 9. If you find just one example for this where it gives it as a false result it's not possible to do that then you can say that the whole thing is false just by finding one contra counter counter example. So let's say number three is divisible by three. Obviously it's like one but it's not divisible by 9 because it will not give you a whole number as a result.

[00:10:12]So therefore this whole thing is just false. I think this is relatively nice and simple.

[00:10:21]And statement E. So x is divisible by 12 and x is not divisible by 11 is true for every it's true for every positive integer multiple of 24.

[00:10:37]So is it really true for every? Not really because again if you want it to be divisible by 11 the first thing that you can think of to get the multiple of is do 24 * 11 because that's going to be guaranteed divisible by 11 because this is like the harder thing to find because divi divisible by 12 it's relatively easy for 24 to find such numbers but by 11 you just go straight into 24 * 11. So this is a positive multiple. So the multiple is this result. So you do 24 * 1. So 24 is a multiple of 24. 24 * 2 48 48 is a multiple of 24 and so on and so forth. So 264 is a multiple of 24 when you're multiplying it by 11 which is a positive integer number and then it is also it also happens to be divisible by 12 gives you 22 without any remainder. So therefore this is false.

[00:11:31]the there is such an example where it is divisible by 12 and also divisible by 11 but the statements were done relatively short like a short description for me to explain it on the video because now you can kind of hear me explaining it's fine but I will also make them a bit more longer and detailed for the people I'm publishing it for on the website because I will do it in the blog section of my website as well as to save them here.

[00:12:03]So the correct statements are A and C.

[00:12:06]And when you're solving this part of the you can also double check if you want.

[00:12:10]You can go down the statements like at the very end and see the right answers.

[00:12:21]Another important note that I would like to mention on this file is that I've also receive questions about it. This is the formula sheet. As you can see, it's not very detailed. Like I've told you in one of my previous reels that it's not going to be really really helpful.

[00:12:34]Um yeah, just like how they decide that but basically at least one correct, right?

[00:12:43]At least one answer I should correct because before in the Viso platform, in the online platform, you had true or false like this.

[00:12:57]And then you could choose all true or all false. You can get some partial points and so on so forth. And your strategy was never to leave anything blank because you would get zero points something blank and some partial points if at least get something at least partially correct. But now we is trying to prevent you from uh basically guessing and getting any like lucky points. There's no lucky points this year because here you have the boxes B C D E and they're trying to prevent the fact that if you leave it all blank assuming everything is false you get zero points because you didn't get any correct uh answers. You didn't choose any correct options. Therefore you get zero because you didn't choose anything right? So yeah, and that's why also if you crossed all of them out and some of them were right, let's say A and C were right, then you got like some plus I don't know two points and plus two points out of I don't know out of four or five doesn't matter or three depending on like the number of points you have but then you have minus and then I don't know minus and then minus two for example they will weight the minus and positive differently depending on the question the number of correct um solutions like the number of correct statements and everything. So they're just trying to point if you also just cross all of them out you also get zero points. So there's no guessing available because if you leave all blank zero points if you cross all zero points as well.

[00:14:27]Of course all of them could be true but if you do this for every statement you're going to be losing points. So yes, there is a possibility that all answers are correct.

[00:14:35]But for most questions, if you do something like this, if you cross all of them, you will very likely just get zero.

[00:14:42]Maybe there is a possibility to get partial points if the negatives weigh a bit less than the positives. But uh let's see from my year they actually just published the partial point grading system explanation on the website as a link. So once that is published, I will also let you know as soon as I know.

[00:15:01]Wait, but do we get negative points uh if we guess one or two wrong or just if we cross out everything?

[00:15:10]>> Uh you also get negative points if you guess something wrong. Let's say you can also just not cross this one but you still get minus one and minus two for this month.

[00:15:23]You just get less minus.

[00:15:25]>> Yeah. Okay. Thank you.

[00:15:26]>> So you the lowest you can go is zero. So at least there's no negative points for the whole question. But even if you don't guess, you can still yeah get some negatives. So you get zero here and then yes it's better to bling. So that's why this here is as important as ever that you study so that making educated guesses is a bit better than just guessing. So if you like have a feeling for okay it's more likely to be true more to be false you will more pro more likely get the point for that this one some things look scary but they're not and always pay attention to the definition for example x y and z are real numbers including zero right but here they say that y isn't equal to zero this is the only reason you can just cancel it out eventually so these statements where it's not equal to 0 or it's not equal to minus plus - one making the zero are the only reasons you can actually cross them out so confidently. If there is no such point where like y is not equal to zero or something like this and you say y is a real number including zero thenh you cannot do this what we're going to be doing here with the simplifications.

[00:16:40]So really be careful with the definitions they are there for a reason like it's not just like fun facts.

[00:16:49]So here, okay, this is just you're just messing up. Not messing up, but you're messing around with the what you can cancel out and how. Not too much to do here. Like this is 8 y. This is 4 and y^ 2 because if you square it, you get -2 * -2, you get 4. y^2 is y^ 2. And then you get 2 over y and not - 2 over y.

[00:17:16]Good question.

[00:17:18]But you have the inequalities. So you could Yes, there were some annoying inequalities in one of the previous years like really bad ones that yeah because in 2024 I made an extra task for the course with updated versions for the logger like for the the irrational inequalities and the absolute value inequalities based on the well the previous year 2023 but in 2025 they made it more text based. So the inequalities task that we will see later and the elementary algebra task that we saw now is arguably a bit easier if you prefer text over over solutions or like over solving an equation because some people just prefer solving it and it's easier for them. So yeah, but subjective.

[00:17:59]So then B here we're just messing around again with a bunch of fractions. So we're multiplying these two fractions dividing by this one. And when you're dividing by a fraction, you're multiplying it by the flip version of the fraction here. Then you simplify it, cross out everything that crosses out and you get this as the final answer.

[00:18:20]I don't think I have to explain much here because x cancels out. Then y to the^ of 3 - 2 is equal to y ^ 1. And for z just stays and then three cancels out. Four cancels out and 25 stay cannot simplify that further statement C another honestly masterpiece of a statement because here x - one how beautiful how beautiful and y - x are different so if you see it is the difference of squares it's the same thing as this essentially the lower Uh that uh one second.

[00:19:20]Yeah, basically if you don't pick one of the right options, just get zero points.

[00:19:23]If you pick one of the wrong options, you get minus points. That's But please wait until we publishes the full calcation procedure.

[00:19:35]Yeah, exactly.

[00:19:37]But again, they can weigh them differently. A positive answer can weigh more than a negative answer. Please wait. Like, okay, like guessing is not ideal, right? We should really think about it or leave it blank. But let's wait until the but because you also lose points if you leave a correct option blank.

[00:19:58]Yes, it would be better to not. But something like what is actually nice.

[00:20:01]like this is not this is not not as bad as you might think it is. There was a differentiation task that's much more annoying than this or the language probability task that's much more than this to solve.

[00:20:11]Yes, there yes there is you can go lower than zero. Correct.

[00:20:16]Also, I know that in the one of their info sessions, it said it's like more or less the same points per per part, but they have also said that in 2025 or 24 and then it still stayed 40% economics, 21% English and 39% mathematics even after the program coordinator said that hey, it's more or less equal. So, you will see the number of points next to each question and you can go from there. I would say I would say wait until the exam day and here to basically have the common denominator you're just adding what you're missing.

[00:20:54]Uh but again like but English is also yeah I would I like it I like the fact that it's a bit less because then it tests your economics demand skills more because English you're kind of you're they assume you have it anyway because they ask you for the matura or for the ISO exam. Okay let's get back to sol because otherwise you won't have enough time. So here 1 + x and x+1 doesn't matter you just multiply it by x - one.

[00:21:18]Here you multiply by x + one and here you multiply it by minus x + one. So -1 * because you want to change the order from 1 - x to x - one. That's why you have -1 * x + one as the multiplier here. This is a very common mistake. Um it's very easy to make if you're in a rush.

[00:21:42]Once you do that, you'll get this basically.

[00:21:49]Once you also look at all the signs with the minus or with the plus because here you had a minus but you had a minus as well. So in this part this minus and this minus cancel each other out cancel but it becomes a plus.

[00:22:21]So you essentially get this. This is just like the final not to write out a huge line and then as the final thing you get this and you can say okay this you can get four out x + one and this you know what it is equal to it's x - 1 x + one and since you know that x cannot equal to + -1 you can cancel this out otherwise you wouldn't be able to do that And that's how you get uh 4/x - 1 as the final result of simplifying all of this and solving.

[00:23:01]So the left side is equal to the right side. It's true.

[00:23:06]Statement D is kind of very obviously false because here you would have multiplication xy and not x + y. So if you can see it, you don't don't solve it. Just go for it and say it's false because in one of the interviews I did with Max. So he got 12th place on the exam in his year and he's like he became the top of his cohort and yeah he's going into Cambridge I think for masters. So a very smart young man and he told that okay it was more true for the online exam that you shouldn't if you can calculate something in your mind or you can see something clearly if it's true or false just cross and move on because again two hours not a lot of time but this advice has like there's two sides. It's either you know it and you save some time for the rest of the tasks or you rush and then you get a really easy mistake that you could have easily avoided by just calculating it further. So be careful here. But yeah, it's kind of obvious because like you to get the common denominator you have to multiply them by each other not add them to each other. I hope everyone knows this rule. So yeah, this would be false.

[00:24:10]And in statement E again you have the difference of squares just in a different format. So it's basically This and then you do can also write it like this. really up to you how you write it because it's the same thing as 4 / x^2 is equal to 2 / x^2. Different representations, some just look a bit neater. Whatever you prefer, go for it.

[00:24:50]So yeah, that's how you have this and not that.

[00:24:56]So that's what makes it false.

[00:25:00]So you have 4x^2 minus 1 as the final answer and not this as the final answer that they stated in the statement and that's why it is not correct.

[00:25:13]So seeing the difference of squares or seeing the common denominators and seeing how you can simplify a fraction is really useful for this task for elementary algebra. But in 2023 it was much harder. It was a bunch of inequalities there and now they have separated elementary algebra into inequalities and equations like two subtopics of it. So you have quite a lot of potential there for annoying things.

[00:25:35]As I mentioned equations looks like a lot of text looks like no way you can solve it. But actually it's very nice.

[00:25:44]Yeah, don't move the camera. And yeah, let's let's go for it. And here again out of attention traps as as always cannot really avoid those.

[00:25:56]We have a rectangle right and one of them one of the sides is 3 cm longer than the other side and the area is 40 cm. So the length of the longer side is five.

[00:26:09]If it helps you to draw the the thing draw it. If you don't need to don't don't. But if you like it it's just basically like like this. This is the longer side. This is the shorter side.

[00:26:22]The areas you multiply the side by the side.

[00:26:26]And then you get the parabola. Then you can get the discriminant. You move everything to one side. Get the roots la. And then you get a negative and a positive root. Of course, you pick the positive root because the length of a side can be negative.

[00:26:40]So the short side is five and the long side is eight because long side is 5 + 3 because x is five.

[00:26:55]Then for statement B, our car travels at an average speed of 64 km/ hour. At 3 p.m. it has traveled to a distance of 112 km. Therefore, if this is the case, it's traveling at 115.

[00:27:10]So let's see and with ours is super annoying just to keep the minutes and the fractions and all those intact.

[00:27:17]So here we have the average uh the distance the average speed we get the time. So, it traveled for 1.75 hours. In other words, 1 hour and 3/4 of an hour, which is 1 hour 45 minutes because 45 minutes is 3/4 of an hour. And at 3 p.m., so let's see, let's look at our start time. So, if it's 3 p.m. is the end time and we have traveled for 1 hour and 45 minutes, then our start time must have been 1:15. Here, just careful with minutes and hours.

[00:27:56]A double check. 15 minutes plus 45 gives you 2 p. p.m. + 1 gives you 3 p.m. In case you're not sure, you can reverse it and see if it matches or statement C a recipe. Okay, I see a question in the chat.

[00:28:22]Uh so this is one to one task from 2025.

[00:28:26]This is the recent year. This is the most recent year. So here we have they might make them the same like they make a bit easier a bit more difficult but overall to pull that stuff out. We have some easy task. We have some hard tasks every year.

[00:28:42]Of course if they want to make hard tasks they can but this is the most recent information from VU officially published on their website.

[00:28:54]It seems easy, right? Doesn't seem so difficult now when you have the solutions running in front of you because imagine you have two hours, you're sitting, you have thousands of pe thousands of people around you and then it feels a bit different because now you're at the comfort of your own home. You don't have the time pressure, you don't have the stress pressure, no people around you.

[00:29:11]Of course, it will feel a bit not as stressed and it's more for also a time exam. The tasks themselves are very much doable. They're fine. It's the time that gets you because two hours for all of this for all three parts. If you're like under all these conditions with not the best calculator like it's it's a like simple scientific one then this is the time gets eaten up. So to get a very high score you need to solve and solve and solve without stopping too much.

[00:29:38]Yeah.

[00:29:42]So, a recipe calls for 5% vinegar if the cook has has only one liter of 8% vinegar and then he needs to mix it with some kind of water. Let's say 0.6 lit.

[00:29:52]That's true or false to get a concentration. So, from eight from a concentration of 8% we want to go down to 5%.

[00:30:01]So, yeah, here we have the concentrate on the top. So, 0.08 08 L would be per vinegar out of one liter because you have 8% of it in the liter. And below you have the one liter that you have plus some volume of water that you don't know yet what has to be but you can find it out.

[00:30:25]Yeah. No, they will not really tell.

[00:30:27]Yeah. Yeah. Of course they will change the questions like they will test more or less the same skills but questions will be different. That's why I'm guessing like if they haven't released some of the tasks like the remaining ones maybe they will make them the same. I don't know.

[00:30:41]Let's see for the ones that I haven't published because there are 13 of them not eight.

[00:30:46]So yeah here we have liters of water. So the total volume uh of the liquid and the concentrate on top and then you see okay how many liters of water do you need to add to go from 8% to 5%.

[00:30:59]And at 0.6 you just solve for V here with the cross multiplication rule.

[00:31:06]like this.

[00:31:17]Then this one again amazing equation I would say here you immediately have to see that these are all powers of x and what you can do with powers is you can put them in front of the logarithm or statements like c yes there is a formula if you just look up like concentration tasks or like mixture tasks you will find it there is a there is theory behind this but here I'm just explaining the tasks because otherwise it's going to be like a five hour lesson so here we notice that this is the Same thing as x ^ 1/3.

[00:31:52]This is the same thing of course. Okay.

[00:31:54]Logarithm. Yes. Log is just log in our case is lg. This is the logarithm with the base of 10.

[00:32:02]And then we have log x ^ minus 3us.

[00:32:09]And here we just keep it the same. Log x2 + 16 / 3 is equal to this.

[00:32:17]And this part is just log 10 over 100 gives you two. This is two. So 1 + 2 is equal to 3.

[00:32:28]And here we keep the log grid. So now then we put the power in front. This is a property. So that's why when you know the properties and the formulas and the rules very well, you can immediately see which one of them you should apply and how you should apply it. So it's a mixture of knowing all the theory and knowing the test does.

[00:32:48]So here you have 1/3 in front. Then here you have minus 3 goes in front and here you have two goes in front but the minus was here.

[00:32:57]So essentially you have 1/3 logarithm of x - 3 log x - 2 log x plus 6. This is the left side.

[00:33:07]Then these are all log of x. You can combine them together.

[00:33:16]So basically if you want to multiply it by three is the same thing as - 9 and - 6.

[00:33:30]So -4 because this is -5 and this is + one.

[00:33:43]Yes, I will publish it every I'll publish it like openly on YouTube so everyone can see.

[00:33:54]So that's how you get this final left side simplification. The right side we discuss is equal to three. And here you can just put two in front of the logarithm using the same rule.

[00:34:06]And that's how you get this part. So 2/3 basically it's like two / 3 * log x just written in a nicer way where you put blog below and the fraction by itself.

[00:34:17]Same thing as log x / 3 just in my mind just a bit better like easier to see for this part.

[00:34:28]Then you simplify down further. So this are just intermediate steps I will skip.

[00:34:31]You multiply them by 3 and then you eventually get 16 is equal to 16 log x and log x is equal to 1. So logarithm with the base of 10 of x is equal to 1.

[00:34:44]So this to the power that is equal to x.

[00:34:46]So 10 to the^ 1 should be equal to x using logarithmic properties. Therefore x is two. It's not more than five.

[00:34:53]Therefore it's false.

[00:35:05]For statement E, oops.

[00:35:12]A prize of 12,200 is supposed to be split among the winners. Second place gets 80% of the first place and third place gets 80% of the second place.

[00:35:23]And then you want the price for the second place. Is it four or not? 4,000 or not.

[00:35:29]So okay, first first place price is let's say 8 whatever you want. Second place is 20% less. So like it's 80% of the initial price for the first place and third place that third place it's 80% of the second place because we know the second place is 0.8 eight a and if we do 80% further we get this.

[00:35:56]So the price of the first place, second place and third place in terms of a we solve for a we get a is 5,000. But this is the price of the first place. To get the second place you multiply the 5,000 by 0.8 to get 4,000. And that's correct.

[00:36:13]Here common mistake would be just to see 5,000 and say it's false. But you actually have to then do one little more like one little one more calculation and multiply 5,000 by 0.

[00:36:32]Now task four. So we will be halfway done. If you have questions as we go, please feel free to ask them in the chat or by muting yourself.

[00:36:42]And you can also be able to ask them in the comments on YouTube in case you want to kind of chat later.

[00:36:48]Here we have this actually the first time that they ask something like this for the linear questions. Usually it's two companies or two pizzeras or something like pizza one, pizza two, quantity one, quantity two. This is a bit more creative and it's like work productivity task. There is also formulas for this specific subtopic.

[00:37:05]It's called like your productivity task like work per hour tasks. You can also find it online if you want more theory.

[00:37:11]But here we're discussing the task itself.

[00:37:16]So here let the total work be one order. No matter like be 100 cookies, 200 purses, whatever it is, we don't we don't need to know. So it's one job. It's one order that it's made. We know that Frank and Julia, if they have had worked together the entire time, they need six hours.

[00:37:39]So for one order Frank and Julia need six job per hour formula just job divide by the hour. So one job divide by six.

[00:37:48]So one six plus one six plus one six like per hour what you're doing six of the job. If you do it six times you get one job. Yeah that makes sense.

[00:37:57]Then Julia here we know that they work together for three hours. So they finished half of an order.

[00:38:07]speak to me.

[00:38:10]>> I will. Yeah. Um if uh basically this was half of an order and then Julia had to work another five hours to finish the other half. So she finishes half of the order in 5 hours. Meaning that she would need 10 hours to finish the entire order.

[00:38:28]And Frank, we don't know. We don't know if it's productivity. So it's like one job over X. But what we know is that the productivity of both of them combined is equal to 16.

[00:38:39]So if we add 110th plus 1 /x, we get 16.

[00:38:44]And you can solve for x. So Frank, it actually takes 15 hours. Frank is a bit slower than Julia. So for one whole job, if he had to do it by himself, he would need 15 hours.

[00:38:55]After you figure out this part takes a bit more time, but then you can solve all the rest of the statements pretty easily. So sometimes on the exam it's worth to invest like two or three minutes into like the beginning to then solve everything in like 30 seconds per state. So don't be afraid if something is taking you too long at first. It gets it usually gets easier as you find more and more things.

[00:39:18]So yeah takes hours we just found out.

[00:39:21]And then for statement B, if the order was 120 150 purses, then the difference between the times Frank and Julian need to assemble one purse is more than 3 minutes. So we're just comparing how fast Julian how fast Frank assemble the purses.

[00:39:39]You have the Frank's rate. So you have 150 times the productivity of Frank and 150 times the productivity of Julia, 110.

[00:39:52]So she does 15 pesos per hour. He does 10 purses per hour. Time per purse is 110 or 115th and six and 4 minutes.

[00:40:10]So difference is 2 minutes and not more than 3 minutes. Therefore it is false.

[00:40:17]Yep.

[00:40:20]Because yeah, even if you do 10 pesos per hour, it means you do one purse in six minutes, 60 minutes.

[00:40:33]You do 15 pes per hour, that means you do one purse in 4 minutes. I think that's clear.

[00:40:42]Then for statement C, if it's reversed, so that is Julia would feel sick and left after three hours. Frank would need more than 10 hours to finish the order.

[00:40:53]So here we have the reverse situation.

[00:40:56]They have done together with the three hours that they had one half of the order. The remaining half is done. If Frank needs to do half of the order with his productivity 1 over 15, he needs 7.5 hours, not more than 10. That's less than 10. Therefore, it is false.

[00:41:13]Because now you divide the job, but you only do one half of the job and the productivity rate is still the same. It doesn't change. It's 115. So you get 7.5 hours.

[00:41:29]For statement D, if the order were twice as big as the original one, Julia would need 10 hours to finish the order after Frank left due to sickness.

[00:41:40]So let's say instead of having one order we have two orders. I think that's just like also in my head it just works a bit better this way like to explain it.

[00:41:47]So or twice as big there is a total work of two. So two jobs basically two orders together they work for three hours.

[00:41:56]So they did half of the normal order. So they did like 0.5 together. Therefore, they have one full order and 0.5 of of the remaining order left to get to get to produce the two orders.

[00:42:13]And Julia is doing it alone. So, she needs to do one and a half of a job with her productivity one over 10. So, she needs 15 hours, not 10.

[00:42:24]You can do it in other ways. You can do okay 5 hours to finish the first half because you know Judy's productivity.

[00:42:29]You know that she takes 10 hours to finish one whole order alone and she takes therefore five hours to finish one half of an order alone. So you do 10 hours for one new order like the whole one like plus plus one and 5 hours for the half that was remaining when we did the other half with Frank.

[00:42:55]Then statement E If they had completed the entire order together, Frank would have completed 40% of the order.

[00:43:07]Let's see.

[00:43:09]So, they work together for 6 hours to finish one full order themselves. And Frank's productivity is 115th of the total time. So, it's 0 it's 0.4 40%.

[00:43:24]Should be the percentage. I will change it.

[00:43:27]So if the order was 100 units, Frank would make 40 of them. Julie will make 60 of them because her productivity is just more. She's faster.

[00:43:46]Then task five inequalities please we have question just ask because otherwise I'm assuming everything is clear. a lot of text, but it is easier compared to 2023 as Philip said.

[00:44:05]So yeah, like the text just becomes very nice linear equations or parabola at most. Okay, this one is a bit annoying, but the rest of them are fine. So within the questions, you can say, okay, I will do A, B, C, and D. I know how to do them. Statement E, I will come back to later. You can put like a little star or question mark there because this will take you more time than the other ones.

[00:44:28]So here we have a farmer is placing a field. He has 80 m of fencing available.

[00:44:34]So the perimeter has to be 80 m because otherwise he runs out. And he wants the field area to be at least 48 kilome squared.

[00:44:44]And to maintain the ratio 3 to1 between the longer and the shorter side of the field. Then with all of this given what you have what you have to check if it's true or false that the shorter side can be between four and 20 m long.

[00:45:06]So here we have let's say the shorter side is a the longer side is 3 a to have the ratio 1 to 3. Right? This is just like in a bit simpler terms like 1 2 3 perimeter has to be less or equal to 80 because that's how many meters of fence he has. So 8 a because if you do the rectangle with a a 3 a and 3 a you have 8 a together it's 10. So the yeah the shorter side is less or equal to 10.

[00:45:41]And the area has to be when you're multiplying 3 a * a 3 a 2 greater or equal to 48. You solve for a. You obviously choose the positive answer here because you cannot have a negative a negative side of the length of the field. And thus the thingy because this is a system of equations of inequalities has to be between 10 and four.

[00:46:08]So less than 10 but greater than four.

[00:46:10]the shorter side.

[00:46:20]Then if the position of an object above ground in meters after x seconds is described by the it's a basically this is how you you throw you throw the ball or whatever it is and it goes because like I said it goes up and it goes down and you want it it's a concent parabola.

[00:46:36]It's more than 100 above the ground. So at some point this is 123 m and you're trying to see the time when it was 123 m above the ground as we're trying what like what's the how do I say the picture here what you're trying to solve in graph terms if it helps you to draw this draw it not to confuse but in other words you can just do it with equations.

[00:47:01]So here you want this parabola to be greater than 123 m because you want above 123 m not above or equal to 123 m.

[00:47:09]And then you solve the parabola. You move everything to one side. Divide by minus 5. Switch the inequality sign because you're dividing by a negative number. And then you get the final answer between two and two and 12.

[00:47:25]And be careful like this is the final thing that you're solving. Even though it's very different from here, you got to this part by making this look nice by getting to one side and everything. So, this is the final thing that you're going to be looking at for your final answer, not whatever happened here.

[00:47:48]Then C is the average cost per unit.

[00:47:53]So if the cost of producing x units of per product are 150 plus 0.2x into x.

[00:48:02]Yeah. No, between 2 and 12, I don't include here. They're not very strict the definition. So then to keep the average costs, yeah, if you want to plug in numbers, yes, takes a bit more time. I think it takes a bit more time in this case to do it with the plug-in numbers, but why not? If you want to I don't I'm not preing it.

[00:48:28]Then here the cost of producing X units of product are 150 plus 0.2x at least 83 units must be produced for the average cost to be below €2.

[00:48:41]And of course you can only produce the whole units. You can't produce like a 0.5 of something or 0.5 of the t-shirt would look not very nice.

[00:48:50]And then here let's say uh the average cost below €2. So you just want to take the cost function divide by x to get the average cost and has to be below two and you just have to solve this to find it. You solve for x and you find that x has to be greater than 8.333.

[00:49:11]Therefore, the next closest integer that would make sense would be 84 because at least 83 includes 83. If you produce 83, you have the average cost of more than two. Here you can also just plug in number 83 and see what happens.

[00:49:29]Yeah, as an option I'm just like also like how I think how they to be solved.

[00:49:37]So yeah, therefore the average cost of 83 would be more than two. The next best unit is 84. It's kind of the answer is in between, but you cannot have non whole units. So that's why we pick 84.

[00:49:49]So it's really this close because it's kind of 83.33. If you're rounding it up based on mathematical logic, it's closer to 83. But if you're doing based on the production logic of a company who's producing units, like whole units, has to be at least has to be like 84, not at least 83.

[00:50:17]Then for statement D, it looks super long. Don't worry, it's not that bad.

[00:50:23]To produce one unit product, there are three raw materials, A, B, C. You need three materials of A, two units of B, and four units of C. And the raw materials cost 40 15 to 25 respectively.

[00:50:37]So respectively just means this is A, this is B and this is C.

[00:50:44]We also know that the production of one unit of the product cost 12. So like labor and machinery used and the producer has a total budget of 21,400.

[00:50:58]Yeah, it's up to them. They can make them harder. It's it's really up to them cuz it's like the examinators who are making the tasks. If they want to make new tasks, they can be could be easier, could be harder.

[00:51:15]They're just changing like they're just changing the theme like it's either just inequalities with like normal mathematical terms like here in statement E or in text. It's up to them what they want to choose for. As you can see, they just mixed in a bunch of things here, text and inequalities.

[00:51:30]So here we have the to materials per product.

[00:51:38]It's 8 units because we also have the storage capacity.

[00:51:47]So you can have the budget of €21,400 and storage capacity for at most 475 units of all raw materials combined.

[00:51:57]Then if you have all these conditions the maximum number of products that can be produced is less than uh 50.

[00:52:04]So let's see you have the raw materials per product is nine units and the storage is like so nine units. So how many products you can store less or equal to 475 is less or equal to 20 52.

[00:52:23]Then the cost per product in raw materials you have three units of €40, two units of 50 and four units of 25 years. So these are the costs in raw materials and you have the production costs being 12 years. So total cost per unit is 332.

[00:52:48]Yeah, exactly.

[00:52:51]Yeah.

[00:52:53]Good point.

[00:52:56]Uh then the budget is uh basically well the total times the units that you want to produce of one whole product not the raw material but the whole product because one product needs nine units of raw materials and this is the cost. So this is the end for the budget. So 64 units of products is fine with the budget that we have.

[00:53:18]But basically we have the maximum storage of 52.

[00:53:24]So the maximum that you can produce is not less than 50. We're actually pushing it because we're over the maximum but we have we have the storage limit. So the closest we can get from 64 up until the storage limit is 52 and 52 is less than 50. Therefore limit is false. It's more than 50. It's actually 52 exactly like we are filling up the capacity to the mean maximum.

[00:53:49]That's statement E. We just want to see the if and only if this so the solution of these is satisfied if and only if the absolute value of X is greater than two.

[00:54:00]That's let's see this is a double inequality which we can just put into a system of two with the n bracket. So this is the n bracket. This is the or bracket. So yeah union intersection to say. So this is intersection of the intervals and this is the union of the intervals.

[00:54:23]So let's start. This is pretty nice and simple and this is also as well. So here we just put to one side get the common denominator like simple transformations I think you know and for the absolute value it's either it's greater than x or less or equal to minus x because if you want something Oops.

[00:54:47]To the greater than x on the interval it it's either greater than x right to greater or less than minus x because absolute value let's say this is five and this is minus 10 is less than minus 5 then you would still get absolute value 10 being greater than five it will still work. So that's why you have either this or this possibilities for the absolute value. And of course there are like a lot of formulas for the absolute values that you can memorize. You can also learn how to understand them and then don't have to recall the full formula.

[00:55:21]You can just write this just from understanding what the absolute value does.

[00:55:27]Then you solve and basically get the solution set being between minus2 and zero and to infinity.

[00:55:35]and something equivalent to this because this would give you either over two less than two.

[00:55:43]This is what's this part and this thingy that you actually solved for it goes from where is zero around here - 2 to 0 and then two and above. So yeah, it doesn't go below minus2 it stops there.

[00:56:05]So they're not equivalent solutions solution sets. Therefore is false functions. This is a very nice relatively easy task to do.

[00:56:23]So here you have a production function W of L. So the V output of labor is 0.25 L to the^ of R. This loi reminds you of the cob production function on macroconomics a bit later. And then to produce four kilograms of wheat, the farmer needs to work for 33 hours, 32 hours. So we immediately see that after 32 labor hours, we get 4 kg of weight. This is one point that we can use to find the r that's missing. we know that it's a real uh a real number and of course therefore L cannot be negative now because work late work work hours can be negative work hours.

[00:57:07]So by doing that we can solve with this one point function itself and we can find out that r is equal to 0.8. So like these small math tasks I'm just honestly going to be skipping because I'm assuming yeah people are familiar with the metal algebra rules and if you want to take it a bit slower at home by yourself you can time yourself and see if it takes you like it should take you anywhere between four to six minutes to solve a task on your own with a calculator that's allowed and here I'm just going to answer so yes r is greater than 0.5 and then B is a nice statement where we just say okay if we are working for 64 hours we have more than 8 kg of wheat.

[00:57:54]So we plug in 64 would be we have our small 0.8 we have everything and we see that we actually producing over eight kilogram of it we are producing a bit less than that. So it's false and then this is a messed up way of asking you to know how the function looks like.

[00:58:14]This is a power function with a power between 0 and one with a positive beginning value. Even if it's less than one, it's still positive. It's still okay. And here we have L1 and here we have L2.

[00:58:40]So here the marginal increase in labor would the marginal increase in anything is just the first derivative and the first derivative is the slope of the tangent line here and here. Here it is flat like flatter and this is steeper compared to the other thing.

[00:59:02]So assume that for Ben's neighbor the production function is the same. If Ben works L1 hours then the Ben's increase in production from additional lab hour of labor is greater than neighbors increase working additional hour. Yes.

[00:59:15]Because if like Ben does it here he is more productive here when he goes a bit up. But since for neighbor for L2 if you go up one more you're already super tired. It's like physical work. You're going to be working for one more hour but that one hour is going to be less productive than the beginning hours. It also makes sense in in real life terms.

[00:59:41]You can also build the marginal product function with the first derivative. See, it's decreasing enough. So, it's going to be like the first derivative is decreasing.

[00:59:50]It makes sense because the slope gets like less and less and less steep. On the exam, you can just put your pencil next to the graph and see how it behaves because the first derivative is just the value of the tangent to the graph.

[01:00:03]So that's true.

[01:00:08]Then for D, we're just trying to solve for a function of L.

[01:00:15]A marginal product is the slope of the tangent line because marginal is the first derivative. The margin marginal something is the slope of the tangent line that gives you the first derivative.

[01:00:31]Then this part, the amount of labor necessary for a given wid output is a power function too. So we're going to be switching W and L sides.

[01:00:43]So here we have the original function and now we want to transform it for L.

[01:00:52]So L stays then you have W over 0.25.

[01:01:00]same thing as 4 W and then you take the root of 0.8 of both sides to get L is the root of 0.8 of 4 W and that's a power function actually the same thing as to the power of 1 / 0.8 Okay, because this is one goes up if this is a root power goes down in the fraction.

[01:01:32]So, so yeah, it fits this description.

[01:01:35]It's a constant times x to some power.

[01:01:37]Now, w is our x is our independent variable instead of l.

[01:01:45]Then to double the output of the wheat.

[01:01:52]So to double the output, the amount of labor must be more than doubled.

[01:01:58]True.

[01:02:00]There is this way where you put two W's here into this function and you solve for a. But I don't like this way. Like it's kind of the mathematical way with the labor out of wheat. I prefer to do the plugin numbers way here. So I will explain that one.

[01:02:16]Uh the minimum for 2025 was 86.8.

[01:02:21]Now it should fall with the same in conditions for everyone, less people participating and also negative point system. I would assume it's between 75 to 80 something. I don't I think it's going to fall.

[01:02:37]So what I like to do here is okay in 33 hours we produce 4 kg of wheat. How many hours do we need to produce 8 kg of weight? That's the simplest thing to do here. And so we solve basically the function for eight.

[01:02:53]What is this? I think it's a type of code like 0.25. Yeah it's the power every time. every time it's like this is equal to eight because when you do the power in latic and you don't do the small brackets it makes the second thingy go down and then you solve for for L. So L 0.8 is equal to 8 over 0.25 and therefore L is equal to the root of 0.8 of 8 of 0.25 25 and it is 76 something. And if you compare the L new with the old L, it's more than doubling the time. Yes, because 76 hours is more than double of 32 hours. It also visible even without dividing them by each other.

[01:03:47]As you can see here, the majority of the statements are actually correct.

[01:03:52]Here we have we're almost done. If you have questions about the tasks, please ask because I see you have a lot of general questions. But if you have question about also feel free to ask me and I just in case.

[01:04:16]So denote denoted by FT the population of the country.

[01:04:21]So the Korean population is 10 10 millions and it is assume that it grows by 1.2% per year.

[01:04:30]Okay, this one it's rage bait again.

[01:04:33]This should be 10 10 million not 10 like everything is correct here with the grow rate and everything but it's just it should be 10 million not 10.

[01:04:44]Great, great, great. Thank you.

[01:04:46]Honestly, would move because you see 10 minutes and you think it's 10, but it should be 10 like with six zeros after then. Yeah, after 30 years the population had grown more by 50 will have grown by more than 50%.

[01:05:05]So here we have 30 years have passed.

[01:05:08]Here we have our 10 to the^ of seven.

[01:05:09]This is our 10 million. We have seven zeros here.

[01:05:15]And then this is just a growth rate.

[01:05:16]Like we actually don't really care about this one. We only care about what this does to this number.

[01:05:28]And then it gives us a growth of around 43% which is less than 50%.

[01:05:40]Yeah. So it should be either it should actually if it's like this it will be correct here but it's not statement C the head economist of the country predicts that the GDP of the country growth by 4% per year. So then the GDP per capita GDP per capita is basically divide GDP by the population. So I added a concept from economics and grows by more than 3% per year. Let's see. False.

[01:06:18]Honestly, it's like sounds a bit too big. Like just logically like intuitively it sounds a bit too much. So it's more likely to be false than true even if you don't have enough time to solve it.

[01:06:29]But if you do, you just divide the growth factor of the GDP by the growth factor of population which is like 1.2%.

[01:06:35]And you see the total growth of GDP per capita because of GDP in this population.

[01:06:43]So it is around 2.78% something like that which is less than 3%.

[01:07:00]Then assume that after five years the growth slows down to 1% per year.

[01:07:05]Then the population of 12 millions will be attained at t greater than 15.

[01:07:15]So here we have after 5 years has slowed down.

[01:07:21]So before that it was fine. Before it was 1.2% and this is was like until year five. This is was the case. Then we take this as our value and we keep increasing it for the remaining years.

[01:07:39]Some years that are still left but now it's the growth the population growth is 1% 1.2%.

[01:07:45]So down to 1% means from 1.2% to 2%.

[01:07:51]Also be careful with percentages with increase by slow down two value of or percentage points because then it differs what what kind of percentage you're applying.

[01:08:04]Actually in one of the previous years they have also select percentage points.

[01:08:10]So just to kind of just in case it comes up again. So if I say that I have 5% and I increase by 20%.

[01:08:26]That means I increase five by 1/5 of five so I get 6%.

[01:08:34]If I increase it by 20 percentage points, I get 25%, not 6%. So, be careful with the wording.

[01:08:51]Just a little side note here. Then you're basically trying to solve how many years it takes to get the to 12 million. This is 12 million just written with a nice factor. And you solve for t using ln using ln because you can only pick lg or ln on calculator. You can already pick the base. So you pick ln or lg as a way to solve it because you're just taking l of both sides. C goes in front and then you're dividing ln of this number by whatever this was.

[01:09:21]So this number divided by ln of this gives you 12.32 years. And then you had the remaining of the other five. So 5 + 12.32 gives you 17 years and something which is already more than 15.

[01:09:35]Therefore, it's true. You need more than 15 years to get to 12 million people.

[01:09:43]Then the last statement is about the continuous rate growth. So you have 8 million whatever it is doesn't matter like this is the beginning value. It plays no role in the growth rate. Then the growth rate of every country is smaller than 2% per year. This is a continuous growth rate of 2%. a continuous growth rate of 2%. If you want to do it in um discrete terms, it would be actually 2.02 because if you're going from continuous to discrete, e to the power of k is your a small. So e to the power 0.02 is your a that gives you the discrete growth per year and that is a bit more than uh 2.02% 02% growth in growth terms. I actually calculated this very quickly on the calculator for you to show you.

[01:10:43]So it is around in discrete terms.

[01:10:56]So here you have only one correct second.

[01:11:10]before in the previous year it had it ranged around from 78 to 82 or something.

[01:11:21]Then the last task for today binomial distribution and we will be done in one and a half hours more or less as I planned because I knew fresh is going to take more than one hour and right now honestly when I'm explaining this I'm like in my head it's like because I gave two group lessons already before that you had to work before so this is like the final lesson for the day. Thank you for spending your weekend evening with me. This is the answer sheet from from basically the math um tasks that has published but yeah this tasks by normal it's at the end of the exam amazing task super easy to solve takes you so much less time compared to differentiation or something else that's why I advise to start with these like you can go from the lower tasks to the upper tasks amazing idea and then follow observation has been calculated that tennis player wins on average 17 out of 25 games amazing that's it that's only like no Next uh grid and here we have the probability of winning a game is well on average how many he wins by how many games are in total. The probability of losing is the opposite of that. So it's one min just found and binomial distribution you have to have just two outcomes and then they have to be independent of one another. Sometimes you might think that there is an experiment say like the throwing a die you have six outcomes 1 2 3 4 5 six but if you phrase it in a way like even or odd number or five or not five then you can make a discrete probability like an elementary task that's binomial depending on the context like what's how it's asked so probability to lose the next game. So here all the games are independent. So it's binomial. It says right here binomial distribution right the the name. So the binomial distribution properties apply. The probability of losing or winning any game in any order whatever 10th game 20th game first game is 0.3. It's true. That's what just found here.

[01:13:18]The expected wins in a game is expectation value in binomial distribution just n * p.

[01:13:24]In elementary probability the expectation value is a bit more complex than that. You have the sum of the probability oops times but this is for elementary probabilism for here for exponential for binomial distribution is just n * p great it is 6 86 not 4.8.

[01:13:59]And here the expected value is not something that comes up in 50% of the outcome. It's just something you might expect. It doesn't even have to be a whole number to make sense here. Just like a calculation based thingy like you expect around like eight or like seven or nine games to do one. But again, this doesn't have to be exactly number. It doesn't have to make exact sense or doesn't have to happens in 50% of the times. So the definition value and the variance you just uh multiply it all by each other. That's the formula for variance and standard deviation if you're ever asked. So just sigma because this is sigma square for variance would be the square root of variance. In case you ask you that just yeah my spelling is amazing but I guess I know with you. So you multiply the n times the probability of winning and the probability of losing.

[01:14:47]Uh then the probability of winning next three games in a row. So you want game one and game two and game three to be one. So you multiply winning times winning time winning because when you say and in elementary probability rules you usually multiply to be you have to be careful what you multiply if it's dependent or dependent events but just multiplying say and the last one the probability the player wins at most four out of the next six games is more than 0.6 so at most four. So either one either zero game win game wins one two three or four wins.

[01:15:30]This is when using the complimentary event rule makes a lot of sense because you want at most four to be one. This is what you want.

[01:15:44]This is what you don't want.

[01:15:46]So one minus what you don't want will give you what you want because the probabilities of all events in probability distribution have to add up to one. And this is just a bit faster to instead of adding up five numbers, you're just doing one minus two numbers and you find. And the way the binomial distribution formula works is you do n k p to the^ of k one p to the^ n minus k and then out of six choose five games. The probability of winning times five because you're not winning five times. The probability of losing the opposite one and then losing and winning all six would be just 6 out of six would be one. Probability of winning six and 1 minus e to the^ of 0.

[01:16:30]So this becomes one. This also becomes one. You don't have to write it.

[01:16:47]Yeah.

[01:16:51]And please this is not vectors because some people say it's vectors. This is binomial coefficient and it can be calculated on your calculators. There is a button for it. Um one second I'll tell you what it is. In my calculator, it would be nr.

[01:17:13]This is for combinations when the order doesn't matter. For permutations would be P n R and the formula changes slightly. You can look it up for combinatorics in case you're interested.

[01:17:23]But here we're using combinations for binomial.

[01:17:27]And this is permutations where the order matters.

[01:17:36]As you can see, you have to be careful with rounding because it is only slightly more than 0.6 and that makes the same true. So, please don't cut down like don't round them up too like too much because otherwise you might get drunk even if your working out is right because only exams at when you have open questions if they see that your working out is right but your rounding is wrong they will still give you partial points for knowing the solution. On exams multiple choice no working out will be graded. So, it's either true or false and you get it right or wrong or correct and correct.

[01:18:10]I would assume this would be it from my side for today. Do you have any questions you would like to ask me?

[01:18:26]>> No.

[01:18:27]>> Perfect. And I'll answer this question in chat. And another thing, I will publish all the tasks here in the blog of my website and you will find them as the latest post as a PDF file because in YouTube I cannot attach a PDF file to the description.

[01:18:44]Uh you're welcome and this year the time was reduced but the reason behind reducing the time is because you don't have to have the annoying mouse with you to solve stuff. Now you have a pen and paper which arguably makes you solve it faster. So they I don't think they will decrease the number of tasks and usually yes they have one question per math topic. So 13 m questions.

[01:19:10]Yes, you have 13 tasks and I see someone rose their hand.

[01:19:25]>> Okay, I see. So, yes, don't think that they will make it nice like I've never seen will make it nicer like in in the history of it. So yeah, that's why you should expect around 10 tasks, some English tasks, and 30 math tasks as usual with five segments each. And for math, it's one question per topic. Makes sense. And Dia, what's your question?

[01:19:47]Um, so for the multiple choice questions, they won't say if one answer is like only one answer is correct. They will all basically just be or they specify whether the question only has one answer correct or any answer can be correct. They will just say at least one is correct. That's it.

[01:20:05]>> Okay. Thank you.

[01:20:06]>> Welcome.

[01:20:08]They don't give you too many hints unfortunately.

[01:20:13]Then thank you so much. You will see the recording of it soon on YouTube and the tasks we will published in the blog. Uh you can get it doesn't matter what kind of pen it is. You can bring any pen that writes bring a bring a few pens with you like a blue and a black one just in case. Uh if you have a lucky pen at home, feel free to bring it. And yeah, and there is no difference.

[01:20:41]Okay, then I'll give people just one more minute to ask any questions that they might have.

[01:20:49]And if you're wondering for the YouTube channel link, just DM me later, either on Instagram or an email or via the website. It's up to you.

[01:21:00]So you can find me on Insta in case someone does not know. I mean I think most of you have to send the stories on Insta.

[01:21:06]No, no, it's pen. No, don't do this.

[01:21:09]Only pens are allowed or email if you would prefer to connect with me. Email.

[01:21:20]Yeah, tried to undermine the competition.

[01:21:24]Didn't work.

[01:21:26]And boom. Yeah.

[01:21:28]And website in case you want to check out the post later.

[01:21:32]Uh blog.

[01:21:36]Perfect. Those are all the contact details. The video will be ah okay.

[01:21:40]Thank you. Okay. Sorry. I thought you like you were mad at me for saying that pencils. Okay. Good. Thank you. Uh so yeah like here here we have we had around 80 participants and um uh technically will get in. Please study. Please give it your all one and a half months. It's worth a shot for sure because VB so far when I was comparing it to like Kulu even to Bonei to other nurses in Austria and um yeah I I would say it's one of the best combinations of everything price-wise, quality wise, professors wise and location wise and campus wise. Thank you so much for appreciating. Thank you for It should I think it doesn't matter but please bring one of each just in case. Blue or I don't remember. I think it it could be whatever color.

[01:22:25]Uh so yeah, thank you so much. Thank you for directions and I'll probably see you in another open lesson because I'm hosting at least one more in June. Uh open offline and online as well.

[01:22:36]Welcome. Chowo chiao. Thank you for the hearts. So cute. Thank you.