# Day 7 – Soon getting into the hardest part

Ok, so here I am, it’s been an extremely long day, reached home 8pm absolutely shattered. I have 2 taks that take some hours that I will have to do before tomorrow ends and there’s no way I can do them today. I have taken a 30min nap (otherwise it’d be impossibe to function) and although it was tough to wake up, managed and here I am ready for probably about 2 hours max 2:30 of focused study. I know the hardest part comes soon and I am not looking forward for it, so I need to re-wire my thoughts. Bring it on. Bring the hardest part in, once I learn it I will be able to do so much more! Let’s enjoy it, let’s have fun with it.

First Im gonna finish the word problems section, and I will then go to Geometry.

## Finishing word problems

DId some work on rates etc similar like speed nothing new.

### Double matrix method ^ Venn diagrams

This seems a very popular question type so need to be careful.

Ok I did this question right, but got blocked beause I missed the statement “7 students take physics and sociology” :(. Stupid me. And I actually double checked to see that I wasn’t missing anything.

Need to be more careful next time.

Ok I have a huge problem with venn diagram which is a lack of process that causes the probelm to take way longer than it should. So I am gonna practice a process.

Ok, main issue **is that I am writing the equations etc. I should just fill the venn diagram with the numbers directly. Doing that it took me 2 min to find the answer. Will try this approach from here onwards. **

## Sequences

Nice, sequences is an interesting hard topic. Hmm simple sequence I see can be given by a simple equation… then can be used to calculate other values. This should be fine. The only little issue might be me having to come up with the equations myself. That might cause some confusions if I am not sharp on the day.

## Recursive Sequences

Hmm… so far seems one just needs to substitute and need the values of the starting of the sequence to calculate the ones in the future. Let’s see if in the future they give a method to calculate a far term like t80 by using a formula or something.

Ok this exercise totally blocked me…. because I am given a recursive series but no terms to play with.

Ok, so right after pasting that image above and not having watched the answer yet, I realized I missed something very important. Basically I do have the information I need. I know the formula for Xn can be solved if I know Xn-2 and Xn-1. Hence to know n = 4 I need to know 3 and 2. I know 3 already. So just need to know 2. And the thing is, because I already know 3, and I know 1 also, I can use the formula of X3 to find X2, hence find X4 which is the solution.

Hmm… ok got it and will realize much quicker next time.

## Sum of Sequences

Ok I know this kind of stuff comes up so need to learn it well.

Ok so the technique I already knew, but learning the formula might be be nice to speed things up. For the moment I will just use logic. Also then it teaches a formula to calculate how many numbers from 1 to 20 for example (inclusive). This also I already know that is 20 – 1 + 1 = 20. It’s very easy to know if u check 1,2,3 then you do 3-1 = 2 which is wrong, so you know you need to add 1 to the result to get the number of integers in that series.

Alarm sounded 1:45 passed. Put 1:45 more.

Ok so consider this question:

Now, I was doing it almost perfect, understood the whole dynamics of it quickly. My mistake was with the timings. I took L (in the pic they call it P, but I chose L) as being the volume NOW, but in my mind I confused it by thinking it is the volume 6 hours ago… which doesn’t make sense.

If I had just chosen L to be the volume 6 hours ago, and then multiplied by 3/4 to get the one now , and then 2 times again to get the one in 12 hours… then It’d all have been fine.

The concepts are there, I am just making some pretty careless mistakes… that I will have to tackle in the future with diligence.

Ok consider this question:

Here I took a wrong approach by splittin the salt and water components. Hmm It works also for sure but hmm I guess it made me do more errors? Main error was that I did Xsalt/Xother = 80/100 which is wrong . it should be Xsalt/Xother+Xsalt = 80/100. Then one can solve the equation.

It’s probably better to do what the video suggest. Every addition of volume of the solution X brings 0.8 salt and o.2 of other. Hence the new solutino is (50 + 0.8X added)/(250 + xadded). And then solve. **This approach is much much quicker. The key is to realize that adding X volume adds 0.8X salt. Next time will solve using this approach. **

Ok 1 hour passed since last time I put clock. Im done with the section. Hmm… I should go to sleep now but there is still 12 questions related to this section that I haven’t done. Should I do them or not… If I do them it’ll certainly take me 1 hour or so I guess… hmm… ok look I’ll take them. Then tomorrow I can focus on the other sections. Btw I see the remaining sections have less videos than some of the ones I did before so hopefully by Tuesday I should have done all… let’s see, I will try.

Consider this question:

I have a big issue with this question. When evaluating statement 1 I got this wquation 11p+5b = 100. Now… although with 1 equation and 2 variables we cant know the answer… if p and b are integers… then we might. I already knew this… and when looking at the equation I thought… damn… looks non sufficient but I bet you it is… but then I decided to ignore it and just put NS. XD! As I had thought, statement 1 IS sufficient. My big problem is that one needs to do the table and check every case… and that’s very time consuming. I want to know a technique that can tell me if an equation likea bove has just 1 solution if variables are integers… not sure if it exist.

Consider this question:

Now this took me 3min 29 sec unnecessarily. The main issue was that I was not clear how many terms are there between 5 and 200 when split in 5’s. It turns out it is (200-5)/5 and then add 1. This I should have known much faster. Then it’s easy.

Another approach which is also smart is the one given in the video. It relies on realizing that 5 + 10 + 15 … is equal to 5(1+2+3…). I will totally keep this in mind because it might be helpful for some other kind of questions. By doing that then one just needs to solve sum from 1 to 40 which is easy as it is 41*20 and then multiply by 5 and you have your answer.

Ok consider this question:

Well it caught me totally of guard, made me waste a ton of time . **For problems with 2 variables like this one… I need to try the matrix approach instead of venn… I need to practice this. **

Ok, so I am done with this section