GMAT Ninja Quant Ep 7: Percentages

[@fullc0de]

You're a gifted teacher!

[@thesurferontheside]

Trying so much to 1)read twice, 2)be flexible and see the different ways of solving and chose the most efficient,3)check my work as I go,4)reread the question actively, BUT I TAKE SO MUCH TIME, like, I just finsihed doing the second step when Harry interrupts us to solve the question. I would probably solve each question in more than 4mn and many questions in my practice are longer than 6mn. I can't beleive how slow I am

[@imthebest6974]

This is amazing Harry. Your explanations are top notch. Thank you so much !

[@harryduthie]

Thank you for the kind words! I'm so pleased you found the video helpful

[@KeyserTheRedBeard]

impressive video GMAT Ninja Tutoring. I broke that thumbs up on your video. Maintain up the very good work.

[@meghasrinivas6660]

This helped a lot!! Thank you so much Harry!

[@GG-Faithandlove]

One question How did you know the last question required a compound interest?

[@radyahhassan]

Thank you so much, Harry! I just have a quick question. For question 8, instead of writing (1-p/100), I rewrote it as (1-p) for ease of calculation since none of the answer choices had p in them, and I actually have the habit of doing lengthier calculations when I do percent calculations. For instance, I isolated p and used its value in b(1-p) as its my default way of thinking. So, with the 100 in there, it would've made my calculations tedious (where I'll multiply and then take 100 common, etc.) So, in questions like these, is it okay to just write the variable down without 100 in the denominator? Also, can you provide suggestions on how to do percent questions more efficiently? Using algebraic method usually takes me over 5 mins to solve, so I resorted to plugging in values to shorten my time. Since you mentioned it's not useful, how else can I improve my efficiency?

[@GMATNinjaTutoring]

Thank you for your comment -- this is a great question! The bad news is that aside from the extra time taken in writing '100' down, I don't think you saved any time by writing (1 - p) instead of (1 - p/100). If you follow the solution for question 8, I didn't do anything with the 100 in that fraction so I don't think leaving it out made the calculations any easier. In general, I wouldn't recommend just leaving out the 100 in any question as you never know when you'll need to do a calculation involving the full (1 - p/100) expression. Even if you're looking at a question and deciding whether you could leave out the 100 to save time, you're still adding an extra decision to each solution. My recommendation would just be to include the 100 in the expression and work through the problem as efficiently and accurately as possible. The key to answering GMAT questions more efficiently almost always comes down to finding the right solution path. There are notable exceptions to this rule, but you should be able to answer most GMAT questions in 4-6 lines of algebra. That amount of algebra shouldn't take over five minutes to work through, so the first place I'd look to reduce the amount of time you're taking in these questions is at the start of a question when you're generating your first line of algebra from the text of the question and deciding which way to solve the problem. I hope that helps!

[@radyahhassan]

@@GMATNinjaTutoring thank you so much for the feedback! I guess I need to find less tedious ways of doing algebra, or, even calculating so I can reduce the time.

[@anvayjoshi]

Hi Harry, In Q6 at 45:07, how did you equate by increasing the value by a third with 4/3? We have to increase the value by 33 1/3 right? 33% equates to 1/3 with additional 1/3. Will you please clarify? Thanks.

[@GMATNinjaTutoring]

If we want to know 33 1/3% OF something, we'd find a 1/3 of it beacuse 33 1/3% is equivalent to 1/3. This works in the same way as if we wanted to find 50% OF something, we'd find 1/2 of it because 50% is equivalent to 1/2. The same thing would work for 25% being equivalent to 1/4 and 20% being equivalent to 1/5, and so on. If I wanted to INCREASE something by 33 1/3% then we need 1/3 MORE than the original amount. Rather than thinking of the original amount as 100%, we can use fractions and think of it as 1. Then we'd increase that 1 by 1/3 to get 4/3 -- this will work in the same way as if we started with 100% and increased it by 33 1/3% to get 133 1/3%. I hope that helps!

[@anvayjoshi]

@@GMATNinjaTutoring yes it does now. Thank you.

[@varun110291]

Hello in this question at 25:10, I got till 9C=10B part Then instead of writing C=10/9B What I did was write B=9/10C Then i subtracted this from C as we are asked what percentage value is greater in C compared to B. So i got C - 9/10C which is 1/10C. I marked 10% Can you help me what wrong I did. I understand your way but I fear in the exam what If i make this mistake again. What is the thought process behind this concept.

[@harryduthie]

Hi Varun, The problem comes from doing the subtraction. The question asks us to find a relation between the price at store B and the price at store C. We can do this by saying C = 10/9B or B =9/10C. The first option is the one that tells us the price at C is 11 1/9% higher than at store B. However, when you did C - 9/10C, what you were really doing was C - B = 1/10C. Algebraically, you haven't done anything wrong, but 1/10C represents the DIFFERENCE between the prices at the two stores. It doesn't tell us what the percentage difference is. To find the percentage difference we need the relationship between the prices at the stores shown in the video. I hope that helps!

[@paulcieri78]

Hi Harry, for Question 4, couldn’t it be confusing that we don’t know how many hours the firm worked each year? The question doesn’t directly state that the hours were unchanged. Now I know that since it was a problem solving question and not data sufficiency the answer could be found, but how can we be certain that the revenues aren’t an even bigger percentage different if we don’t know that the hours are the same?

[@harryduthie]

Hi Paul, Given another chance to write these questions, I'd probably be a bit more strict with the wording of Q4 to remove any possibility there's some ambiguity in the wording. We didn't have the opportunity to do as much testing as the official question writers at GMAC have, so you shouldn't have any issues like this in the real exam. In this problem, we're told that the firm sold 30% fewer hours of consulting time this year than in the previous year. The implication is that the firm gets paid for the hours of consulting time worked and not for any other time. This is the potential ambiguity that I'd remove if I had another chance to write this question. If you treat the number of consulting hours mentioned in the question as the time the company spent working, everything should work out. I hope that helps!

[@agasthyathalakala948]

Hi Harry, thanks for these video series been a massive help. I'm slightly confused with the last question, i assumed they wanted us to annualize the last quarter growth rate? by assuming 300*4 and using 9600 aren't we using a simple interest i.e 300k growth every quarter? My question is basically this if the compounded growth in the last quarter is 300k, shouldn't each quarter prior be lower? isn't that how compounding works. Do let me know what you think

[@GMATNinjaTutoring]

Finding an ANNUAL growth rate is equivalent to treating the year as a single compounding period. This means we assume the growth will be steady in each quarter, but you can think of the year as four simple interest periods if you like. So if the user base grew by 300,000 users in the first quarter, we assume it grew by the same amount in each of the four quarters to get an ANNUAL growth of 1,200,000 users. I hope that helps!

[@krishdudani2205]

This clears it up thanks@@GMATNinjaTutoring

[@ashishsinha9035]

The penultimate question was extremely tough (for me)

[@connorf8638]

almost all these were tough

[@kopaltyagi1589]

Hi Harry, Q8 - I am a little confused with the wordings used in the question here. Because the car loses a certain part of its value each year should it not start losing its value right from the first year - provided the car was worth a dollar on 01st Jan 2019. Consequently - Assuming that the car is losing its value each year, then shouldn't the value on 31st December 2019 be A(1-p%) and then Dec 2020 till be A(1-p%) ^2 and so on?

[@harryduthie]

Hi! I'm sorry if I've missed something in your question, but the car does start losing its value immediately. If we start on January 1st, 2019, and move forward exactly one year, we'll land on January 1st, 2020. So if the car was worth a dollars on January 1st, 2019, it will be worth a(1-p%) on January 1st, 2020 and a(1-p%)^2 on January 1st 2021. I hope that helps!

[@kopaltyagi1589]

@@harryduthie This helps - thank you very much. I was making a mistake in reading the dates incorrectly. I was taking the value of the car at the end of year 23 i.e., 31st Dec,23 which is not what the question is asking.,

[@glenchezzie6593]

Hi Harry, worked Q3 all the way but could not figure out the where the 11 came from. Please help. Thanks

[@DanialBhasin]

Hi Harry, The last part of Q9 feels a little convoluted. Couldn't we rather use the info we find (Q1=300) as 9,600*x/100*3/12=300 giving us, 24x=300 which is x=300/24 Leaving us with x=12.5 or 12 1/2. Just thought this was a easier method Essentially, its the same, you just did the 300*4 separately. Just that the method of getting there feels a little confusing, to me at least.

[@harryduthie]

Hi Danial, You absolutely could use that method, and thank you for adding it to the comments! I split the process up and explained each bit separately in the video as I didn't know how much explanation any one viewer would need. If you can see what I was doing and create a shorter, more efficient version, that's great!

[@kuhunyawilliam9877]

very good. thanks

[@GMATNinjaTutoring]

Thank you!

[@mandarmitra007]

Loved the last one!

[@GMATNinjaTutoring]

I'm glad that you enjoyed the pain. :) Thank you so much, and have fun studying!

[@gianniniolu2218]

Do we know what the approximate level of question 9? It seems like even knowing the exact method with which to solve this problem would lead to more than 2 min.

[@CarmenHorse]

agree

[@KLEAKULE]

i just started studying for the gmat and i'm currently using those videos since harry is so good. to understand a bit my situation.. are those exercises considered easy or hard compared to the possibile question on the gmat?

[@GMATNinjaTutoring]

Hi there, it's Harry here -- thank you for your kind words! To answer your question on the difficulty of these problems: I'm guessing a little here as we can't do as much testing on these questions as we'd like, but I'd say questions 1-3 are about nailing the basics of percentages in a GMAT-style question and are probably up to the level of a mid-40s quant question. I think questions 4-5 are the sort of questions you'd want to get right to get a score in the mid to high 40s, questions 6-7 are in the Q47-49 region, and the final two questions are difficult and are designed to stretch most people, even those aiming for a Q49-50. I hope that helps a bit!

[@soulreaperichig0]

I just don't get how you turned (9/4 )* x to x + 5/4x in 17:40

[@GMATNinjaTutoring]

You can think of (9/4)x as [(4+5)/4]x = (4/4)x + (5/4)x. Since (4/4)x = x, we can say (4/4)x + (5/4)x = x + (5/4)x. I hope that helps!

[@nabidishtiaque9303]

Sameeee

[@karimkaan8700]

Great insights and explanation as always

[@GMATNinjaTutoring]

Thank you so much, and have fun studying!

[@tomso11]

I'm a little bit confused on question 5. The question read: "made a profit of 150% on the cost", doesn't that mean that P = C + C * 3/2 ? So if C = 100, and P = 250 then the (P-C)/C = 150 % If we do P = C* 3/2 then : C = 100, P = 150 and (P-C)/C = 50% Thanks in advance

[@harryduthie]

Hi tomso, Thank you for pointing this out! Looking back at this video 9 months after it was filmed, I think you're probably right. If I was given the chance to do this question again, I'd probably rewrite it to remove any doubts. I'd now say something like "...made a profit of 150% *of* the wholesale cost." I hope that helps!

[@tomso11]

@@harryduthie it does, I just wanted to make sure I was getting it right. Appreciate the reply. Your videos are great!

[@bluegeraniol2626]

Hello, I have a question for Q7: the text says that the 5% interest rate of Vlad is compounded semi-annually. How do we know that the 5% is the yearly rate and not the 6months rate? couldn't it be the semi-annual rate?

[@GMATNinjaTutoring]

You're right, we could possibly have worded this question slightly more carefully to make that more clear. However, the wording of the question mirrors the that of some official questions, such as Q220 from the 2022 OG. Your best bet in a situation like this is to assume the interest rate is an annual rate, unless the question tells you otherwise. I hope that helps!

[@kartikeyyy123417]

Hi Harry, I interpreted the same and got 210 as the answer. Could you cite 1-2 more official previous year GMAT questions that state the information wrt compound interest rate similar to this question? @@GMATNinjaTutoring

[@JinghanYun]

Hi Harry, how did you translate 112.5/100C to 9/8C? I didn't get that from the video. Thank you!

[@GMATNinjaTutoring]

If we convert between percentages and fractions, 12.5% = 1/8. Since we know 100% = 8/8, then 112.5% = 100% + 12.5% = 8/8 + 1/8 = 9/8. I hope that helps!

[@nikitasingh1111]

For the last question, can we simply try solving what percent of 9.6m gives 300k users? And then multiply that rate by 4? I got the same answer doing so

[@harryduthie]

Hi Nikita, You can certainly do that. It's actually the same process, you're just multiplying by 4 after finding the percentage, whereas I multiplied by 4 before finding the percentage. You get the same answer in both cases. I hope that helps!

[@nikkilautner7085]

Got it thank you so much 🌸

[@sarveshyadav6902]

Hi in question 6 I just consider 100 as my base amount and got 100 in year 2014 please can you check again the answer. 44:09

[@sarveshyadav6902]

Because when values goes down by percentage need to minus the value from the main value and when the value increases in percentage need to add the amount hope that will help

[@harryduthie]

Hi @@sarveshyadav6902, The answer in the video is correct. If you choose to make 100 your base value, you'd have 120 after one year, 90 after two years, 105 after three years, 93 1/3 after four years, and 124 4/9 after five years. The closest to 100 is the 105 you'd have after three years, so the correct answer to this question is (C). I hope that helps!

[@pierof6837]

Hi, do you have any suggestions to calculate, without memorizing them, the conversion between % and fractions? e.g., 12,5% --> 1/8

[@GMATNinjaTutoring]

While you could do this, I'm not sure it's a more efficient path or less effort than just memorizing the conversions. The word "percent" means "one part in every hundred", so we can always create a fraction with a percentage by placing it over 100. For example, 12.5% is the same as 12.5/100. We could convert this to 25/200 so the numerator and denominator are both whole numbers, before cancelling this down to 5/40 or 1/8. This method works relatively well for nice numbers, but is much more difficult for something like 44 4/9 %. We can say this is the same as (44 4/9)/100, but writing it like this doesn't make things much nicer. It would probably be much quicker to memorize the conversion of 11 1/9 % = 1/9, so four times this gives 44 4/9% = 4/9. I hope that helps!

[@pierof6837]

@@GMATNinjaTutoring you re the top!

[@mohdshijas21]

Hi Harry , great video and explanation but I have a doubt regarding Q8. We got (1-p/100) ^ 3 = b/a. Isn't that the answer ?

[@GMATNinjaTutoring]

If you take another look at the answer choices, you'll see that none of them have a 'p' in their algebraic expression. This means that we need to find some way of substituting the 'p' out of our expression to get an answer. We know that the value of the car on Jan 1 2023 will be b(1 - p/100), but we need to do some more work to eliminate the 'p'. We can use the equation we found for the value of the car on Jan 1 2022, b = a* (1 - p/100)^3. We can rearrange this to find (1-p/100) = (b/a)^1/3 and substitute this into b(1 - p/100) to find our final answer of (b^4/3) / (a^1/3). I hope that helps!

[@rikhrajghosh9897]

In Q.4 pls explain me, why was 49/50 multiplied by 2 (both in numerator & denominator)

[@GMATNinjaTutoring]

By this stage of the solution, we know that this year's revenue is (49/50) times last year's revenue. The question asks us: "the firm's revenue [this year is] what percentage of its revenue the previous year?" If we multiply the numerator and denominator of 49/50 by 2, we get 98/100. Since the denominator of this fraction is 100, the percentage we're looking for as the answer to this question is the numerator of the fraction, or 98. I hope that helps!

[@nabidishtiaque9303]

where is the Algebra translation video? someone plz give me the link🙏

[@GMATNinjaTutoring]

The algebra translation video is now called the word problems video. You can find it here: kzbin.info/www/bejne/qKTOeJqqgLyYiqMsi=Rp4EbL5cgY_2fIjl I hope that helps!

[@preeti280]

Hi sir, I have a question for example in a question when do we decide to assume 100 or P when exact value not given. This really confuses me a lot.

[@harryduthie]

Hi! I can't think of a question when I'd start by assuming a value of 100 for an unknown value. There might be one or two out there where doing that turns out to be an easy way of completing the question, but my first thought would always be to use a variable for the unknown value. There are just too many situations where a question can get really nasty if you assume an unknown value is 100 for me to recommend you do that in any given question. I hope that helps!

[@mohdshijas21]

Another confusion if you could please clarify - In q6 , when there was a % increase of 16 2/3 , you took it as 7/6. But on q9 , you just added 1/6. Why is that ?

[@GMATNinjaTutoring]

In Q6, I wanted to find the multiplier that would increase the original value by 1/6. If we consider the original value as 100% or 6/6 then increasing by 16 2/3% or 1/6 means that I want to find 116 2/3% or 7/6 OF the original value. This means that I would multiply the original value by 7/6. In Q9, I could have done the same thing. If I'd multiplied 9,600 by 7/6, we would have increased the original value by 1/6. However, I wanted to know the actual amount of people that were added to the user base when the number of users increased by 1/6 for a different part of the solution. Because I wanted to know the value of that 1/6, I found that value separately first before adding it on later. I hope that helps!

[@mohdshijas21]

@@GMATNinjaTutoring Yes thanks a lot

[@vanshikasaluja]

In the last question- Q9, I am unable to understand why we did x% of 9600 =…. I dont understand why how this step occurred and how this would come to my mind. Also 9600 is the value for past year why are we using it now. I am very confused, found the last question very hard. Awaiting your response

[@GMATNinjaTutoring]

I wouldn't worry if you found the last question very hard. Even if you're aiming for a quant score in the high 80s, you can probably afford to miss a question like this. This problem was meant to challenge all but the very strongest mathematicians. In this question, we want to know what annual rate of increase in users would the company have needed to ensure they reached their goal. The x% of 9600 is the equation we need to solve to answer the question. The x represents the percentage increase in the 9,600(,000) users the company had at the start of the period. I hope that helps!

[@sparshsinghal7307]

Heads up for those doing question 3, don't make the same mistake I did NOTE: If A is 25% greater than B, then A=1.25B, but that does not mean B is 25% less than A. If you said B was 25% less than A, in that instance, B=0.75A, and if you said A is 25% greater than B, then B would be 0.8A=B, and 0.75A is NOT equal to 0.8A

[@zinuchifim357]

No idea what happened with question 2…

[@sagarmehta2335]

yes same please explain

[@redhood2170]

Let no of people who used the internet in 2003 be " x ". Now as per the question no of people who used the internet in the year 2000 is 44.444... percent of " x ". Therefore number of people who used internet in the year 2000 can be written as?..= 44.44x Now to find percentage change: Original value-new value/ original value Question is asking for a percentage change from the year 2000 to 2003. So think of it as a reference point to measure the percentage from.. in this case the reference point is the year 2000. So the original value is 44.44x New value is : x We only need to find difference between original and new value which is the magnitude hence you don't care about the negative sign. 44.44x - x = - 55.5555x Hence we only need the magnitude to calculate percentage change we should take it as : 55.5555x Now according to formula= 55.555x/44.444x Which can be written in fraction as 5/9//4/9 By cancelling 9 we get 5/4 which translates to 125 percent..

[@CarmenHorse]

can you give an estimate on the level of difficulty? are the last 2 questions ~700 level questions or are we still at 600 here?

[@harryduthie]

Hi Joann, I'm guessing a little here as we can't do as much testing on these questions as we'd like, but I'd say the final two questions are above a 700 level in terms of difficulty. I hope that helps!

[@Sakshi_Pundir]

can someone please explain me any other way of doing the last question?

[@BSA77]

Question 9 really confused me. First, how did you come to the conclusion that we need to use compound interest? after finding the 300 I though we only need to do 300/9600 x 100 to get the interest we need in the first quarter. so ≈ 3% is needed. Second, we easily calculated the first quarter, which is 300k. We can easily find their end of year goal of 11.2 m. the problem is if we plugin the answer 12.5% back into the Compound interest formula, we will get 9.6(1+0.125/4)^4 = 10.857m, so the answer falls short of the 11.2m target. Am I missing something?

[@harryduthie]

Hi BSA, The clue as to why this is a compound interest question comes from the wording of the final sentence. This says: "Approximately, what annual rate of increase would the company have needed in the first quarter to ensure they reached their goal?" The key here is that we're looking for an *annual* rate of increase that's only going to be applied in the *first quarter* . The implication from the question is that the percentage 'interest rate' applied in each quarter is going to change and would have to be applied to the new number of users at the end of each quarter, i.e. 9.9 million at the end of quarter 1, 10.3 million at the end of quarter 2, etc. So this is a 'compound interest' problem but since the 'interest rate' changes in each compounding period, we can't just plug the numbers into the compound interest formula. As an alternative, there is a way of solving the problem without worrying about compound interest: if we know that the company needs to grow by 300,000 users in the *first quarter* , we can convert this to an *annual* rate of increase by multiplying this by 4 to give us 1.2 million. *If* the company had an *annual* rate of increase of 1.2 million users from its starting point of 9.6 million, this would mean an *annual* interest rate of 12.5%. The reason the compound interest rate formula isn't working for you is that the interest rate changes each compounding period. The 12.5% is only applied for the first quarter, i.e. the first compounding period. If you do 9.6(1+0.125/4)^1 you'll get 9.9, which means the figure has increased by 0.3 or the 300,000 user increase we're looking for in the question. I hope that helps!

[@AndreMusic2000]

@@harryduthie Thanks for the answer Harry. I understood the approach in the video but this reply helps clear up some more things.

[@tonyassamoi9688]

Harryyyyyyyyyyyy

[@bhushanshaligram1995]

In the 6th ques, when you increase the value by 6 in the 3rd year, why do you not just write 1/6 times 9/10x? Why does it has to be 7/6 times 9/10x? It is hard for me to comprehend.

[@GMATNinjaTutoring]

If we multiply something by 1/6, we don't increase it by 1/6. Instead, we would find 1/6 of it's value. If we increase something by 1/6, we have (1 + 1/6) = 7/6 of what we had originally. This means we can find the value after we increase somethiung by 1/6 by multiplying the original value by 7/6. I hope that helps!

[@s.t.aravindswamy6509]

In the compound interest simple interest question can we say vlad will definitely earn more than 0 beacuse of compounded twice so Option a is wrong Rest of the options c,d,e are way too big so it should be 2.5 which is option b specifically for this question’s constraints? Is this way risky or smart?

[@harryduthie]

Hello! This feels quite risky to me. While (D) and (E) might be too big, I don't think you can be certain that (C) is DEFINITELY way too big without doing the calculation. There isn't a big difference between $2.50 and $5 and I'd feel very uncomfortable about choosing (B) over (C) in this question without working through the problem. I advise my students to avoid shortcuts like these. One of the keys to getting an awesome GMAT quant score is avoiding making unnecessary errors, and taking a shortcut like this makes it much more likely that you'll miss something small and make a mistake in a question you *know* you can get right. In my opinion, the opportunity to save a few seconds isn't worth the gamble of missing a question you should be able to answer correctly. I hope that helps!

[@OmarAbolnasr]

In Q1 can we say the percentage is the ratio X 100? as (16/800,000).100 = 2/1000

[@GMATNinjaTutoring]

Yes, you can say this, and thank you for sharing an alternative method to solving this problem. You've effectively jumped into the solution at somewhere between the second and fourth step in the solution shown in the video, and you'll get the right answer at the end of the process. Thank you for your comment!

[@KanupriyaSharma-en4ep]

can someone explain in Q6 why are % ages not taken wrt to base year ( 2010 ) ?

[@GMATNinjaTutoring]

This is all in how the question is written. Let's assume the value of the asset was $100 at the start of this question as it will make it easier to see what's going on. The question then tells us the value of the asset increased by 20% in year 1. This means that our hypothetical asset was worth $120 at the end of year 1. The question then tells us the asset decreased in value by 25% in the second year. Notice that it said *IN* the second year and not "compared to the asset's original value". This means we have to take the value of the asset at the start of year 2 ($120) and decrease this value by 25%, giving $90. In the question, all the percentage changes were given in the year they took place, so we need to consider that change with reference to the value of the asset at the start of that year, not at the start of the whole scenario. In the solution, we found the change compared to the base year. That was the final column in the table on the whiteboard. That column showed that the asset had changed by 10% at the end of year 2 with respect to the original value. It is these overall changes in the final column of the table that allowed us to see which answer choice was correct. I hope that helps!

[@ianlekeboam5346]

any help with how 5/4 was gotten in question 2

[@harryduthie]

Hi Ian, Please tell me if I'm wrong, but I'm going to assume you're ok with the explanation up to the point where we got 9x/4. We wanted to find what the percentage change in the number of internet users was between 2000 and 2003. By finding 9x/4, we knew that we needed to multiply the number of internet users in 2000 by 9/4 to find the number of internet users in 2003. So, we could say the number of internet users in 2003 was 9/4 of the number of internet users in 2000. In order to find the percentage change, we needed to find out how many MORE users there were in 2003 than in 2000. The way I did this in the video was to split 9x/4 up into the number of users in 2000, x, and the increase above that value. We could split that process up into more steps and say that 9x/4 = (4x + 5x)/4 = 4x/4 + 5x/4 = x + 5x/4. I hope that helps!

[@daniellee2023]

@@harryduthie would there be a way of solving this problem if you didn't know that 44 4/9 = 4/9? Tried to do % change and ended up with the 55 5/9 answer. I understand conceptually/logically that this is the wrong answer, but I'm not quite sure how to approach it otherwise unless you know the trick that you showed of knowing what 1/9 is as a %. Thank you! edit: What I did was take 44 4/9 divided by 100 and turn that into the 4/9 ratio then used the percentage change formula which ended solving for 5/4 and then *100 to give me 125% at the end. I guess this could be another way of solving if you weren't as comfortable / hadn't memorized the % to fractions numbers you mentioned, but correct me if I'm wrong here :)

[@GMATNinjaTutoring]

Hi @@daniellee2023 The method you've put in your edit looks good to me. It's probably not as quick as the method shown in the video, but if it gets you there within a reasonable amount of time then that doesn't matter. I recommend you do memorize those percentage to fractions conversions as they're so helfpul when you don't have a calculator in the GMAT exam. I hope that helps!

[@DerahAchieves]

I dont understand how we got that year3 is closest to original. 1/20 isnt that the smallest no. Please help me understand!!!

[@GMATNinjaTutoring]

In this question, we're asked to find the year-end value that is closest to the original value. The difference between the original value and the value on December 31st 2013 is (1/20)*x, which is the smallest difference of the five options. Since the difference between the original value and the value at the end of any other year is greater than the difference between the original value and the value on December 31st 2013, (C) is the answer to this question. I hope that helps!

[@kanikamalhotra818]

I am still confused with Q9, the last part. I don't really understand the language and what we just did. 😕

[@GMATNinjaTutoring]

Hi there, if you could say a little more about what part of the question you don't understand, I'll do my best to help! Remember, this question is meant to be really challenging even to those people aiming for a Q49 or Q50, so I'd expect a lot of people to be struggling with this one.

[@rikhrajghosh9897]

In Q.5 pls explain me, (54/150)×100 part of it

[@GMATNinjaTutoring]

We're asked, "what was the store's profit as a percentage of the recommended retail price?" The store's profit was $54 and the recommended retail price was $150. So to find the store's profit as a percentage of it's recommended retail price, we can set up the equation (54/150)*100. I hope that helps!

[@emailsfw]

I have no idea how you went from 9/4X to x + 5/4x

[@emailsfw]

Ok 2 hours later and now I got it ksdfjs thank you for this amazing video!

[@02Shassan]

I still don't get it

[@shirsendumaiti5682]

@@02Shassan solve x+5/4x and you will know

[@quocanhnguyen4108]

The last one is so confusing to me

[@khushbu0713]

Last two questions made me doubt my self confidence

[@GMATNinjaTutoring]

Please don't lose confidence over two silly quant questions! In most of our videos, the questions get pretty nasty towards the end. Depending on your score goals, those last few questions might be completely irrelevant to you -- and even if you have really ambitious goals for your quant score, there's no shame in struggling with some of these. After all, ifyou aren't struggling, you probably aren't learning much. :) I hope that helps a bit, and have fun studying!

[@ahonafshariarnihal7277]

He looks like messi

[@delfin3701]

Hey I believe you made a mistake in the explanation of Q7, if your earn 5% annually, yes the first year your make 200, but next year, you will earn 4200*0.05 =/ 200 and so On. It doesn't change the answer but the explanation is confusing.

[@harryduthie]

Hi Delfin, I'm guessing you're referring to the explanation of Pavel's investment, but please tell me if I've got that wrong. Pavel invested his money in an account that provides 5% *simple* annual interest. The way simple interest works is we figure out what amount that interest rate would provide in year one, then add that amount to the total each year. For example, if we invested $4,000 at 5% *simple* annual interest, the first thing we'd need to do is find 5% of 4,000 which is 200. This account will then earn $200 for each year the money is invested. So Pavel will have $4,200 after one year, $4,400 after two years, $4,600 after three years, and so on. The situation would be different if Pavel had invested his money in an account that paid 5% interest *compounded annually* , but that's not what the question asks us to do. I hope that helps!

[@delfin3701]

@@harryduthie Thanks

[@JinghanYun]

Q6: I couldn't rationalize: when it was decreased by 33 1/9 in year four, why could you translate it to 8/9 of year 3 value? I am confused where did that 33 go? Same thing applies to year 5 🥲 Thank you!

[@GMATNinjaTutoring]

In the fourth year, the value of the asset decreased by 11 1/9%. If we convert 11 1/9% to a fraction, we get 1/9. This means if we decrease something by 1/9, we can multiply it by 8/9. For year 5, increasing something by 33 1/3% is the same as increasing it by 1/3. This means we can multiply the value of the asset by 4/3 to increase it by 1/3. I hope that helps!