GMAT Ninja Quant Ep 14: Statistics

[@shashwatdev3645]

people don't appreciate you enough for adding great humor in the video, it makes the learning process fun, thanks charles!

[@GMATNinjaTutoring]

Aw, thank you so much! I'm glad that somebody out there thinks I'm funny, and not just funny-looking. Have fun studying, and thank you again for the kind words!

[@olgak4059]

In addition to being a life-saver in GMAT prep, as a foreign student I also find the videos incredibly informative in terms of casual English language - I'm literally writing down all the idioms you're using, Charles 😄 thank you for that!

[@GMATNinjaTutoring]

Thank you so much for the kind words, Olga! I'm honored that you're getting something useful from my funny American speech patterns. :) Have fun studying, and thank you again!

[@xunderoathx73]

Man that last question helped with about 5 concepts at once. Thank you!!

[@GMATNinjaTutoring]

Awesome, that's exactly what I was hoping for. I'm glad that it helped a bit, and have fun studying! - Charles

[@lucasettanni3301]

Incredible content, as usual - thanks Charles and GMAT Ninja team for creating this and sharing it for free with everyone!!!

[@TheAmigoBoyz]

I have been struggling with the weighted averages for a while now, and i will have to say -this intuitive method of calculating the distance from the mean is TRULY a life saver! Thank you GMAT Ninja for all these free resources

[@GMATNinjaTutoring]

Thank you so much! I'm glad that this helped a bit. And thank you for all of your positive comments on our channel -- we read all of them, and it makes us happy to see all of the participation.

[@andreaaversano220]

I'm so stressed out due to the Gmat's preparation, but I laughed so hard when I 've read about the big nosed tutor!! Thanks for that!

[@GMATNinjaTutoring]

Haha, I'm glad that my nose could be useful for something. Have fun studying!

[@kshitijjain2979]

the GOAT. Thank you so much Charles as always!

[@GMATNinjaTutoring]

Thank you once again for making me blush! I'm glad that we could help a bit.

[@sid99varma]

I love the weighted average approach in question 5! I solved it using algebraically, just putting my solution here in case someone's curious: M: number of male employees and F: number of female employees Total number of employees: M+F. We know that: 70% of the male employees received a negative performance review. 38% of the female employees received a negative performance review. We're asked to find M/total or M/M+F. Statement 1: 42% of Company X employees received a negative performance review. This means that if we take the total number of employees, 42% of them received a negative review. The equation that represents this statement is: 0.7M+0.38F=0.42(M+F) 0.7M+0.38F=0.42M+0.42F 0.7M−0.42M=0.42F−0.38F 0.28M=0.04F 7M=F Thus for every male employee, there are 7 female employees. This means that male employees make up 1/8 of the workforce. Statement 2: Company X has a total of 440 employees. This provides the value of T, the total number of employees, but without information about how many received a negative performance review, we cannot use this to determine the ratio of M/T. Statement 2's explanation is just the same as that in the video, but you can also deduce this algebraically.

[@rebeccahart9341]

Thank you so much for this actually. My stupid head was doing 70m + 38F = 42T, T as in total. Obviously the total is M + F, so thanks for writing this comment haha.

[@anishakapoor4689]

What an amazing class Charles!! As Ive mentioned earlier, I can’t help but watch the videos ; I am more of a go take the longer route on every quant problem even though it’s irks the crap out of my engineer husband. For me, it’s always been that I need to know the path , the story of a question ; I know so dumb!! However your videos make problem solving fast , fun and easy to understand! Keep doing what you’re doing, students like me will always be grateful for these lessons.

[@GMATNinjaTutoring]

You're awesome, thank you so much for the kind words yet again, Anisha! I'm honored that you're enjoying these so much. Have fun studying, and keep us posted on your progress!

[@lucastromann5135]

I think as a general strategy to calculate the Standard Deviation, you can do the following: 1. Calculate the mean of your Dataset 2. Sum up the absolute difference of each of your values to the mean 3. Divide the Sum from Step 2 by the number of values you have

[@deansakata8619]

the GMAT Ninja Team never misses! 💯

[@yonaprochnik]

This is a great video, especially the last question. I found the weighted average method you use for this to also be a faster way to answer many of the "mixture" type problems I was solving algebraicly before. Thanks!

[@TheAmigoBoyz]

same! I did not know this shortcut

[@ashishsinha9035]

Thanks Mr. Charles. You are a great tutor

[@GMATNinjaTutoring]

Thank you so much, Ashish! I'm blushing. :)

[@joyfulcancer003]

Merc and Elon. Average is +6. So she has to run at least +6 in the last race but also compensate for the difference with +6 ( 8 and 13) in the 1st and 2nd race. Total of 21+ 6 = +27

[@corrayatom]

Hi Charles, hope you're doing great. Wasn’t there total 19 episodes in the Quant playlist? Ep 1 was Coordinate Geometry Ep 2 was Plane Geometry Ep 3 was Intermediate Geometry Ep 4 was Arithmetic which is now Ep 1 So, it makes total 16 now. This is because of the Focus Edition right? Do you have a detailed video on this new edition? What changes and how it will impact the admissions for overseas students in America etc.

[@GMATNinjaTutoring]

Yes, you're exactly right: we removed some videos from the playlist to account for the demise of geometry. For the most part, the rest of the GMAT quant content is basically unchanged, so these videos will still help, hopefully. We filmed several videos describing the differences between the "old" GMAT and the GMAT Focus Edition, but those were really only relevant during the few months when both versions of the test were available. If you're curious about the changes, this article should cover everything you need to know: www.gmatninja.com/gmat/articles/basics/gmat-focus-edition-changes. At this stage, the changes won't really affect your life very much, since there's only one version of the GMAT available now. Nothing has fundamentally changed in terms of your overall odds of admission -- you'll just study a little bit differently than you might have if you'd taken the GMAT in early 2023. I hope that helps a bit, and have fun studying!

[@joyfulcancer003]

For the 150 average and 135 median question. The middle number is 135. So the left two numbers at most can be 135. We know the average is 150. The rightmost two numbers must balance for the ( 150-135) * 3= 45 So that the average remains 150. If we divide equally between the two we get 22.5. 150+ 22.5 = 172.5.

[@sazimordecai6124]

I like your intuitive approach

[@GMATNinjaTutoring]

Thank you so much, Sazi. Have fun studying!

[@EmilAliev-rf7ov]

I really love the style of the presentation !

[@GMATNinjaTutoring]

Thank you so much! ❤️

[@kshitijjain2979]

➡ You’re an insomniac & stats help you sleep - this had me 😂😂😂

[@GMATNinjaTutoring]

Haha, thank you, Kshitij!

[@navneetarora6369]

Hey Charles, great video. Had a slight tweak in logic on the second question, would be great if you could confirm it for me- so, H1: < or = to Median (135) H2: < or = to Median (135) H3: = to Median (135) H4: > than Avg (150) [ to cover for shortfall in first 3 houses and drive avg price to 150] H5: > than Avg (150) [ to cover for shortfall in first 3 houses and drive avg price to 150] Now assuming the max value of H1 and H2 (135,000), the shortfall from first three houses below average price is 45,000 (15,000 X 3) So, the last two houses need to be 150,000 + (45,000/2) = 172,500. We divide the shortfall equally amongst the two houses because H4 < or = to H5, so equal division makes for the case of H5 to be the least pricy. I find this method eliminates the calculations and equations we had to create. could you please let me know if this is a valid reasoning? Thanks!

[@GMATNinjaTutoring]

Yup, I think that's spot-on! In a way, you're bypassing the actual prices in your calculations, and you're instead thinking of each price in terms of its difference from the mean. It's a great way to handle the problem, and an excellent example of the type of flexibility that we encourage on quant. You've saved yourself a bunch of arithmetic here, and that general way of thinking can help you on other questions that involve averages. Nice work!

[@diya772364]

THANK YOU CHARLES!

[@GMATNinjaTutoring]

Thank you for watching! ❤️❤️❤️

[@Shauracool123]

Hey, in 2nd question why did we maximized 4th house also. Is it because we are trying to find the minimum value and that is only possible if both the houses will share the burden of skewness equally. So, any other value of 4th house would lead to higher value of 5th one and not minimum. Also, if the question was slightly different and we were asked to maximize the value of most expensive house. In that case will we say that 4th house also cost $135,000. Because then all the skewness in the data will be only due to 5th house? Also, thank's for this series. It's a life saver

[@karanjeetsingh922]

Hey Charles, would you please clarify whether NORMAL DISTRIBUTION is a part of GMAT syllabus, as your video description says that normal distribution is also covered in this video. I have seen questions of Normal Distribution ( with all the percentages and all ) in an old official guide, but going through some test prep material , it doesn't seem to be covered at all neither did i notice you talk anything about it. Was wondering whether it has been scrapped

[@GMATNinjaTutoring]

Thank you for catching that! At one point, we'd planned to include some content on normal distributions in this video, but ultimately decided against it, because those questions are exceedingly rare on the GMAT. We'll get the video description edited to reflect the final content -- thank you again for bringing it to our attention. In the overwhelming majority of cases, statistics-related questions on the GMAT don't require you to know anything about normal distributions. In a small handful of cases (this one, for example: tinyurl.com/34fu67ue), it might be vaguely helpful to know something about normal distributions -- but you can certainly answer the question without any formal knowledge. So I wouldn't worry about them too much. If we start to see normal distributions crop up frequently on Data Insights questions, we'll update this video accordingly. I hope that helps!

[@karanjeetsingh922]

Thanks a ton 🙏 saved myself time and worries 😊

[@cablom200]

Hello Charles, thank you for all the good work that you guys do. For the last question, solving with 2 equations and 2 variables doesn't take that much time at all don't you think? (7x + 22y = 5000 and x+y = 500) probably could take 30 seconds more than using the weighted average method.

[@GMATNinjaTutoring]

Thank you so much for the kind words! You're correct: you certainly could use simultaneous equations on that last question, but why spend those extra 30 seconds if you don't have to? More broadly, there are usually quite a few different ways to solve any particular GMAT question, and if you can find relatively efficient solution paths a bit more often, you'll ultimately save enough time to make a meaningful difference in your score. So we try to show relatively efficient paths in the videos -- especially when those paths aren't the first thing that jumps to most test-takers' minds -- even if we can't possibly show every possible way to solve each question. I hope that helps a bit, and thank you again for watching!

[@tarun21gaur]

Thank you for a really good session.

[@GMATNinjaTutoring]

Thank you, Tarun! Glad that you enjoyed it.

[@anukritigupta9837]

Hi Charles, first of all a big thank you to you and your team at GMAT ninja! In question 2, I intuitively didn’t think of the maximum value for cheapest house as 135k..can you explain the rationale behind choosing that value? Thanks in advance 😊

[@GMATNinjaTutoring]

You're welcome! I'm so pleased you're enjoying these videos. If we want to maximize the value of the cheapest house, we should look for any constraints given in the question that might give us a clue what this maximum value will be. In this question, we're told that the median house value is $135k. The cheapest house cannot be more expensive than the median house, otherwise it wouldn't be the cheapest house. This means that the maximum value the cheapest house can take is $135k. The constraint might be different in another question, but we can still look at the information given in the question to find a constraint that would help us find the maximum value. I hope that helps!

[@theeternalloser6885]

Last question was wonderful

[@calvinisaac2181]

For last question, how did you conclude the Weighted average is 10

[@GMATNinjaTutoring]

This is explained in the video between about 55:35 and 56:00. Check that section and let us know if you have any further questions!

[@sanjogsandhu3031]

For the DI question (Second last one), how can we say that C would be the answer? What if we have 90 on both the ends [90,0,0,90]which makes the range 0 but also expands our Standard deviation since the Standard deviation is now spread out to 90 [while ideally it should be between 35-55 [+and - of the mean i.e. 45]. Shouldn't the answer be E? Since both the explanation given and my reasoning make us arrive at statements not enough answer?

[@GMATNinjaTutoring]

If we use the information in statement (1) that the four numbers in set N have a range of zero, then the greatest number minus the smallest number must equal zero. The only way for this to happen is if all four numbers are the same. This means that the numbers in set N can't be [0, 0, 90, 90] as this set would have a range of 90. The only way we can have a set of 4 elements with a range of zero and whose elements sum to 180 is to have the set [45, 45, 45, 45]. As Charles said at about 51:00, if we add more numbers to set M that equal the mean of that set, it will reduce the standard deviation of set M. This means both statements combined are sufficient to answer this question and the answer is (C). I hope that helps!

[@sanjogsandhu3031]

@@GMATNinjaTutoring yes it does! I missed the basic concept of range I believe; confused it with 1st and last vs. Highest and lowest. Thanks for the explanation!

[@600juank]

Hello Charles! Why are we assuming in Q5 that the proportion of women to men in the workers that had good performance is the same as that of the workers that had a negative performance? Couldn't the remaining 58% have other proportions?

[@GMATNinjaTutoring]

I'm not sure that I'm interpreting your question correctly, but I'll give it a shot. The key here is that you don't need to know anything about the people who did NOT receive a negative performance review. All we need to know is that 70% of male employees, 38% of female employees, and 42% of all employees received a negative review. That's enough to calculate the ratio of men to women -- and that's all you're being asked for here. Did the rest of the employees receive positive reviews, or neutral reviews, or no reviews at all? It doesn't matter. We're not at all concerned with those folks, given what the question is asking. I hope that helps!

[@hemajapardeshi6237]

Hi Mr. Charles, I have a query in que 5. I understood till W:M ratio 7:1 but how u calculated 87.5 % and 12.5%?

[@GMATNinjaTutoring]

If the ratio of women to men is 7:1, that means that 7/8 of the total are women. If we convert that to a percentage, we get 87.5%. Similarly, 1/8 of the total are men, which is 12.5%. I hope that helps!

[@amanjagtap]

@@GMATNinjaTutoring But how do we calculate that so quick? do we memorise that?

[@navdeep.singh29]

Hi Charles, regarding the last ques, can you please verify if my method (not based on statistics) is correct here? 25 sets of 20 tickets = 500 tickets Now, since we know this, we can formulate two equations: Let's let C= # of tickets for children and likewise A= # of tickets for adults Therefore, (1) C + A = 500 (denoting the total # of tickets here) (2) 7C + 22A = 5000 (Quantity x Cost = Overall Revenue) Now, since we are required to solve for A, we can multiple (1) by 7 and hence eliminate C : (7C + 22 A = 500) - (7C + 7A = 3500) Simplifying : 15A=1500 Hence, A=100. Thus, option (B) Kindly let me know your thoughts

[@SatishSahoo-s1h]

Hi, that's actually how i solved first before even realizing that weighted averages can be used here.

[@shivambansal1644]

Hi Charles! This is in regard to question 8 The numbers in the set aren't specifically mentioned to be positive. If we proceed with negative numbers in set N or M, then E is the right answer. Am I missing something here?

[@GMATNinjaTutoring]

In Q8, we know from the question itself that set M has a mean of 45 and a SD of 10, so most (or all) of the numbers in that set must be positive. When we look at statement #1 by itself, you're correct: the four numbers in set N could be negative or positive or zero, and that's part of why the statement is insufficient on its own. But statement #2 tells us that the sum of set N is positive, so at least some of the numbers must be positive. And as shown in the video, once we combine statements #1 and #2, it becomes clear that set N must consist of four identical positive numbers. I hope that helps!

[@tobymapa5979]

Hey Charles! Not sure if I'm just missing something but, in Q9, at the very end, why do you say adults make up 20% then divide 500 by 1/5 when you show beforehand that the ratio is 1:4? If it's 1:4, shouldn't you divide 500 by 1/4?

[@GMATNinjaTutoring]

If the ratio of adults to children is 1 to 4, that means that the ratio of adults to the total is 1 to 5? So 1/5 of the total are adults -- and that's why we multiply 1/5 * 500 to get 100 adult tickets. I hope that helps! If not, just let us know.

[@hardikjagga7190]

at 55:00 , can you explain how there are 25 tickets per hour

[@GMATNinjaTutoring]

The zoo doesn't sell 25 tickets per hour. It sells "tickets to groups of 20 people every 10 minutes from 5:00 p.m. to 9:00 p.m. inclusive." This means the zoo sells one batch of 20 tickets at 5:00 p.m., another at 5:10 p.m., another at 5:20 p.m., and so on until the final batch of tickets is sold at 9:00 p.m. If we count up all the batches of tickets, we'll find that the zoo sold 25 batches of 20 tickets, meaning 500 tickets were sold in total. I hope that helps!

[@VeenaManuel]

Hello, For q8, S1- when range is 0, it implies set of N is similar or closest to set M. When Charles mentions as an example 1000 to prove insufficiency, doesn't it mean range will change? So, when it's given as 0, why isn't it sufficient. Thanks

[@GMATNinjaTutoring]

If we know the range of set N is zero (and therefore the standard deviation of set N is zero), we still don't know anything about the relationship between the numbers in set N and the numbers in set M. We know set M has a mean of 45 and a standard deviation of 10. If all the numbers in N are equal to the mean of set M, then the standard deviation of the combined set will be less than 10. If all the numbers in N are something much bigger or much smaller than the average in set M, +/- 1000 for example, then the standard deviation of the combined set will be greater than 10. Since we cannot tell whether the standard deviation of the combined set will be greater or less than 10, statement (1) is insufficient to answre this question. I hope that helps!

[@anvayjoshi]

Hey Charles, In Q1, for the forth house which we need to maximize, why didn't we consider $135000 just as we did for the first two ones?

[@GMATNinjaTutoring]

If we want to minimize the value of the most expensive house, we need to maximize the value of the other houses. Since we know the median house value is $135,000, the maximum value of the three cheapest houses is $135,000. The maximum value of the fourth house, however, is *not* $135,000. The value of this house could be anything from $135,000 up to the same value as the most expensive house. This means that in order to maximize the value of the fourth house, we should set its value to be the same as the most expensive house. Since we don't know what that is at the start of the solution, we give it the same variable as the most expensive house, which in this case is x. I hope that helps!

[@anvayjoshi]

@@GMATNinjaTutoring yes it does now. Thank you.

[@basharabuein409]

Hello Charles, thank you! You are an amazing teacher, and I love your videos guys. I have a quick question. In Q5, I am confused about the intuition behind taking the average of 70% males and 38% females if they are completely different categories (and the number line in general)? I don't see how % women having negative reviews and % men having negative reviews relate to the general % of the company. What does the number line represent? The total % of -ve performance reviews of the company as a whole?

[@GMATNinjaTutoring]

We don't take the average of 70% males and 38% females. We know that 70% of the male employees and 38% of the female employees received a negative performance review. We're then told that 42% of the company's employees (males and females combined) received a negative performance review. These are the figures we use to set up the solution path, but we haven't 'done' anything with the 70% and 38% to 'find' the 42%. The men and women are employees of the company, so the overall percentage figure comes from combining the two groups into a single group of people. If we knew how many men and how many women were in the company, we could use a different process and this would be an easy question. Since we haven't been given these figures, we need a method to work around this lack of information. The line helps us do this but it doesn't really represent anything. It's just a visual aid to help set up the solution process. The first question we want to answer is: how far away from the overall percentage is each separate value? This tells us how much 'weight' the value at each side of the bar has as the closer the overall value is to either side of the bar, the greater the proportion of the total population coming from that side. In this case, the distance between the female percentage and the overall percentage is 4 points and the distance between the male percentage and the overall percentage is 28 points. If we put these distances into a ratio, we get f:m = 4:28 = 1:7, so the overall value is 7 times closer to the female value than the male value. The final step is to flip this ratio to move from a ratio of the 'distance' from each value to the combined value to a ratio of the number of people in each group. This gives us a new ratio of f:m = 7:1. From this ratio, we can conclude that males make up 1/8 or 12.5% of the people working for Company X I hope that helps!

[@teenadurgani]

Hello, Thank you for the video. I have a question on Q3. To maximise the first value, we are minimising the next 3 values - to the value of a. However, as the number of digits is odd, and the avg price is given as 12, shouldn't we take the third value as 12?

[@GMATNinjaTutoring]

If the question told us that the median price was $12, then the third value in the list would be $12. However, the question tells us that the mean price of the books is $12, so the value of the third item in the list could be $12 but it doesn't have to be. In this case, it turns out that four of the books have a value of $10 and one of them has a value of $20, so the total sum of the value of the books is $60 and the mean value is 60/5 = $12. I hope that helps!

[@gurendersingh8957]

Regarding the first question for find median, why didn't we sort the number of items, if we do that 45 is the middle number so based on that E should be the answer. Please let me know your thoughts.

[@GMATNinjaTutoring]

The question is asking about the median number of calories per item. So yes, we'd want to sort something, in theory, but it's not the right-hand column -- that's the number of ITEMS in each calorie range. Instead, we'd want a list of the number of calories in each item, and then we'd want to sort THAT list. Sure, we don't have the exact number of calories in every item. But if you take that general approach, you should be able to get a rough sense of how many calories are in the median item on the list. I hope that helps a bit!

[@apurvjain18]

hey charles, first of all thank you and my doubt is in 1q why we didn't choose the 3rd and the 4th range it cumulates 112 and pls correct me.

[@GMATNinjaTutoring]

In this question, we can figure out that there are 200 items by adding the numbers in the second column. This means the median will be the average of the 100th and 101st items, so we're looking for which row in the table contains the 100th and 101st items. In the first row, there are 12 items. In the first and second rows, there are 12 + 21 = 33 items In the first, second, and third rows, there are 12 + 21 + 65 = 98 items In the first, second, third, and fourth rows, there are 12 + 21 + 65 + 57 = 155 items So we can see that the 100th and 101st items are both in the fourth row in the table, so an item in this row will have somewhere between 601 and 800 calories. The only answer choice that lies between 601 and 800 is (D), so (D) is the answer to this question. I hope that helps!

[@VeenaManuel]

Hello! For Q2, at 12.00, for the 4th slot, why can't it be 135? as it can be 135 (median) or more and it will be lesser than the biggest house value still, isn't it? is it because we've used 135 before the median as well? Thanks much!

[@GMATNinjaTutoring]

We wouldn't be breaking any rules of math to make that slot 135, but we wouldn't get the right answer to this question if we did that. In this question, we want to minimize the value of the most expensive house. To do this, we're trying to maximize the value of all the other houses in the sample. We figured out that the maximum value of the first three slots is 135, but the fourth slot is different. The fourth slot is greater than or equal to the median value, so it's MAXIMUM value will not be 135 unless the fifth slot is also 135. We don't know what that maximum value of the fourth slot is yet but we know that whatever it is, it's equal to the value in the fifth slot. Since we don't know what this is yet either, we can put 'x' as a variable in for both the fourth and fifth slot and continue the solution from there. I hope that helps!

[@kms13dz81]

Hello Charles, I have a question regarding Q5 : Since the ratio is 7:1, why does the percentage of men becomes 1/8 of the total ? Should'nt it be 1/7 ?

[@GMATNinjaTutoring]

If the ratio of women to men is 7 to 1, then we have eight "parts" in this ratio. The men make up one part out of the eight, and the women make up seven parts of the eight. This means we could say the men account for 1 out of every 8 employees in the scenario, or we could say the men make up 1/8 of the employees. This translates to the men making up 12.5% of the employees. I hope that helps!

[@kms13dz81]

Ok got it ! thank you very much @@GMATNinjaTutoring

[@AnnieOnTheMove]

I typed in Q5 in ChatGPT and it gave me C. Both statements together are sufficient. Can you explain how you got A as your answer?

[@GMATNinjaTutoring]

Charles explains this in the video starting from about 23:00. Check that out and please feel free to ask if you have any questions after watching that!

[@VeenaManuel]

Could you please explain the concept of choosing X for the 3 values in the middle for Q3. As in if X is the smallest and that's what we're maximizing, then the next 3 which we want to minimize should be lesser than X? Why would they be X, even if repeats were allowed. Thank you!

[@GMATNinjaTutoring]

In the solution to this question, we had a list of five numbers on the board. The number on the left was defined as the smallest number, and we called this number x. The number on the right was defined as the largest number and, from the the information given about the range in the question, we gave that number a value of x + 10. Then, in order to maximize the smallest number, we want to minimize the other values. However, there are limits to what we can do with the three numbers in the middle. We called the number on the left the smallest number, so the three numbers in the middle can't be less than x because then the number on the left wouldn't be the smallest. The question doesn't prevent us from using repeated values, so the smallest value the three numbers in the middle could be is the same as the smallest value in the list. This means we can give each of these three numbers the value of x. I hope that helps!

[@VeenaManuel]

@@GMATNinjaTutoring Thank you very much! Definitely helped.

[@VeenaManuel]

Hello, Thank you for this session! For q4, the ans is 27 and not 18 to accomodate the 9 sec delay in the 1st 2 races? I'm a little confused because the total 18 accounts for 3 races and not 1. Thanks much!

[@GMATNinjaTutoring]

You're absolutely right: the answer to question 4 is 27, which is the answer Charles found in the solution. If Mercedes was 6 seconds faster than Elon, on average, across the three races, then she will have taken 18 seconds less than Elon in total across the three races. If she was 9 seconds slower than Elon in total after the first two races, she will have been 27 seconds faster than Elon in the third race. This means the answer to this question is (E). I hope that helps!

[@lancezhou2644]

Hi man, thank you so much for the video, it helps a lot!! Just got a stupid question in Q8, if the range is 0, I got that's the biggest - smallest = 0 but how does it imply that they are all same numbers?

[@GMATNinjaTutoring]

Consider the scenario in which you have three numbers: a, b, & c and we know the range is zero. If we assume a is the 'smallest' number and c is the 'largest' then knowing the range is zero means we can say c - a = 0. From this, we can say c = a. The final question we have to answer is how do we know b is the same as a and c? If b were any smaller, then the range wouldn't be zero because b would be less than a. If b were any bigger, then the range wouldn't be zero because b would be greater than c. The only way we can have the range equal to zero is if b is the same and a and c, which means all three numbers are the same. You can extend this argument to a set with any number of elements. If the range is zero, all the numbers in that set must be the same. I hope that helps!

[@puneetsonpal5340]

hi @GMATNinjaTutoring, do you have a set for all the important questions for quants to practice for GMAT for a score of ~48/49

[@GMATNinjaTutoring]

Are you looking for a homework set that includes a variety of practice questions on these topics? Unfortunately, we don't currently offer anything like that publicly at this time. Very possible that we'll offer something like that in 2024, but for now, official GMAT materials are your best bet. Statistics questions aren't a huge proportion of the overall quant questions, but you'll find the principles in this video generally align with the official statistics questions that you'll encounter in the OGs and official question banks. I hope that helps a bit, and have fun studying!

[@puneetsonpal5340]

@@GMATNinjaTutoring hi thanks for replying, I was hoping for a set of questions for the entire portion, I have already solved all your questions and the OG questions and was hoping to have a set with all important questions Thanks for the videos, they have been very helpful, much appreciated :)

[@lucademian1739]

Isn't for Q3 the least expensive 5? if you have books for 5, 10, 15, 15, 15 then the average is 12? Range is 10 and mean the same

[@GMATNinjaTutoring]

You're absolutely right that we could have books priced at 5, 10, 15, 15, 15 and that would satisfy the conditions given in the question. However, this question asks us to find the GREATEST possible value for the least expensive group. This means that pricing the books at 10, 10, 10, 10, 20 will give us a greater value for the least expensive book. We cannot make the least expensive book any more expensive than $10 and still satisfy the conditions given in the question, so (C) is the answer to this question. I hope that helps!

[@i025-jashithshah8]

For the fifth question, can you instead do it with that matrix that you showed in the previous video

[@GMATNinjaTutoring]

Can Q5 be done using that matrix in the overlapping sets video? Sort of. You could use that matrix to organize your information, but then you'd still have to do some funky algebra to get to the answer on Q5. But I suppose it's possible. The more important question: SHOULD you use that matrix? If you'd like, give it a try, and see what you think. Even if you can find a solution using that overlapping sets matrix, you'll find that it's a lot more work than the solution shown in this stats video. I hope that helps a bit!

[@balpreetsingh6834]

Great video as always. I had a question regarding second to last question. Taken alone, statement 2 can be used to calculate new mean of dataset with 104 entries which is (4500 + 180) / 104 that is 45. So now that we know mean remains unchanged, does this have any affect on standard deviation?

[@GMATNinjaTutoring]

Thank you for the kind words, Balpreet! Glad to hear that you're enjoying the videos. If it helps, you can think of standard deviation as a measure of "spread": if the numbers are, on average, farther from the mean, you'll have a larger standard deviation. In question 8, you're correct that statement 2 tells us that the mean is unchanged. But knowing the mean tells us nothing about the standard deviation, or how the standard deviation changes when we add new numbers to the set. In this case, if every number in set N is exactly 45, then adding those numbers to set M would cause the SD to decline, since we'd be adding new terms that are identical to the mean. If set N is very spread out, on the other hand, it might cause the SD of the combined set to increase. Since we don't know anything about the "spread" of set N, we can't know what it would do to the SD of the combined set. So statement 2 is not sufficient by itself. I hope that helps a bit!

[@balpreetsingh6834]

@@GMATNinjaTutoring Thanks for the prompt reply. And yes, every bit helps.

[@kartikgosain1896]

Hey Gmat Ninja! Really great questions in all the videos in this series, it really made me think a lot to answer many questions. Just one doubt in this video, can we also do Q5 through 2X2 Set?

[@GMATNinjaTutoring]

Thank you for the kind words, Kartik! I'm glad that the video helped a bit. When you mention the 2x2 set, I assume that you're referring to the little chart that we like to make on overlapping sets questions? (As shown in this video, for example: tinyurl.com/yxcxeaw8.) If so, that little matrix won't really help on Q5. I'll be deliberately cryptic: try it and see what happens if you'd like. You'll end up getting stuck pretty quickly, and will have to think of something else. :) I hope that helps a bit, and have fun studying!

[@srilanka739]

for Q2 - if we were trying to maximise the sale price - what would the method be? could we make 2 of the sales before 135,000 = 0? or is it illogical to say you made a sale for $0?

[@GMATNinjaTutoring]

That's not the sort of thing that the GMAT would ever expect you to assume on your own -- in the unlikely event that you see that variation on this question, the language will always specify that the homes sold for a minimum of $1 or $100 or whatever. Generally speaking, the method would be nearly identical to the version of Q2 shown in the video. If you're trying to maximize the LARGEST sale price, then you'd want to minimize everything else. So the two lowest prices would be $1 (or whatever the question specifies as the minimum for an actual "sale"), and then two of them would be $135,000. From there, it's just a bit of arithmetic. I hope that helps!

[@srilanka739]

@@GMATNinjaTutoring Thank you :)

[@santoshinimahadev]

charles the best

[@GMATNinjaTutoring]

Thank you! I'm blushing.

[@lucasaparicio6634]

Hi! Very useful video. I have a doubt in Q8. When set R is said to have a range of 0, which contains 4 numbers. How do we know we need to assume that the set is in increasing or decreasing order? If it would not be, then a range of 0 implies only the first and last number to be equal, rather than all the numbers. Hope my question is clear.

[@yatibansal6654]

Hi, Range 0 does mean that first number and last number are equal for a given series of number which are either in ascending or descending so let's just say we have following 4 numbers: 43, x, y, 43, if u say x= 45, would not that interrupt the ascending order? New series will be 43,x,43,45 and hence range will be 2 so basically only if all numbers are same only then we can have 0 range. Try experimenting with inserting any more numbers and you will end up with range greater than 0. Maybe this helps!!!

[@akshitsingh3752]

Hey Charles first of all thank you so much for this informative session. I've a small doubt regarding counting which was applied in last question. I've seen Harry's video about the counting and it was pretty much clear about how we subtract and then add +1 if we are including the last number. However I cannot relate this with time perspective. I feel so silly asking this doubt 😔

[@GMATNinjaTutoring]

Thank you for the kind words! I'm glad that the videos are helping a bit. Your intuition is probably telling you that the counting concept doesn't always apply to time -- and you're correct about that in most contexts. If we're talking about the time span between 5:00 and 9:00, that's four hours, right? But if we're counting the integers from 5 to 9 inclusive, that's five numbers. So far, that all probably matches your intuition without too much trouble. Sometimes, this is called the "fencepost problem." Imagine that you want to build a fence that's four meters long, with fenceposts every meter. You'll need five fenceposts, right? In that last question in the video -- which is admittedly a pretty nasty one -- we have specific "entry times" or "time stamps". So now this is more like counting fenceposts, because we need to include the entry times at both the beginning and the end of each interval. In case it helps, imagine that the duration is just from 5:00 to 6:00, inclusive. Sure, there are 60 minutes in that interval -- and 60 divided by 10 is 6 -- but that's not quite what the question is going after. We want to know how many "ticketing times" happen from 5:00 to 6:00 inclusive, so we need to include both "endpoints" in our calculation. Tickets are available at 5:00, 5:10, 5:20, 5:30, 5:40, 5:50, and 6:00 -- so that's 7 entry times, not 6. The same principle holds once we expand the time to 9:00 instead of 5:00. That gives us 25 entry times -- not 24. I hope that helps!

[@akshitsingh3752]

@@GMATNinjaTutoringI got it. thank you much for this wonderful explanation and prompt reply 😀

[@radyahhassan]

@@GMATNinjaTutoring thank you Charles for this reply! I had the same question and now it makes SO much more sense!

[@andyh3909]

Hi charles I use overlapping sets to solve q5 using double metrics men/women and negative/non negative reviews. Is it also the correct approach beside weighted average method?

[@GMATNinjaTutoring]

I suppose you could use an overlapping sets-style matrix to organize the information, but I'm not really sure how it helps you on Q5. If you try to do it that way, I don't think you can really avoid using variables to represent the total number of men and the total number of women. That's fine, but then you're basically just doing the question algebraically, anyway: I end up with .7M + .38F = .42(M+F) -- and then you could solve for M/F. The overlapping sets matrix doesn't really add much to that method. So it can work, but it's certainly not the easiest or most intuitive solution. Personally, I'd prefer to use the method in the video, but if you like the algebra better and can execute it quickly and seamlessly, that's great. I hope that helps a bit!

[@andyh3909]

So can I summarize that if we add some random data to the set, the standard deviation must be change as long as the old standard deviation is not zero?

[@GMATNinjaTutoring]

It depends on what you mean by "add some random data." If you increase (or decrease) EVERY number in a set by the same amount, the standard deviation won't change. If you're talking about adding a bunch of new numbers into a set, then sure -- the standard deviation is very likely to change, unless we're talking about some funny "edge case" in which you're basically duplicating every number in the original set. In other words: with the exception of some special cases (which are unlikely to appear on your GMAT exam), if you add a bunch of numbers to a set, the "spread" of the set will change. I'm not quite sure if that answers your question, but I hope it helps a bit!

[@andyh3909]

Thanks Charles I got the point 🙏

[@ashutoshiet]

Hi Charles, I am facing a lot of issues in solving 700+ level questions. I am trying to time the question and solve. I am getting most questions wrong. How to improve?

[@GMATNinjaTutoring]

There's no easy answer to that question, unfortunately. It all depends on why you're struggling. Is your fundamental knowledge of the quant topics a little bit shaky? Are you doing insanely hard 700+ questions (from, say, GMAT Club or something) that probably won't really hold you back from your score goal? Are your math skills good, but you struggle with reasoning-based questions that require you to think more flexibly? (If you don't know what I mean by "reasoning-based questions", this article might help: tinyurl.com/mv8w67yc) Also, if you're restricting yourself to two minutes per question, that could easily explain your low accuracy. Yes, you have an AVERAGE of 2 minutes per question on GMAT quant, but that doesn't mean that you should spend 2 minutes or less on EVERY question. On most of the harder ones, you'll almost certainly need a bit more than 2 minutes. (But you also don't want to get stubborn. More on that in this video: tinyurl.com/hwvedjsn) So I'm not sure if this is what you mean by "trying to time the question and solve", but I don't necessarily recommend the exercise of limiting yourself to 2 minutes on every hard quant question -- that's just not what happens on the actual exam. I hope that helps a bit!

[@TrialKick]

I love u charles

[@GMATNinjaTutoring]

❤❤❤

[@sanskarmurarka1973]

in the question number 5 the combining part why do we switch from men to women ratio to women to men ratio didnt get that part i mean what is the logic?

[@ARJUNKUMAR-pw1rq]

Hi can you please help me understand Q9? I converted 20 people for every 10 mins, to hours. Getting 480 people in 4 hours (from 5 to 9 inclusive). Why is this method wrong? By logic it seem right. Also how do i avoid making a mistake like this in the exam since this was very subtle.

[@GMATNinjaTutoring]

To help understand the issue, imagine that the duration is just from 5:00 to 6:00, inclusive. Sure, there are 60 minutes in that interval -- and 60 divided by 10 is 6 -- but that's not quite what the question is going after. We want to know how many "ticketing times" happen from 5:00 to 6:00 inclusive, so we need to include both "endpoints" in our calculation. Tickets are available at 5:00, 5:10, 5:20, 5:30, 5:40, 5:50, and 6:00 -- so that's 7 entry times, not 6. The same principle holds once we expand the time to 9:00 instead of 5:00. That gives us 25 entry times -- not 24. Sometimes, this sort of concept is called the "fencepost problem" or just "counting". For more on how these questions manifest on the GMAT, check out this video: kzbin.info/www/bejne/bHjLiKmYiLmll9k I hope that helps!

[@reksta100]

I have a question regarding question 5. I struggle to graps it. I am cofused with is; do the question presume that there is an equal ratio of woman and men receive negative feedback. Would it change the answer if men have a tendency to receive more negative feedback than woman? Why can it not be that a higher precentage of those 42 % are either men or woman. I am really confused😅 would greatly appriciate if anyone could help me clarify this.

[@GMATNinjaTutoring]

The question does not presume that there is an equal ratio of women to men that receive negative feedback. We are not given that information in the question, and we don't figure that information out as we work through the solution. We know that men *do* have a tendency to receive more negative feedback than women: 70% of the men in the company receive negative feedback and only 38% of them women receive negative feedback. I'm not sure what you mean when you ask why we can't have a higher percentage of the 42 % being men or women. We don't know what percentage of the 42% are men or women at the start of the question, nor do we ever work that out as we answer the question. At the start of the question, we know that 70% of the men and 38% of the women who work in the company received negative feedback. That's all we know. We're then asked to whether we can figure out what fraction of the company's employees are male. From the information in statement (1), we could follow the process Charles demonstrates from about 23:05 to answer the question. This is how we know that statement (1) is sufficient and that the answer to this question is (A). I hope that helps a bit, but please let us know if you have any more questions!

[@reksta100]

@@GMATNinjaTutoring cheers! Was a late night session and was really confused. Makes much more sense today. Really appriciate your videos!

[@Kujam88]

i am so dead, my gmat is in jan 19 and im stuck at stats. f

[@GMATNinjaTutoring]

Haha, don't stress! Stats is #17 out of 19 in our quant series for a reason: it's not the most important quant topic on the GMAT. Depending on your goals, it's certainly worthwhile to be good at stats. But you don't necessarily need to be GREAT at stats -- there are far more important battles. I hope that helps a bit, and good luck with your studies!

[@yatibansal6654]

Hey, In the last question I was trying to solve it via 2 eqns i.e. a + c = 500 (equating number of tickets sold) where a and c are no of adults 25 (7c + 22a) = 5000 (equating the cost) But I am getting incorrect solution with these 2 equations, can you let me know where am I going wrong?

[@GMATNinjaTutoring]

Looks like there's something wrong in your second equation. Why are you multiplying the left side by 25? You can definitely solve this one with a pair of equations, but the method shown in the video might be worth a look -- it's more intuitive, and once you grasp it, you're less likely to make an error with it.

[@yatibansal6654]

@@GMATNinjaTutoring Yes, I do understand the prescribed method and that seems easier. Just wondering why eqns are not working? Oh! I multiplied it by 25 because there were 25 instances when a group of 20 were sold tickets but I realize that would give me #of adults in one round and that's why it messed up. Thankyou! Got it now.