GMAT Ninja Quant Ep 14: Overlapping Sets

[@saireddy6261]

The last question is a great help. Just made the video worth double. I like how your videos start off from the absolute basics and gradually ramp up the difficulty. Makes them helpful for most of us. Thanks.

[@lucasettanni3301]

Charles and all the GMAT Ninja Team - you guys are amazing and are saving lives out here. Thank you so much!!!

[@GMATNinjaTutoring]

Thank you for the delightful message! Have fun studying, and please keep us posted on your progress -- we like good news. :)

[@henrycampbell7161]

I have been struggling with overlapping sets for so long, and this really did a great job at explaining. Thank you so much!

[@NR-cn2tr]

This video made the concept very easy to understand and made me confident in answering such questions. Thank you so much for this entire quant series.

[@GMATNinjaTutoring]

Thank you so much for the kind words, and have fun studying!

[@bikrambhandari3997]

Charles..your way of doing simple sets(not midly overlapping) with matrix was a gamechanger and how you simplified max and min questions were eye opening even as a mathematics student. Thank you!!

[@GMATNinjaTutoring]

Thank you so much! I'd be willing to bet that you're MUCH better trained in math than I am, so I'm honored that this helped a bit. We're always trying to find ways to make GMAT and GRE math more intuitive; sometimes really great math students think we're being silly, and I'm glad that wasn't the case for you. :) Have fun studying, and thank you again!

[@purvagupta7640]

your tips are a complete game changer - thank you so so much!!!!

[@GMATNinjaTutoring]

Thank you for the lovely comment! ❤️❤️❤️

[@VidurSeth-b7o]

You all are the best thank you!

[@GMATNinjaTutoring]

Thank you so much!

[@pierof6837]

Hi, for overlapping problems with 3 and not 2 groups, is there a way to leverage on your well explained tabular way?

[@AllThingsAudio420]

Hi - I was curious how I could identify an "overlapping sets" question and that in fact, a grid solution should be the way to go? For ex, I treated q5 as an algebraic word problem but of course the grid solution presented in the video made things much more efficient. Any help here would be appreciated - thanks!

[@marcelagonzaga8989]

I was in doubt about the answer to the last question (q7). The second proposition says "325 said they approve of neither A or B", but didn´t specified how many were neutral about A or B. So, I thought the proposition would not be sufficient.

[@GMATNinjaTutoring]

This is all about the wording of the question. We're asked how many "voters said that they approve of policy A but did not say that they approve of policy B?" It's the last part of this that's all important: how many voters...did not say that they approve of policy B. If we're looking at the people who "did not say that they approve of policy B", we can count both the people who disapprove of the policy and also the people who were neutral about it. As long as they were not approving of the policy, we can count them. This allows Charles to collapse the table from three columns to two and set it out as an overlapping sets question as he does in the explanation. Statement 2 then tells us that 325 voters said that they approve of neither policy A nor policy B. While we don't know how many of these 325 are neutral about the policy, we know that all 325 of them did not say that they approve of the policy. That's enough to allow us to fill out the table sufficiently to find the information we want, as Charles demonstrates in the video. This means statement 2 is sufficient to answer this question. I hope that helps!

[@SwordSaint099]

Can qn6 be done by (0.7+0.85)-1=0.55 ?

[@SatishSahoo-s1h]

Hi Charles, How to solve the below question using "counting's approach"? In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?

[@yolinegarnier2327]

Does someone have an answer to that?

[@user-us1sf4xd8g]

10, is it correct?

[@user-us1sf4xd8g]

make a venn diagram, assume that all common to 3 games are x students. Then students common to Hockey and Cricket only are 7-x, common only to Football and Hockey are 5-x, and common only to Cricket and Football are 4-x.

[@user-us1sf4xd8g]

Then, you can assume that students only playing Cricket are b students, only Hockey are a students and only Football are c students.

[@moneytrail5314]

Got all of em

[@GMATNinjaTutoring]

You deserve a cookie!

[@tdavis5284]

Mr. Him

[@VedangSharda]

Hi, I tried solving the below with your method, but the answer is showing up to be different: Workers are grouped by their areas of expertise, and are placed on at least one team. 20 are on the marketing team, 30 are on the Sales team, and 40 are on the Vision team. 5 workers are on both the Marketing and Sales teams, 6 workers are on both the Sales and Vision teams, 9 workers are on both the Marketing and Vision teams, and 4 workers are on all three teams. How many workers are there in total?

[@VedangSharda]

Total Countings are 90, the 4 workers in all 3 groups imply 12 countings; 5,6 & 9 are counted twice which adds up to 40. The number of workers in 1 group only will then be 90-12-40=38. So total workers add up to 38+20+4=64. Can you help me understand where the logic is flawed? cause as per the formula the answer should be 74. Thanks!

[@GMATNinjaTutoring]

The difference between this question and the ones shown in the video is in the wording. In this question, the people working in all three groups are also included in the people working in two groups. This means that if we count the people EXCLUSIVELY working for two groups, we get a total of 8 people. This figure comes from taking each of the numbers of people working for two groups and subtracting 4. So, 5 - 4 = 1 person works exclusively on the Marketing and Sales teams, 6 - 4 = 2 people work exclusively on the Sales and Vision teams, and 9 - 4 = 5 people work exclusively on the Marketing and Vision teams. From this, we can say there are 4 workers in all three groups, implying 12 countings, 8 workers in two groups, giving us 16 countings, and 62 workers working in one group. This gives us a total of 74 workers and 90 countings. I hope that helps!

[@nitinsethi9338]

Hey, I'm unable to find the answer to this question with the same method. Can you please help here? At a certain 600-person holiday party, all of the people like eggnog, dim sum, or mashed potatoes. A total of 250 people like eggnog, 350 people like dim sum, and 300 people like mashed potatoes. If exactly 75 of the people like all three foods, how many people like exactly two of the foods?

[@sunielbhalothiea5724]

try to follow the solution for Q3. In your case, final answer should be 150.

[@GMATNinjaTutoring]

Yes, @sunielbhalothiea5724 is spot-on. The technique we use in the video doesn't translate elegantly to KZbin comments, but the same exact process will work for the holiday party question. There are 900 "countings" total (250 + 350 + 300), and 600 people. If you let x = the number of people who like exactly two foods, you can punch all of that information into the same chart we use for Q3, and it should solve nicely.

[@alfredoherrera7812]

About Q5: Why is not 8? If i use 1/3R in the total number of rejectes nstead of 3R in the no rejected with no salmonela, i get 8 as a response. It should be the same, is the same logic, but i dont get why i get a different one.

[@GMATNinjaTutoring]

I'm sorry, but I'm not sure where you're getting 8 in your solution. Do you mean you get 8 as your final answer, so your answer to the question is (A)? Or do you mean you get 8 where Charles gets 24 in the top right box? Please let me know and I'll do what I can to answer your question. Thank you!

[@alfredoherrera7812]

@@GMATNinjaTutoring Yes. I get 8 as my final answer. Lets assume Im ussing the same table you are using in the video, but instead of R (total rejected) i use 1/3 (because it is what the text says), and instead of 3R (no rejected, no salmonela) I use just R, so 1/3 R - 16% = 80% - R 4R/3 = 96 4R = 288 R = 72 Then the response would be 8 because 80% - 72% = 8% I dont understand why is it wrong? why the final response is different? It should be the same.

[@GMATNinjaTutoring]

@@alfredoherrera7812 in that case, all your calculations are correct but you've answered a slightly different question to the one that was asked. If the question had asked us to find the percentage of shipments that are rejected but do not contain salmonella, the answer would be 8%. This is just the value from the R and not S box. However, the question actually asks us to find "what percent of the rejected shipments are NOT tainted with salmonella?" This means we are limited to looking at the rejected shipments (24% of the total), and we want to know what percent of those shipments were not tainted. This means we find 8/24 as a percentage, which is 33 1/3%. This is why the answer is (E). I hope that helps!

[@VedangSharda]

Of 20 adults, 5 belong to X, 7 belong to Y, and 9 belong to Z. If 2 belong to all three organizations and 3 belong to exactly 2 organizations, how many belong to none of these organizations? There is no question in the video that includes how to find the number of adults in the "None" category.

[@GMATNinjaTutoring]

It's not possible to build a table in one of these comments, but I'll do my best to explain here. We can use the 3-item overlapping set method Charles demonstrated in the video, but we'll leave the total in the middle column blank. If we do that, the total in the far right column is 5 + 7 + 9 = 21 from the number of people who belong to X, Y, and Z. We can then say that the 2 people who belong to all three organizations take up 6 of these 'countings'. and the three people who belong to two organizations take up another 6 'countings'. That leaves use with 21 - 6 - 6 = 9 'countings' that must be occupied by one person each. In other words, we need 9 people to belong to exactly one organizations to make the right column of the table work. This means we have 2 people who belong to all three organizations, 3 who belong to exactly two organizations and 9 who belong to exactly one organizations. This means that of the 20 people we started with, 6 people belong to none of the organizations. I hope that helps, but feel free to ask if that solution is hard to visualize!

[@VedangSharda]

@@GMATNinjaTutoring Thank you so much for this!!