GMAT Ninja Quant Ep 13: 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.

[@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!

[@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!

[@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?

[@moneytrail5314]

Got all of em

[@GMATNinjaTutoring]

You deserve a cookie!

[@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.

[@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!!