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celine-ms

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Hey guys!

So I just had my mock exam (May 2016) on maths studies paper 2 and I was really confused with the venn diagram question. If 47 people used airplanes, then how did 30 use airplanes and trains and 35 people use airplanes and buses? (apart from the 20 who use the three types of transport)? This makes no sense to me as that's more than 47... Can anyone please explain me this question? I am afraid of getting something similar on my real exam and be as lost as today. 

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As @IB_taking_over mentioned, it would be a lot easier to explain with the full question. With what you've given, though, I may be able to answer, so I'll try my best.

When the question says 30 people use Airplanes and Trains, they mean that 30 use solely Airplanes and Trains AND Airplanes and Trains and Buses (i.e, the entire overlapping part between the Airplane and Train circles if you remove the Bus circle). This is because the people who use all 3 still use Airplanes and Trains.

When the question says 35 use Airplanes and Buses, they mean that 35 use solely Airplanes and Buses AND Airplanes and Trains and Buses. When the question says 20 use all 3, they mean exactly that: 20 use Airplanes and Trains and Buses. Here it is visually:

  Venn2.png

Now, the 30 people who use Airplanes and Trains is represented by the red (R) and purple (P) areas, the 35 people who use Airplanes and Buses is represented by the blue (Bl) and purple (P) areas, and the 20 people who use all 3 is represented by the purple area. The purple area, P, is 20. We can deduce then that the red area, R , is = 30-20 =10, because R+P=30. The blue area, Bl, is 35-20=15, because B+P=35. 

Next, the total amount of people who use Airplanes is given by the white part of Circle A, W, the red area, R, the purple area, P, and the blue area, Bl. We have that W+R+P+B=47, with R=10, P=20, and B=15. Therefore, W+10+20+15=47 => W+45=47 => W=2. This makes sense, because it is positive (and it means that 2 people solely used Airplanes). In what you did, you said that R=30, P=20, and Bl=35, which would mean that W+30+20+35=47 => W+85=47 => W=-48, which doesn't make sense because it's negative. 

You said that the 35 and 30 amounts were apart from the 20 who use all, but if this were true, then (as you said) it wouldn't make sense. Did the original question specify this, or was it a misinterpretation? I know when I was doing these Venn Diagram problems, I had trouble discerning from the two as well. 

 

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@TheNintendoChip Thank you so so much! I now understand it way better and I will find similar past questions to kick this off in case I have it on my real exams :) I think what you asked was a misinterpretation as I just took the exam today and don't remember the question 100% (only what it wanted us to do). But thanks for everything, it was so so useful.

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