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In a group of 70 cars tested by a garage in Delhi, 15 had faulty tyres, 20 had faulty brakes and 18 exceed the allowable emission limits. Also, 5 cars had faulty tyres and breaks, 6 failed on tyres and emission limits, 10 failed on breaks and emission, and 4 cars were unsatisfactory in all aspects, how many had no fault in these 3 checks?

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    $\begingroup$ Hi Buchi, welcome to MSE! What have you tried? This is not a forum where people just do your HW for you. Please see math.meta.stackexchange.com/questions/9959/… The Venn diagram approach you allude to in the title is a good one! $\endgroup$ Commented Apr 17, 2019 at 20:28

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Easy, we have 70 total subtract 15+20+18=53, giving 17. Then add back the overlaps of any 2 as they got subtracted twice, 6+10+5+17=38. Now deal with the threeway overlap, it got subtracted 3 times (not the 6 I thought, because the overlaps overlap), then added back 3 times. We need to subtract it once more. 38-4=34. 34 cars had no fault when checked,70-34=36 did. Next time show what's been tried, and the problem source.

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  • $\begingroup$ Are you taking 4 as the 3 overlaps? I thought they said 4 were unsatisfactory in all 3 aspects? Isn’t it meant to be excluded from all the three aspects? $\endgroup$
    – Buchi
    Commented Apr 18, 2019 at 10:11
  • $\begingroup$ no, it means standards were not satified in all three areas. $\endgroup$
    – user645636
    Commented Apr 18, 2019 at 10:12
  • $\begingroup$ okay found a slight error in my math, but you can use this method for arbitrarily many sets. $\endgroup$
    – user645636
    Commented Apr 18, 2019 at 10:17
  • $\begingroup$ Is there a way I can snap my Venn diagram and the question and send you here? $\endgroup$
    – Buchi
    Commented Apr 18, 2019 at 10:19
  • $\begingroup$ hit the add image option in your original post. $\endgroup$
    – user645636
    Commented Apr 18, 2019 at 10:21
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enter image description here

you start from the middle, (4 unsatisfied all) and work your way out.

Answer is 34 cars

edit: the question states 4 cars unsatisfied all three categories. If a car is being tested in a garage and it fails the test, this means the test was unsatisfied

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  • $\begingroup$ I’m so happy you could solve this, but can you explain? $\endgroup$
    – Buchi
    Commented Apr 17, 2019 at 21:55
  • $\begingroup$ I’ve been having issue with the unsatisfied. I just edited the question to exactly how it was in my test(basically the unsatisfactory). When it said unsatisfactory in all three aspects, doesn’t it mean the 4 were faulty, but couldn’t fall under any of the 3 faults. So I put the 4 outside the circle. If it was to be in the middle of the 3, I felt the statement would have been, “and 4 satisfied all 3 aspects). I hope you get my issue. $\endgroup$
    – Buchi
    Commented Apr 17, 2019 at 22:00

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