From below table structure, Students failed in both subjects = 12


IMO Option E

solve 2x2 matrix
---PE--FE---Total
PM--132--198--330
FM---258--12----270
total--390--210---600
IMO E ; 12

Name:
- a: % student who passed English only
- b: % student who passed Math only
- c: % student who passed both
- d: % student who failed both

a + b + c + d = 100%
* 35% students failed in english: b+d = 35%
* 45% failed in maths: a + d = 45%
We get:
(1) a-b = 10% ~~> a = b+10%
(2) (a+b) + 2d = 80%, so (a+b+c+d) - (a+b+2d) = c-d = 100%-80% = 20%. d = c-20%
(3) 40% of those who passed in maths also passed in english: (b+c)*0.4 = c. So 0.4b=0.6c, or c = 2/3b

Combine (1), (2) and (3) we have:
a+b+c+d = (b+10%) + b + (2/3b) + (2/3b-20%) = (2+2*2/3)b -10% = 100%
10/3b = 110% so b = 110*3/10 = 33%.

c (% of students who passed both test) = 2/3*33% = 22%
d (% of students who passed none) = 22%-20% = 2%
so the absolute value of d (the NUMBER of student who passed none) = 2%*600 = 12. Choice E.

***********************Passed English**************Failed English********************Total
Passed Maths***********132*************************198************************330
Failed Maths************258**************************12*************************270
Total********************390 *************************210*************************600

IMO E
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Bunuel how can you build the table and do the calculations in less than 2 minutes?
Is there a shortcut?

Thank you

The table is not built out of wood , it is on paper.
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