passpadi

2015

Mathematics

POST UTME

in a class of 40 students, 55% passed Mathematics , 25% passed physics and 20% passed both mathematics and physics.How many passed both mathematics nor physics?

A.

10

B.

12

C.

14

D.

16

Correct Answer: 16

Explanation

given n(U)=40n(U) = 40

n(M)=55n(M) = 55 % ofof 40=2240 = 22

n(P)=25n(P) = 25 % ofof  4040 =10= 10

n(PM)=25n(P∩M) = 25% of40=8of 40 = 8


remember 8 is the intersection

thus:

for n(M)228=14n(M) 22 - 8 = 14

for n(P)n(P)  108=210 - 8 = 2

so 14+8+2+x=4014 + 8 + 2 + x = 40 

24+x=4024 + x = 40

x=4024=16x = 40 - 24 = 16

given n(U)=40n(U) = 40

n(M)=55n(M) = 55 % ofof 40=2240 = 22

n(P)=25n(P) = 25 % ofof  4040 =10= 10

n(PM)=25n(P∩M) = 25% of40=8of 40 = 8


remember 8 is the intersection

thus:

for n(M)228=14n(M) 22 - 8 = 14

for n(P)n(P)  108=210 - 8 = 2

so 14+8+2+x=4014 + 8 + 2 + x = 40 

24+x=4024 + x = 40

x=4024=16x = 40 - 24 = 16

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