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jackfr2
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In a class of 60 students , 20 like math , 25 like english 27 Oct 2020, 07:40
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45% (medium)

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71% (02:13) correct 29% (02:30) wrong based on 315 sessions

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In a class of 60 students , 20 like math , 25 like english and 30 like science; if 5 like both math and English , 7 like both math and science , 8 like both English and science and 3 like neither of these subjects , how many like all of the three subjects ?

a. 2
b. 3
c. 4
d. 5
e. 0

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A
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In a class of 60 students , 20 like math , 25 like english 27 Oct 2020, 11:12
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jackfr2
In a class of 60 students , 20 like math , 25 like english and 30 like science; if 5 like both math and English , 7 like both math and science , 8 like both English and science and 3 like neither of these subjects , how many like all of the three subjects ?

a. 2
b. 3
c. 4
d. 5
e. 0

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This question is straightforward and does not require a diagram.

Total = M + E + S - (M and E) - (M and S) - (E and S) + All 3 + Neither 3

60 = 30 + 20 + 25 - 5 - 7 - 8 + 3 + All3

All 3 = 60 - 20 - 25 - 30 + 5 + 7 + 8 - 3

All 3 = 80 - 78 = 2


Option A

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In a class of 60 students , 20 like math , 25 like english 31 Oct 2020, 15:14
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jackfr2
In a class of 60 students , 20 like math , 25 like english and 30 like science; if 5 like both math and English , 7 like both math and science , 8 like both English and science and 3 like neither of these subjects , how many like all of the three subjects ?

a. 2
b. 3
c. 4
d. 5
e. 0

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Solution:

We will use the formula:

Total = #Group A + #Group B + #Group C - #Groups A & B - #Groups A & C - #Groups B & C + #All three groups + #Neither

Substituting elements of the formula with the given numbers, we obtain:

60 = 20 + 25 + 30 - 5 - 7 - 8 + #All three groups + 3

60 = 75 - 20 + #All three groups + 3

#All three groups = 60 - 75 + 20 - 3 = 80 - 78 = 2

Answer: A
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In a class of 60 students , 20 like math , 25 like english 07 Dec 2020, 02:31
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There is something wrong with this question.
I always end up with -1 as answer.

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In a class of 60 students , 20 like math , 25 like english 16 Dec 2024, 06:37
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Method 1: Let a be the number of students who like only 1 subject, b -->2 subjects, c--> 3 subjects and n--> none of the subjects.

a+b+c+n=60
a+b+c=60-3=57
a+2b+3c=20+25+30= 75

Subtracting the two equations:
b+2c=18
5-c+7-c+8-c+2c= 18
20-c=18
c=2.

Method 2: Total no. of kids who like any of the 3 subjects=57. Hence, there are 18 students who like more than one subject. On similar lines, 5+7+8=20. Hence there are 2 students who have like all 3 subjects.
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