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Bunuel
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Each of 74 students in a class studies at least one of the three subje 03 Apr 2020, 07:57
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Difficulty:

65% (hard)

Question Stats:

65% (02:49) correct 35% (02:58) wrong based on 325 sessions

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Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, what is the number of students studying H?

A. 30
B. 32
C. 42
D. 50
E. 52

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E
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yashikaaggarwal
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Each of 74 students in a class studies at least one of the three subje 03 Apr 2020, 08:22
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Let H, P=0(given) and E be the no of students only studying H,P and E.
HE=20 (given), HP and PE be the no. Studying H and E, H and P and P and E.
HPE = 10(given) is the no. Studying all three subject.
Also All students Studying H is equal to studying E
So,
H+HP+HE+HEP=E+EP+HE+HEP
H+HP+20+10=E+EP+20+10
H+HP=E+EP---- (1)
Now.
H+E+P+HE+HP+EP+HEP=74
2(H+HE)+30=74 (from equation 1)
H+HE=22
So total no. Of students studying H is H+HP+HE+HEP=22+30=52.
So. OA is E

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Each of 74 students in a class studies at least one of the three subje 11 Apr 2020, 12:03
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Bunuel
Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, what is the number of students studying H?

A. 30
B. 32
C. 42
D. 50
E. 52

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Hi Bunuel,
Can you please post the solution for this?
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exc4libur
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Each of 74 students in a class studies at least one of the three subje 08 May 2020, 12:38
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Bunuel
Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, what is the number of students studying H?

A. 30
B. 32
C. 42
D. 50
E. 52
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total=a,b,c-both-2mid+neither
total=74
neither=0 (each at least one..)
mid=10
a=b
c=x+y+10
both=20+x+y

74=2a+(10+x+y)-(20+x+y)-2(10)-0
2a=74+20+10=104
a=52

ans (E)
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Each of 74 students in a class studies at least one of the three subje 28 May 2020, 21:52
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Bunuel - can you post the solution for this ?
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GunjanMadan1
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Each of 74 students in a class studies at least one of the three subje 29 May 2020, 00:05
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We can solve this using a Venn Diagram as attached.

As per given information, total number of students = 74

g=10
d =20

Number of students studying H equals E
a+e+d+g = d+g+b+f
a+e= b+f

Also,

a+b+e+f = 74 as p=0

2(a+e)= 74

a+e =22

Hence total number of students studying H = 22+30= 52

Answer: Option E
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Each of 74 students in a class studies at least one of the three subje 29 May 2020, 11:12
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Let the number of students studying only H be h, only E be e, only H and P but not E be x, only E and P but not H be y.

Given that,

Only P = 0

All three = 10

Studying only H and E but not P = 20

Number of students studying H = Number of students studying E

h + x + 20 + 10 = e + y + 20 + 10

h + x = e + y

Total number of students = 74

Therefore,

h + x + 20 + 10 + e + y = 74

h + x + e + y = 44

h + x + h + x = 44

h + x = 22

Therefore, the number of students studying H = h + x + 20 + 10

= 22 + 20 + 10 = 52

The correct answer is 52.
Option E
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Each of 74 students in a class studies at least one of the three subje 12 Jun 2020, 17:29
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GunjanMadan1
We can solve this using a Venn Diagram as attached.

As per given information, total number of students = 74

g=10
d =20

Number of students studying H equals E
a+e+d+g = d+g+b+f
a+e= b+f

Also,

a+b+e+f = 74 as p=0

2(a+e)= 74

a+e =22

Hence total number of students studying H = 22+30= 52

Answer: Option E
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I'm sorry. Could you please tell me why 'P' = 0 ?
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SukanyaRoy
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Each of 74 students in a class studies at least one of the three subje 20 Nov 2021, 07:59
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[quote="Bunuel"]Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, what is the number of students studying H?

A. 30
B. 32
C. 42
D. 50
E. 52


Option E

Total -Neither=H+E+P-(exactly 2)-2*all 3;
74-0=2H+(10+q+r)-(20+q+r)-2k; ….. since P= 10+q+r ; H&E=p=20; all 3=10; exactly 2= 20+q+r;
74=2H-30
H=52

Thanks!!
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Each of 74 students in a class studies at least one of the three subje 03 Apr 2026, 22:26
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Overlapping sets always have this one equation and almost all questions are solvable using it.

Only 1 - 2[Three items] - [Three items] = Total

H+E+P-2[10]-[Two items] = 74
Now H=E
Two items = 20+P-10 = P+10
Now substituting:

2H+P-20-P-10=74
2H-30=74
2H=104
H=52.

Answer: Option E
Bunuel
Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, what is the number of students studying H?

A. 30
B. 32
C. 42
D. 50
E. 52

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Bunuel
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