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Each of 74 students in a class studies at least one of the three subje

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Each of 74 students in a class studies at least one of the three subje  [#permalink]

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New post 03 Apr 2020, 06:57
1
10
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (02:45) correct 34% (02:52) wrong based on 93 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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Re: Each of 74 students in a class studies at least one of the three subje  [#permalink]

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New post 03 Apr 2020, 07:22
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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Re: Each of 74 students in a class studies at least one of the three subje  [#permalink]

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New post 11 Apr 2020, 11:03
Bunuel wrote:
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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Re: Each of 74 students in a class studies at least one of the three subje  [#permalink]

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New post 08 May 2020, 11:38
Bunuel wrote:
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


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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Re: Each of 74 students in a class studies at least one of the three subje  [#permalink]

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New post 28 May 2020, 20:52
Bunuel - can you post the solution for this ?
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Each of 74 students in a class studies at least one of the three subje  [#permalink]

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New post 28 May 2020, 23:05
1
1
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
Attachments

soln.png
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Re: Each of 74 students in a class studies at least one of the three subje  [#permalink]

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New post 29 May 2020, 10:12
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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Re: Each of 74 students in a class studies at least one of the three subje  [#permalink]

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New post 12 Jun 2020, 16:29
GunjanMadan1 wrote:
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



I'm sorry. Could you please tell me why 'P' = 0 ?
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Re: Each of 74 students in a class studies at least one of the three subje   [#permalink] 12 Jun 2020, 16:29

Each of 74 students in a class studies at least one of the three subje

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