# 4 variable Venn diagram, Please help me in solving below que

#### Vishwa137

In Shishu Vidyalaya, students study at least one of 4 subjects from Hindi, English, Science or Maths. The
following additional information is known about the students in Shishu Vidyalaya
Subject(s) Number of Students
Hindi 54
English 77
Maths 91
Science 92
Further, it is also known that;
? 123 students study at least one of English and Science
? The number of students who study Maths-English-Science is twice the number of students who
study Hindi-Maths.
? The number of students who study Hindi-English, Hindi alone and Hindi-Science form an
arithmetic progression of common difference equal to 3.
? The number of students who study Hindi-English-Science, All the four subjects, English alone and
Maths alone form an arithmetic progression of common difference equal to 2.
? The number of students who study Maths alone is equal to the number of students who study
Maths-English, which is equal to the number of students who study Maths-English-Hindi.
? The number of students who study Hindi-Maths is one more than the number of students who
study Maths alone.
? The number of students who study Hindi-Science-Maths is equal to the 3
rd
prime number and
the number of students who study Maths-Science is equal to the 7
th
prime number.
1. What is the total number of students in Shishu Vidyalaya?
a. 150
b. 314
c. 160
d. 170
2. How many students study at least 2 of the 4 subjects?
a. 94
b. 96
c. 112
d. 111
3. If the number of students who study exactly 3 subjects is equal to 8K+1, what is the value of K?a. 4
b. 5
c. 6
d. 7
4. If 16 students who study English, 12 students who study Science and 14 students who study
Hindi leave the school, what could be the minimum number of students left in the school who
study Maths? –
a. 55
b. 60
c. 49
d. 57

#### kiuhnm

Re: 4 variable Venn diagram, Please help me in solving below

Vishwa137 said:
In Shishu Vidyalaya, students study at least one of 4 subjects from Hindi, English, Science or Maths. The
following additional information is known about the students in Shishu Vidyalaya
Subject(s) Number of Students
Hindi 54
English 77
Maths 91
Science 92
Further, it is also known that;
[...]
? The number of students who study Hindi-English-Science, All the four subjects, English alone and
Maths alone form an arithmetic progression of common difference equal to 2.
I find that difficult to believe, since |E|=77 and |M|=91.

#### HallsofIvy

Math Team
Re: 4 variable Venn diagram, Please help me in solving below

kiuhnm said:
Vishwa137 said:
In Shishu Vidyalaya, students study at least one of 4 subjects from Hindi, English, Science or Maths. The
following additional information is known about the students in Shishu Vidyalaya
Subject(s) Number of Students
Hindi 54
English 77
Maths 91
Science 92
Further, it is also known that;
[...]
? The number of students who study Hindi-English-Science, All the four subjects, English alone and
Maths alone form an arithmetic progression of common difference equal to 2.
I find that difficult to believe, since |E|=77 and |M|=91.
You are misunderstanding. There are 91 students who study math. At this point we do not not know how many study only math.

#### kiuhnm

Re: 4 variable Venn diagram, Please help me in solving below

Wow... two answers, two stupid mistakes

#### kiuhnm

Re: 4 variable Venn diagram, Please help me in solving below

I think there's something wrong.
We know that
$$\displaystyle \qq |EM|=|HEM|$$
then
$$\displaystyle \qq |\bar{H}EM|=0.$$
Now,
$$\displaystyle \qq |EMS|=|HEMS|+|\bar{H}EMS|=|HEMS|\leq|HM|$$,
but
$$\displaystyle \qq |EMS|=2|HM|$$
therefore
$$\displaystyle \qq 2|HM|\leq|HM|$$
which means that
$$\displaystyle \qq |HM|=0,$$
but we know that
$$\displaystyle \qq |HMS|=5.$$
Oops.