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 October 27th, 2012, 12:34 AM #1 Joined: Oct 2012 Posts: 1 Thanks: 0 4 variable Venn diagram, Please help me in solving below que 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
October 27th, 2012, 04:29 AM   #2

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Quote:
 Originally Posted by 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; [...] ? 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.

October 27th, 2012, 07:55 AM   #3
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Quote:
Originally Posted by kiuhnm
Quote:
 Originally Posted by 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; [...] ? 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.
Quote:
 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.

 October 27th, 2012, 08:02 AM #4 Joined: Oct 2012 Posts: 45 Thanks: 0 Re: 4 variable Venn diagram, Please help me in solving below Wow... two answers, two stupid mistakes
 October 27th, 2012, 12:54 PM #5 Joined: Oct 2012 Posts: 45 Thanks: 0 Re: 4 variable Venn diagram, Please help me in solving below I think there's something wrong. We know that $\qq |EM|=|HEM|$ then $\qq |\bar{H}EM|=0.$ Now, $\qq |EMS|=|HEMS|+|\bar{H}EMS|=|HEMS|\leq|HM|$, but $\qq |EMS|=2|HM|$ therefore $\qq 2|HM|\leq|HM|$ which means that $\qq |HM|=0,$ but we know that $\qq |HMS|=5.$ Oops.

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