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A school has 63 students studying Physics, Chemistry and Biology. 33 study Physics, 25 Chemistry and 26 Biology. 10 study Physics and Chemistry, 9 study Biology and Chemistry while 8 study both Physics and Biology. Equal numbers study all three subjects as those who learn none of the three. How many study all three subjects?

Can someone show me the calculation. The ans is 3.

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6 answers

  1. Venn diagram problem
    P only=33-18-x
    B only =26-17-x
    C only =25-19-x
    15-x+9-x+6-x+8+10+9+x=63
    -2x=63
    X=-3
    Which means you have to work with 3 in the middle

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  2. actually
    physics = 33 - (10-x) - (8-x) - x
    chem = 25 - (10-x) - (9-x) - x
    bio = 26 - (9-x) - (8-x) - x

    physics + chem + bio = 63
    63 = 30 + 9x
    33/9 = x
    x = 3.6....
    we cant take 18 - x and subtract with 33 because its the collection of physics and chem, phy and bio students so we have to subtract the common students

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  3. 18 is the sum of the physics included pair in all three pairs(10+8=18)

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  4. Venn diagram problem
    P only=33-18-x
    B only =26-17-x
    C only =25-19-x
    15-x+9-x+6-x+8+10+9+x=63
    -2x=63
    X=-3
    Which means you have to work with 3 in the middle

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  5. Why u to take 18-x

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  6. P only=33-18-x
    B only =26-17-x
    C only =25-19-x
    16-x+7-x+6-x+8+11+4+x=63
    -2x=63
    X=-3
    Which means you have to work with 3 in the middle

    (I dont think I'm right)

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