GATE2017 EC-2: GA-5

Question

$500$ students are taking one or more course out of Chemistry, Physics, and Mathematics. Registration records indicate course enrollment as follows: Chemistry $(329)$, Physics $(186)$, and Mathematics $(295)$. Chemistry and Physics $(83)$, Chemistry and Mathematics $(217)$, and Physics and Mathematics (63). How many students are taking all $3$ subjects?

• A. $37$
• B. $43$
• C. $47$
• D. $53$

Comments

Use this formula

P(AuBuC) = P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + P(AnBnC)

where we want to find P(AnBnC)

500-329-186-295+83+217+63 = 53

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when to take the given data as universal set .Like here we have taken 500 as (A u B u C) but when to take it as universal set?

Answer 1

Answer: $D.$ 53

Total number of students $= n(P)+n(C)+n(M)-n(P \cap C)-n(P \cap M)-n(C \cap M)+n(P \cap C \cap M)$

$\implies 500=329+295+186-217-83-63+x$
$\implies x=53.$

Answer 2

All 3 subjects =53