In a school there are 3 subjects - Mathematics, Physics and Chemistry

Question

In a school there are 3 subjects - Mathematics, Physics and Chemistry. The students of the school have to select at least 2 subjects from the pool of 3 subjects. It is known that number of students who like have selected all 3 subjects is 18, number of students who have selected Mathematics as one of their selections is 23 and number of students who have selected Physics as one of their selections is 25. What is the minimum number of students who have chosen Chemistry as one of the selections.

A. 22
B. 19
C. 23
D. 20
E. 24

Show Answer

Official Answer

D

A. 22
B. 19
C. 23
D. 20
E. 24

madhuri14 · Answer

Posted from my mobile device

Shubhradeep · Answer

Consider rechecking Your answer. 
How is 18+5+(3) = 23  , and why do you consider it to be (3) ??

Seems to be a silly mistake

sset92 · Answer

The question says that the students of the school have to select at least 2 subjects from the pool of 3 subjects. This means that Only Math = 0, Only Chem = 0, Only Physics = 0.
Let us call the number of students who have taken all three as k, and k = 18 (Given).

Let us consider, those who have taken both Math and Physics only as p, Math and Chem only as q, and Physics and Chem only as r.

It is given in the question the number of students who have selected Mathematics as one of their selections is 23.
Therefore p+q+k=23
Since k = 18
Therefore, p+q=5

It is also given that number of students who have selected Physics as one of their selections is 25.
Therefore p+r+k=25
p+r=7

Subtract : (p+r)-(p+q) = 7-5
Therefore: r-q=2

We need to find minimum number of students who have taken chem. We know chem is r+k+q.
We also know that k = 18 and that r>q (r-q=2)

Since we can not change k, and considering r>q and can not be minimised below q, so only q can be made minimum which in this case can be 0 if r = 2.

With that we get Minimum students in Chem as r+k+q = 2+18+0 = 20.

kanikaa9 · Answer

n(All 3) = 18
n(M) = 23
n(P) = 25
n(C) = minimize

so maximise n(M + P) = 23 (all maths kids chose physics)
which leaves out 2 (25-23) as the kids who chose chem

so total chem is 18 + 2 = 20 (D)

In a school there are 3 subjects - Mathematics, Physics and Chemistry

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In a school there are 3 subjects - Mathematics, Physics and Chemistry

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