How many students majoring in engineering?

Let us assume the number of students majoring in math, physics, chemistry, biology, and engineering are m, p, c, b, and e, respectively.

So, m:p = 5:3 and p:c = 5:8 ---> m:p:c = 25:15:24
As, (m + p + c + b + e) = 100, only possible value of m, p, and c are 25, 15, and 24, respectively.

As 1/4 of the course students not majoring in math, physics or chemistry are majoring in biology, (1 - 1/4) = 3/4 of the course students not majoring in math, physics or chemistry must be majoring in engineering.

So, e = 3/4 of [100 - (m + p + c)] = 3/4 of [100 - (25 + 15 + 24)] = 3/4 of [100 - 64] = 3/4 of 36 = 27

Hello.
Could you please explain the underlined statement in the solution.

Thanks.

Atekihcan wrote:Let us assume the number of students majoring in math, physics, chemistry, biology, and engineering are m, p, c, b, and e, respectively.

So, m:p = 5:3 and p:c = 5:8 ---> m:p:c = 25:15:24
As, (m + p + c + b + e) = 100, only possible value of m, p, and c are 25, 15, and 24, respectively.

As 1/4 of the course students not majoring in math, physics or chemistry are majoring in biology, 1 - 1/4) = 3/4 of the course students not majoring in math, physics or chemistry must be majoring in engineering.

So, e = 3/4 of [100 - (m + p + c)] = 3/4 of [100 - (25 + 15 + 24)] = 3/4 of [100 - 64] = 3/4 of 36 = 27

iamniladri wrote:Could you please explain the underlined statement in the solution.

Atekihcan wrote:(1 - 1/4) = 3/4 of the course students not majoring in math, physics or chemistry must be majoring in engineering.

All the students are majoring in exactly one of the following: math, physics, chemistry, biology, and engineering. So, the students not majoring in math, physics or chemistry must be majoring in either biology or engineering.

As 1/4 of the students not majoring in math, physics or chemistry is majoring in biology, (1 - 1/4) = 3/4 of the students not majoring in math, physics or chemistry must be majoring in engineering.

Hope that helps.