Problem Solving

A school has a total enrollment of 90 students. There are 30 students taking physics, 25 taking English, and 13 taking both. What percentage of the students are taking either physics or English?

(A) 30%
(B) 36%
(C) 47%
(D) 51%
(E) 58%

The OA is C.

The "13 students taking both courses" confused me. Can any expert explain to me this PS question?

Vincen wrote:A school has a total enrollment of 90 students. There are 30 students taking physics, 25 taking English, and 13 taking both. What percentage of the students are taking either physics or English?

(A) 30%
(B) 36%
(C) 47%
(D) 51%
(E) 58%

The OA is C.


The "13 students taking both courses" confused me. Can any expert explain to me this PS question?

The students taking physics or English can be placed in 3 categories: physics only/English only/both physics and English

If 30 students take physics and 13 take both physics and English, then 30-13 = 17 take only physics.
If 25 students take English and 13 take both physics and English, then 25-13 = 12 take only English

To summarize
Physics only: 17
English only: 12
Both: 13
Total taking physics or english = 17 +12 + 13 = 42.

42/90 = a little under 50%. The answer is C

(The question should have been worded more precisely: it should have asked for the approximate percentage taking English or physics or both.)

Vincen wrote:A school has a total enrollment of 90 students. There are 30 students taking physics, 25 taking English, and 13 taking both. What percentage of the students are taking either physics or English?

(A) 30%
(B) 36%
(C) 47%
(D) 51%
(E) 58%

The OA is C.

The "13 students taking both courses" confused me. Can any expert explain to me this PS question?

Hi Vicen,
Let's take a look at your question.

It is a probability question that asks us to calculate the Probability of Event A or B.
Whenever we are asked to find the Probability(A or B), We need to decide if events A and B are mutually exclusive or not.

Mutually exclusive events are the events that cannot occur at the same time, whereas, the events that can occur at the same time are not mutually exclusive events.

For Mutually exclusive events
P(A or B) = P(A) + P(B)

For Not Mutually exclusive events
P(A or B) = P(A) + P(B) -P(A and B)

Let's get back to our question now.
Let
Event A = Student can take Physics
Event B = Student can take English
The students can take both Physics and English at the same time in the college, which shows that events A and B are not mutually exclusive.

Therefore, we will be using the formula,
P(A or B) = P(A) + P(B) -P(A and B)
P(A or B) = 30/90 + 25/90 - 13/90
P(A or B) = (30+25-13)/90
P(A or B) = 42/90
P(A or B) = 0.4666

To find the percentage multiply it by 100%
= 0.46666 x 100% = 46.66% approximately 47%

Therefore, Option C is correct.
Hope this makes sense

I am available if you'd like any followup.