A school has a total enrollment of 90 students. There are 30 students

Question

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%

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

amanvermagmat · Answer

Students taking physics = 30 (these 30 include those 13 that take both)
Students taking english = 25 (these 25 also include those 13)

So those that take either physics or english or both = 30 + 25 - 13 = 42.

Required percentage = 42/90 * 100 = 47% approx

Hence answer is  C

ScottTargetTestPrep · Answer

Since we need to determine the number of students who are taking either physics or English, we can use the following formula:

# of students who take physics or English = # who take English + # who take physics - # who take both

Either = 30 + 25 - 13 = 42

Thus, the percentage of students who are taking either physics or English is 42/90 = 0.4667 = 47%.

Answer: C

guenthermat · Answer

If the questions asks for students who take EITHER physics OR English.

Thus, if I pick a student who studies physics AND English, he studies both subject --> so he doesn't study EITHER physics OR English.

I focused on 
a) the people studying only physics but not English (30-17 = 17) 
b) and on the people only studying English but not physics (25-13 = 12)

17 physics students + 12 English students = 29/90 = 32,33%

Happy to hear your thoughts.

Thanks!

sashiim20 · Answer

Total Students = 90
Students taking Both Physics and English = 13
Students taking Physics = 30 
Students taking Only Physics = 30 - 13 = 17
Students taking English = 25
Students taking Only English = 25 - 13 = 12

Therefore Total Students taking Either Physics or English = 13 + 17 + 12 = 42

Percentage of the students are taking either physics or English =  \frac{42}{90}  x 100 = 46.666% = Approximately = 47%
Answer C...

guenthermat · Answer

But if I add Students taking Only Physics (17), Students taking Only English (12) AND Students taking both (13), then I DON'T end up with students taking EITHER Physics OR English as the 13 students taking both subject have both subjects - and not Either English OR physics.

Do u understand my point?

amanvermagmat · Answer

Hi

In Mathematics, especially in questions of sets/probability etc, if you come across a phrase  'Either A or B' it automatically means 
'Either A or B or both'.

So if 5 people drink Only Pepsi, 7 people drink Only Coke, and 2 people drink both Pepsi and Coke, then it means 
(5+7+2) = 14 people are there who drink 'Either Pepsi or Coke'. (Both is automatically included in this).

That's my understanding. Maybe Experts can confirm.

guenthermat · Answer

This clarification helps a lot - thank you!

Arro44 · Answer

Thank you for pointing this out, I also solved for students that attend only one of the respective classes.
After reading the respective explanation it makes sense to me that 47% is the right answer though.

SBLight · Answer

Sorry guyz but honestly can't understand this one.
If the question is either Physics or English but not both, when we use the equation P+E-both we are still considering the "both" part.
To be more specific:
Physics group --> 30 people composed by 17 (only physics) + 13 (both)
English group --> 25 people composed by 12 (only english) + 13 (both)

If we remove 13 only one time we are still considering both of them and this is not what is asked.

What am I missing? 
Thanks in advace

Bunuel · Answer

The question is not good. Ignore.

P.S. The topic is archived.

A school has a total enrollment of 90 students. There are 30 students

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