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

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Joined: 29 Jan 2015
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Location: India
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A school has a total enrollment of 90 students. There are 30 students [#permalink]

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19 May 2017, 01:25
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Question Stats:

57% (01:02) correct 43% (01:48) wrong based on 76 sessions

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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%
[Reveal] Spoiler: OA

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DS Forum Moderator
Joined: 21 Aug 2013
Posts: 786
Location: India
Re: A school has a total enrollment of 90 students. There are 30 students [#permalink]

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19 May 2017, 02:26
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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

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Re: A school has a total enrollment of 90 students. There are 30 students [#permalink]

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22 May 2017, 17:47
rohan2345 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%

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%.

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Joined: 18 Mar 2017
Posts: 42
Re: A school has a total enrollment of 90 students. There are 30 students [#permalink]

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25 May 2017, 04:11
rohan2345 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%

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%

Thanks!
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A school has a total enrollment of 90 students. There are 30 students [#permalink]

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25 May 2017, 04:54
rohan2345 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%

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%
Intern
Joined: 18 Mar 2017
Posts: 42
Re: A school has a total enrollment of 90 students. There are 30 students [#permalink]

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25 May 2017, 05:25
sashiim20 wrote:
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%

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?
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Joined: 21 Aug 2013
Posts: 786
Location: India
Re: A school has a total enrollment of 90 students. There are 30 students [#permalink]

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25 May 2017, 09:58
1
KUDOS
guenthermat wrote:
sashiim20 wrote:
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%

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?

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.
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Joined: 18 Mar 2017
Posts: 42
Re: A school has a total enrollment of 90 students. There are 30 students [#permalink]

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25 May 2017, 14:36
amanvermagmat wrote:

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.

This clarification helps a lot - thank you!
Re: A school has a total enrollment of 90 students. There are 30 students   [#permalink] 25 May 2017, 14:36
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