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In a group of 90 students, 36 are taking History, and 32 are taking

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In a group of 90 students, 36 are taking History, and 32 are taking [#permalink]

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New post 10 Sep 2015, 00:56
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In a group of 90 students, 36 are taking History, and 32 are taking Statistics. If 59 students are taking History or Statistics or both, then how many students are taking History but not Statistics?

A) 9
B) 19
C) 23
D) 27
E) 31


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[Reveal] Spoiler: OA

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Re: In a group of 90 students, 36 are taking History, and 32 are taking [#permalink]

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New post 10 Sep 2015, 07:33
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Applying the formula:

AUB = A + B - AnB + any element that is neither A or B

Here,
AUB=90 (total # of students)
A=36 (# of students taking history)
B=32 (# of students taking statistics)
and # of students who take neither subjects is 90-59 = 31

Therefore substituting in the values,
90= 36 + 32 +31 - AnB
AnB= 9

Therefore since the number of students taking both history and statistics is 9, this means that the number of students who only take history but not statistics is 36-9= 27

Ans D.

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Re: In a group of 90 students, 36 are taking History, and 32 are taking [#permalink]

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New post 10 Sep 2015, 08:09
Bunuel wrote:
In a group of 90 students, 36 are taking History, and 32 are taking Statistics. If 59 students are taking History or Statistics or both, then how many students are taking History but not Statistics?

A) 9
B) 19
C) 23
D) 27
E) 31


Kudos for a correct solution.


Number of students taking history =H=36
Number of students taking statistics =S = 32
Total number of students = T = 90
Number of students taking History or Statistics or both = B = 59
Number of students taking neither history nor statistics = N = 90-59=31
Let X be the number of students taking both history and statistics.

Then
T = H + S + N - X

or 90 = 36 + 32 +31 - X
or X = 9

Now,
Number of students taking only history will be
H-X
or 36-9 = 27

Answer:- D

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Re: In a group of 90 students, 36 are taking History, and 32 are taking [#permalink]

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New post 06 Nov 2015, 21:29
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I just think with simply way
Number of students taking history =H=36
Number of students taking statistics =S = 32
Number of students taking History or Statistics or both = B = 59
if B-S = How take only history
then 59-32 = 27 :)

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Re: In a group of 90 students, 36 are taking History, and 32 are taking [#permalink]

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New post 07 Nov 2015, 02:17
both history and statistics = 36 + 32 - 59 = 9
taking only history = 36 - 9 = 27

Ans choice D

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Re: In a group of 90 students, 36 are taking History, and 32 are taking [#permalink]

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New post 07 Nov 2015, 03:02
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Bunuel wrote:
In a group of 90 students, 36 are taking History, and 32 are taking Statistics. If 59 students are taking History or Statistics or both, then how many students are taking History but not Statistics?

A) 9
B) 19
C) 23
D) 27
E) 31


Kudos for a correct solution.


Answer: option D

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Re: In a group of 90 students, 36 are taking History, and 32 are taking [#permalink]

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New post 11 Sep 2017, 11:07
Bunuel wrote:
In a group of 90 students, 36 are taking History, and 32 are taking Statistics. If 59 students are taking History or Statistics or both, then how many students are taking History but not Statistics?

A) 9
B) 19
C) 23
D) 27
E) 31


Kudos for a correct solution.


Since 59 students are taking history or statistics or both, 90 - 59 = 31 are taking neither. We can use the following formula to determine how many are taking both:

90 = history + statistics - both + neither

90 = 36 + 32 - b + 31

b = 9

Therefore, 36 - 9 = 27 students are taking history but not statistics.

Alternate Solution:

Since 59 students take history, statistics, or both, and since 32 students take statistics (which includes the students who take both history and statistics); 59 - 32 = 27 students take only history.

Answer: D
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Re: In a group of 90 students, 36 are taking History, and 32 are taking   [#permalink] 11 Sep 2017, 11:07
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In a group of 90 students, 36 are taking History, and 32 are taking

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