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

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Joined: 02 Sep 2009
Posts: 58381
In a group of 90 students, 36 are taking History, and 32 are taking  [#permalink]

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10 Sep 2015, 00:56
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Difficulty:

25% (medium)

Question Stats:

76% (01:57) correct 24% (02:20) wrong based on 193 sessions

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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

Kudos for a correct solution.

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Joined: 06 Nov 2015
Posts: 1
Re: In a group of 90 students, 36 are taking History, and 32 are taking  [#permalink]

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06 Nov 2015, 21:29
3
2
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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07 Nov 2015, 03:02
2
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.

IN all such questions of 2 sets, Double-Matrix Methods serves best purpose.
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Posts: 155
Re: In a group of 90 students, 36 are taking History, and 32 are taking  [#permalink]

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10 Sep 2015, 08:09
1
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

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

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11 Sep 2017, 11:07
1
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.

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Intern
Joined: 01 Jun 2015
Posts: 4
Re: In a group of 90 students, 36 are taking History, and 32 are taking  [#permalink]

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10 Sep 2015, 07:33
1
2
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.
Manager
Joined: 01 Mar 2015
Posts: 69
Re: In a group of 90 students, 36 are taking History, and 32 are taking  [#permalink]

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07 Nov 2015, 02:17
1
both history and statistics = 36 + 32 - 59 = 9
taking only history = 36 - 9 = 27

Ans choice D
Re: In a group of 90 students, 36 are taking History, and 32 are taking   [#permalink] 07 Nov 2015, 02:17
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