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

Question

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 .

GMATinsight · Accepted Answer

Answer: option D

IN all such questions of 2 sets, Double-Matrix Methods serves best purpose.

adamlee · Answer

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

Jsalim2710 · Answer

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.

kunal555 · Answer

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

v12345 · Answer

both history and statistics = 36 + 32 - 59 = 9 
taking only history = 36 - 9 = 27

Ans choice D

ScottTargetTestPrep · Answer

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

nikitamaheshwari · Answer

Shouldn't this question have only history, only statistics or both ?

GMATinsight · Answer

nikitamaheshwari

The rule of GMAT is never use assumptions in a quant problem.

Till the question doesn't specify that everyone is taking atleast one subject, don;t assume that students taking none are zero

Here question is pretty clear though.

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