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In the results of a survey administered to the students in a particula

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Bunuel
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In the results of a survey administered to the students in a particula [#permalink] New post   21 Aug 2019, 22:47
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In the results of a survey administered to the students in a particular class, 1/3 identified themselves as citizens of the U.S. only, 1/3 identified themselves as not U.S. citizens, 1/10 identified themselves as citizens of both the U.S. and at least one other country, and 28 students did not reply to the survey. What is the number of students in the class?

A. 60
B. 110
C. 120
D. 200
E. 400
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C
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Archit3110
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In the results of a survey administered to the students in a particula [#permalink] New post   Updated on: 22 Aug 2019, 08:08
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Bunuel wrote:
In the results of a survey administered to the students in a particular class, 1/3 identified themselves as citizens of the U.S. only, 1/3 identified themselves as not U.S. citizens, 1/10 identified themselves as citizens of both the U.S. and at least one other country, and 28 students did not reply to the survey. What is the number of students in the class?

A. 60
B. 110
C. 120
D. 200
E. 400


given
x/3+x/3+x/10 ; 23x/30
7x/30 = 28
x= 120
IMO C

Originally posted by Archit3110 on 22 Aug 2019, 03:55.
Last edited by Archit3110 on 22 Aug 2019, 08:08, edited 1 time in total.
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teja18892
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Re: In the results of a survey administered to the students in a particula [#permalink] New post   22 Aug 2019, 04:48
In my Opinion, the answer is C

Assuming the class size is 120 students.

1/3 - Are US Citizens = 120 *1/3 = 40 students
1/3 - Non US Citizens = 120 * 1/3 = 40 Students
1/10 - Are dual nationals = 120 *1/10 = 12 Students
Did not answer survey = 28 Students

40 + 40 + 12 + 28 = 120 Students

This was the only one that satisfies the criteria.
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AcetheGMAT2019
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In the results of a survey administered to the students in a particula [#permalink] New post   22 Aug 2019, 06:11
Easiest way to solve this is by using a Venn diagram

Please see attached sheet
Let total number of students be x
Thus 1x/3 + 1x/3 +1x/10 = 23x/30
Which means 7x/30 equals 28
So x equals 120
That's the answer
Attachments

venn.jpg
venn.jpg [ 88.58 KiB | Viewed 1189 times ]

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Re: In the results of a survey administered to the students in a particula [#permalink] New post   24 Aug 2019, 05:37
Expert Reply
Bunuel wrote:
In the results of a survey administered to the students in a particular class, 1/3 identified themselves as citizens of the U.S. only, 1/3 identified themselves as not U.S. citizens, 1/10 identified themselves as citizens of both the U.S. and at least one other country, and 28 students did not reply to the survey. What is the number of students in the class?

A. 60
B. 110
C. 120
D. 200
E. 400


Letting n = the total number of students in the class, we can create the equation:

n = n/3 + n/3 + n/10 + 28

Multiplying by 30, we have:

30n = 10n + 10n + 3n + 840

7n = 840

n = 120

Answer: C
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Re: In the results of a survey administered to the students in a particula [#permalink]
24 Aug 2019, 05:37
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