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23 Apr 2020, 03:32
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
66% (03:17) correct
34%
(03:36)
wrong
based on 138
sessions
History
Date
Time
Result
Not Attempted Yet
In a class of 345 students, equal number of students enrolled in English club, Math club and Science club. 30 students enrolled both in English club and Math club, 26 students enrolled both in Math club and Science club, 28 students enrolled both in Science club and English club and 14 students enrolled in all three clubs. If there are 43 students who didn’t enroll in any of the three clubs, how many students enrolled in both English and Math clubs but not in Science club?
A. 108
B. 124
C. 178
D. 246
E. 286
Are You Up For the Challenge: 700 Level Questions
A. 108
B. 124
C. 178
D. 246
E. 286
Are You Up For the Challenge: 700 Level Questions
ArunSharma12
Joined: 25 Oct 2015
Last visit: 20 Jul 2022
Posts: 513
Given Kudos: 74
Location: India
Schools: IIML-IPMX '22 (A)
GMAT 1: 650 Q48 V31
GMAT 2: 720 Q49 V38 (Online)
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23 Apr 2020, 07:05
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Bunuel
Attachment:
img1.png [ 8.5 KiB | Viewed 9401 times ]
x + m =30
z + m = 26
y + m = 28
m = 14
x = 16, y = 14 & z = 12
a + b + c = 302 - (x + y + z + m) = 302 - 56 = 246
all three clubs have equal number of students
a + x + y + m = b + x + z + m
b = a + 2
a + x + y + m = c + y + z + m
c = a + 4
a + a+ 2 + a + 4 = 246
3a = 240; a = 80 & b = 82
required number of students enrolled in both English and Math clubs but not in Science club = a + b + x = 80 + 82 + 16 = 178
Ans: C
25 Apr 2020, 06:29
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In a question on Venn diagrams, we try to evaluate the word problem in small chunks without trying to consume the whole question in one go.
When the Venn diagram is being drawn, we try to populate the common regions first followed by the exclusive regions i.e. we proceed outwards from the inner regions.
We also ensure that we don’t ignore the numbers that can be outside the circles but inside the rectangle.
Considering all the above, we can draw a Venn diagram for the given question which looks like the one below:
25th April 2020 - Reply 4 - 1.jpg [ 32.01 KiB | Viewed 9032 times ]
The question says that equal number of students enrolled for the English, Math and Science clubs. This essentially means that the total number of people in each of these circles should be the same.
Therefore,
a + 44 = b + 42 which gives us a = b – 2
c + 40 = b + 42 which gives us c = b + 2.
Total number of people inside the circles = 345 – People who opted for none of the clubs = 345 – 43 = 302.
Therefore, a + b + c + 14 + 16 + 14 + 12 = 302 OR a + b + c = 246.
Substituting the values of a and c in the above equation and simplifying, we get b = 82, a = 80 and c = 84.
We do not want the students enrolled in the Science Club, therefore, we consider the regions outside the Science circle (marked in red) i.e. a+16 + b = 80 + 16 + 82 = 178.
25th April 2020 - Reply 4 - 2.jpg [ 33.14 KiB | Viewed 8846 times ]
The correct answer option is C
.
Hope that helps!
When the Venn diagram is being drawn, we try to populate the common regions first followed by the exclusive regions i.e. we proceed outwards from the inner regions.
We also ensure that we don’t ignore the numbers that can be outside the circles but inside the rectangle.
Considering all the above, we can draw a Venn diagram for the given question which looks like the one below:
Attachment:
25th April 2020 - Reply 4 - 1.jpg [ 32.01 KiB | Viewed 9032 times ]
The question says that equal number of students enrolled for the English, Math and Science clubs. This essentially means that the total number of people in each of these circles should be the same.
Therefore,
a + 44 = b + 42 which gives us a = b – 2
c + 40 = b + 42 which gives us c = b + 2.
Total number of people inside the circles = 345 – People who opted for none of the clubs = 345 – 43 = 302.
Therefore, a + b + c + 14 + 16 + 14 + 12 = 302 OR a + b + c = 246.
Substituting the values of a and c in the above equation and simplifying, we get b = 82, a = 80 and c = 84.
We do not want the students enrolled in the Science Club, therefore, we consider the regions outside the Science circle (marked in red) i.e. a+16 + b = 80 + 16 + 82 = 178.
Attachment:
25th April 2020 - Reply 4 - 2.jpg [ 33.14 KiB | Viewed 8846 times ]
The correct answer option is C
.
Hope that helps!
