In a class of 345 students, equal number of students enrolled in Engli

Question

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

A. 108
B. 124
C. 178
D. 246
E. 286

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ArunSharma12 · Answer

img1.png a + b + c + x + y + z + m = 345 - 43 = 302 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

CrackverbalGMAT · Answer

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:

Attachment:

25th April 2020 - Reply 4 - 1.jpg [ 32.01 KiB | Viewed 10542 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 10330 times ]

The correct answer option is C
.
Hope that helps!

Kinshook · Answer

Given: 
1. In a class of 345 students, equal number of students enrolled in English club, Math club and Science club. 
2. 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.

Asked: 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?

Please see the solution in attached image.

Number of students enrolled in both English and Math clubs but not in Science club = 80 + 82 + 16 = 178

IMO C

ScottTargetTestPrep · Answer

We can create an equation using the following formula:

Total = N(E) + N(M) + N(S) - N(E and M) - N(M and S) - N(E and S) + N(all three) + N(none)

345 = n + n + n - 30 - 26 - 28 + 14 + 43

345 = 3n - 84 + 57

345 = 3n - 27

372 = 3n

124 = n

The number of students enrolled in either the English club or the Math club but not in the Science club is:

Total - N(S) - N(none)

345 - 124 - 43 = 178

Answer: C

iammanas · Answer

Thanks for the solution, Sir. I understood what you have done. However, I have a doubt about how the question is phrased - "BOTH English and Maths but not Science. Should the answer then not be 16? That is the only area where students are enrolled in both but not in the third subject.

CrackVerbal 
 ArvindCrackVerbal

chacinluis · Answer

Absolutely!!....The question is not asking for the number of students enrolled in Math or English but not Science, it is saying Math AND English but not Science. So the answer should be 16.

SirSanguine · Answer

I understood the solution but my doubt is : Isn't the final statement confusing? ; "how many students enrolled in both English and Math clubs but not in Science club?". Doesn't this mean E Int M-E int M int S.?

Adit_ · Answer

No..the question says "BOTH" this and that meaning u account for this and that inclusive and not just the intersection.

nnnsss · Answer

I think in the question you mean to say "either" English or Math, not "both". Based upon your solution, question is misleadingly worded.

Adit_ · Answer

no of students in both english and math means inclusive of both individually as well as together. Think of it like, a collection of people belonging to this and that. If the question no.of people in english and math ONLY, then it would be like you imagine.

Hope it helps.

Hope it helps.

nnnsss · Answer

That’s not how we use those words in America. I’ve been teaching math in the US for the last 27 years. We use either A or B to mean A U B. And both A and B to mean A intersection B.

In a class of 345 students, equal number of students enrolled in Engli

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