In a graduating class of 236 students, 142 took algebra and 121 took

Question

In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry?

A. 27
B. 54
C. 121
D. 142
E. 236

Fdambro294 · Accepted Answer

236 Total Students = (# Algebra) + (# Chemistry) - (#Both) + (#None)

236 = 142 + 121 - (B) + N

236 = 263 - B + N

B = 27 + N

Thus, to increase the overlap to its MAX, we want to maximize the number of students who took NEITHER

Since 142 took A and 121 took C ———> the most we can have that took NEITHER Subject would be:

(Total no of students) - (Higher of 2 Variables

236 - 142 = 94

94 is the MAX number of students who took neither (N)

Plugging this into the equation:

B = 27 + N

B = 27 + 94 = 121

Max students who took both is 121

Or

When there is no condition placed on the number of people who took neither (other than the numbers for each category):

Max Overlap = Lower of the 2 Set Values

Lower of (142 and 121) = 121

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Archit3110 · Answer

I solved it using 2x2 matrix IMO C ..

Sadoce18 · Answer

Bunuel  kindly explain why it isnt D-142

Logo · Answer

Since 142+121 = 263 there is clearly an overlap of students that are taking both classes. How much is that? Well, there cannot be any more than the amount of students in the group with less students between the two - in this case that is Chemistry. Answer = C. 121

ishita27 · Answer

Can someone elaborate the explanation of this Problem ?

Ajinkyagupta88 · Answer

121 took chemistry means there is a possibility that some of these took algebra as well. But "maximum student who can take chemistry is 121".

142 took algebra. The same logic applies here.

If we assume 142 students took both, this is logically not possible as "maximum 121 only can take chemistry"

Thus, the answer is 121.

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ishita27 · Answer

My thinking is that if 121 students C and A both, Then students who took C becomes a subset of students who took A. 
Doesn’t this mean that total no of students in class equal to 142 only and not 236 ??
Or are we assuming some students didn’t take either of the subject ?

Ajinkyagupta88 · Answer

Yes, your concern seems correct. The total students then becomes 121+21=142 considering only C & A students. I focussed only the maximum C & A part and the given options. Maybe, as you rightly pointed out some students may have taken neither of the two.

MV94 · Answer

If the question doesn't put a limitation "neither" can't you assume neither = total - largest, and therefore both could be as large as the smallest?

ScottTargetTestPrep · Answer

Solution:
 
The greatest number of students that could have taken both algebra and chemistry is 121, which would occur if all 121 of the students who took chemistry also took algebra.

Note that this would not account for all 236 students mentioned in the problem, so let’s finish the explanation for those who might need additional clarification (even though this is not needed for answering the question):

Total = # Chemistry + # Algebra - Both + Neither

236 = 121 + 142 - 121 + Neither

94 = Neither

Answer: C

axbycz37 · Answer

Given information: 
Class size = 236
Algebra = 142
Chemistry = 121
 None = Info not available  - This is critical to identify

Required:  Max number of students taking both

Since we do not have the number of students who have taken none of the 2 courses, we can use this number as the  balancing figure .

Now, if we assume all chemistry students take algebra as well, we have 121 students who have taken both the courses, 21 students (142-121) who have taken only Algebra and the rest (236 - 142) 94 students who have not taken any of the 2 courses.

Answer - C

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In a graduating class of 236 students, 142 took algebra and 121 took

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