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? 
Fraction answer: 

• A. 10
• B. 15
• C. 20
• D. 30
• E.

Hint:

When dealing with problems involving sets, drawing a Venn diagram can often help visualize the maximum or minimum overlaps between the sets.

Answer 1

The Correct Option is A

Step 1: Represent the problem using a Venn diagram.
The total number of students is 236, with 142 students taking algebra and 121 students taking chemistry. The greatest possible number of students who could have taken both algebra and chemistry is when the number of students in the intersection of the two sets is maximized.
Step 2: Maximum intersection.
The maximum number of students who could have taken both subjects is the number that satisfies both \( 142 - x \leq 121 - x \), where \( x \) is the number of students who took both algebra and chemistry. The largest \( x \) is 10, making the total count consistent with the number of students who took both subjects.
Final Answer: \[ \boxed{\text{The correct answer is (A) 10.}} \]