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Two of the courses from which the 98 freshmen at a high school may choose are French and Creative Writing. 
How many freshmen enrolled in neither course?
Statement 1: 10 freshmen enrolled in both courses.
Statement 2: 21 freshmen enrolled in each course.
  • a)
    EITHER statement ALONE is sufficient to answer the question.
  • b)
    BOTH statements TOGETHER are insufficient to answer the question. 
  • c)
    BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
  • d)
    Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
  • e)
    Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Two of the courses from which the 98 freshmen at a high school may cho...
The question asks for the number of students in the set F′∩C′, where F and C are the sets of students who took French and Creative Writing, respectively.
From Statement 1 alone, a Venn diagram representing this situation can be filled in as follows:
It is known that x + y + z + 10 = 98; subsequently, x + y + z = 88. But no other information is given, so x, the desired quantity, cannot be calculated.
From Statement 2 alone, a Venn diagram representing this situation can be filled in as follows:
Again, no further information can be computed.
Now assume that both statements are true. Then it follows from Statement 1 that w=10, and it follows from Statement 2 that the desired quantity is 
56 + w = 56 + 10 = 66.
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Community Answer
Two of the courses from which the 98 freshmen at a high school may cho...
Given information:
- Total number of freshmen at the high school = 98
- Two courses available for enrollment: French and Creative Writing

To find:
- Number of freshmen enrolled in neither course

Statement 1:
- 10 freshmen enrolled in both courses

This statement alone does not provide any information about the number of freshmen enrolled in neither course. It only tells us that there are 10 freshmen who have enrolled in both courses. It is possible that all other freshmen have enrolled in either French or Creative Writing or both, or some freshmen may have enrolled in neither course.

Statement 2:
- 21 freshmen enrolled in each course

This statement alone does not provide any information about the number of freshmen enrolled in neither course. It only tells us that there are 21 freshmen who have enrolled in each course. However, we don't know if these 21 freshmen are the only ones who enrolled in these courses or if there are additional freshmen who enrolled in only one of the courses or none at all.

Statements 1 and 2 together:

Combining the information from both statements, we know that:
- 10 freshmen enrolled in both courses
- 21 freshmen enrolled in each course

From the given information, we can deduce the following:
- The total number of freshmen enrolled in French = 10 + 21 = 31
- The total number of freshmen enrolled in Creative Writing = 10 + 21 = 31

However, we still don't have enough information to determine the number of freshmen enrolled in neither course. It is possible that all 98 freshmen enrolled in either French or Creative Writing or both, or some freshmen may have enrolled in neither course.

Conclusion:

Neither statement alone is sufficient to answer the question, but by combining both statements, we still cannot determine the number of freshmen enrolled in neither course. Therefore, the correct answer is option C: BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
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Two of the courses from which the 98 freshmen at a high school may choose are French and Creative Writing.How many freshmen enrolled in neither course?Statement 1: 10 freshmen enrolled in both courses.Statement 2: 21 freshmen enrolled in each course.a)EITHER statement ALONE is sufficient to answer the question.b)BOTH statements TOGETHER are insufficient to answer the question.c)BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.d)Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.e)Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.Correct answer is option 'C'. Can you explain this answer?
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Two of the courses from which the 98 freshmen at a high school may choose are French and Creative Writing.How many freshmen enrolled in neither course?Statement 1: 10 freshmen enrolled in both courses.Statement 2: 21 freshmen enrolled in each course.a)EITHER statement ALONE is sufficient to answer the question.b)BOTH statements TOGETHER are insufficient to answer the question.c)BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.d)Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.e)Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.Correct answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Two of the courses from which the 98 freshmen at a high school may choose are French and Creative Writing.How many freshmen enrolled in neither course?Statement 1: 10 freshmen enrolled in both courses.Statement 2: 21 freshmen enrolled in each course.a)EITHER statement ALONE is sufficient to answer the question.b)BOTH statements TOGETHER are insufficient to answer the question.c)BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.d)Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.e)Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two of the courses from which the 98 freshmen at a high school may choose are French and Creative Writing.How many freshmen enrolled in neither course?Statement 1: 10 freshmen enrolled in both courses.Statement 2: 21 freshmen enrolled in each course.a)EITHER statement ALONE is sufficient to answer the question.b)BOTH statements TOGETHER are insufficient to answer the question.c)BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.d)Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.e)Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.Correct answer is option 'C'. Can you explain this answer?.
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