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Many of the students at the International School speak French or German or both. Among the students who
speak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speak
German do speak French. What fraction of the students speak German?
(1) Exactly 60 students speak French and German.
(2) Exactly 75 students speak neither French nor German.
speak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speak
German do speak French. What fraction of the students speak German?
(1) Exactly 60 students speak French and German.
(2) Exactly 75 students speak neither French nor German.
- a)Statement ( 1 ) ALONE is sufficient but statement ( 2 ) alone is not sufficient.
- b)Statemrnt ( 2 ) ALONE is sufficient but statement ( 1 ) is not sufficient
- c)Both Stement TOGETHER are sufficient, but Neither statement ALONE is sufficient
- d)EACH stetement ALONE is sufficient
- e)Statement ( 1 ) and ( 2 ) TOGETHER are NOT Sufficient.
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
Many of the students at the International School speak French or Germa...
Since we are dealing with overlapping sets and there are two independent criteria, the best way to solve this problem is with a double-set matrix.
The first statement in the question stem tells us that of the students who speak French (represented by the first column), four times as many speak German as don't. This information yields the following entries in the double-set matrix:
The second statement in the question stem tells us that 1/6 of the of the students who don't speak German do speak French. This is fact represented in the double-set matrix as follows:
Now since x = y/6, we can get rid of the new variable y and keep all the expressions in terms of x.
Now we can fill in a few more boxes using the addition rules for the double-set matrix.
The main question to be answered is what fraction of the students speak German, a fraction represented by A/B in the final double-set matrix. So, if statements (1) and/or (2) allow us to calculate a numerical value for A/B, we will be able to answer the question.
The first statement in the question stem tells us that of the students who speak French (represented by the first column), four times as many speak German as don't. This information yields the following entries in the double-set matrix:
The second statement in the question stem tells us that 1/6 of the of the students who don't speak German do speak French. This is fact represented in the double-set matrix as follows:
Now since x = y/6, we can get rid of the new variable y and keep all the expressions in terms of x.Now we can fill in a few more boxes using the addition rules for the double-set matrix.
The main question to be answered is what fraction of the students speak German, a fraction represented by A/B in the final double-set matrix. So, if statements (1) and/or (2) allow us to calculate a numerical value for A/B, we will be able to answer the question.
(1) INSUFFICIENT: Statement (1) tells us that 60 students speak French and German, so 4x = 60 and x = 15. We can now calculate any box labeled with an x, but this is still insufficient to calculate A, B, or A/B.
(2) INSUFFICIENT: Statement (2) tells us that 75 students speak neither French nor German, so 5x = 75 and x = 15. Just as with Statement (1), we can now calculate any box labeled with an x, but this is still insufficient to calculate A, B, or A/B.
(1) AND (2) INSUFFICIENT: Since both statements give us the same information (namely, that x = 15), putting the two statements together does not tell us anything new. Therefore (1) and (2) together are insufficient.
The correct answer is E
Most Upvoted Answer
Many of the students at the International School speak French or Germa...
Understanding the Problem
To solve the problem, we need to establish relationships between students who speak French (F), German (G), and those who speak neither (N).
Given Information
- Let \( x \) be the number of students who speak German.
- Among students who speak French, the ratio of those who speak German to those who don't is 4:1.
- Additionally, 1/6 of the students who don't speak German do speak French.
Defining Variables
- Let \( F \) be the total number of students who speak French.
- Let \( D \) be the number of students who don't speak German.
- Let \( N \) be the total number of students.
From the problem, we have:
- \( 4y = x \) (where \( y \) is those who speak German but not French)
- \( \frac{1}{6}D = F - y \)
Analyzing Statements
Statement 1: Exactly 60 students speak French and German.
- We know \( F \cap G = 60 \).
- This gives no direct information about the total number of students or how many speak only one language.
Statement 2: Exactly 75 students speak neither French nor German.
- This provides information about the total number of students, but does not give the relationship among those who speak French and German.
Combining Statements
When both statements are combined:
- Knowing the number of students who speak neither and those who speak both does not give us enough to find the fraction of students who speak German without additional relationships or totals.
Conclusion
Neither statement alone is sufficient, and when combined, they still do not provide a clear relationship to solve for the fraction of students who speak German. Therefore, the correct answer is:
Option E: Statement (1) and (2) TOGETHER are NOT Sufficient.
To solve the problem, we need to establish relationships between students who speak French (F), German (G), and those who speak neither (N).
Given Information
- Let \( x \) be the number of students who speak German.
- Among students who speak French, the ratio of those who speak German to those who don't is 4:1.
- Additionally, 1/6 of the students who don't speak German do speak French.
Defining Variables
- Let \( F \) be the total number of students who speak French.
- Let \( D \) be the number of students who don't speak German.
- Let \( N \) be the total number of students.
From the problem, we have:
- \( 4y = x \) (where \( y \) is those who speak German but not French)
- \( \frac{1}{6}D = F - y \)
Analyzing Statements
Statement 1: Exactly 60 students speak French and German.
- We know \( F \cap G = 60 \).
- This gives no direct information about the total number of students or how many speak only one language.
Statement 2: Exactly 75 students speak neither French nor German.
- This provides information about the total number of students, but does not give the relationship among those who speak French and German.
Combining Statements
When both statements are combined:
- Knowing the number of students who speak neither and those who speak both does not give us enough to find the fraction of students who speak German without additional relationships or totals.
Conclusion
Neither statement alone is sufficient, and when combined, they still do not provide a clear relationship to solve for the fraction of students who speak German. Therefore, the correct answer is:
Option E: Statement (1) and (2) TOGETHER are NOT Sufficient.
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Many of the students at the International School speak French or German or both. Among the students whospeak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speakGerman do speak French. What fraction of the students speak German?(1) Exactly 60 students speak French and German.(2) Exactly 75 students speak neither French nor German.a)Statement ( 1 ) ALONE is sufficient but statement ( 2 ) alone is not sufficient.b)Statemrnt ( 2 ) ALONE is sufficient but statement ( 1 ) is not sufficientc)Both Stement TOGETHER are sufficient, but Neither statement ALONE is sufficientd)EACH stetement ALONE is sufficiente)Statement ( 1 ) and ( 2 ) TOGETHER are NOT Sufficient.Correct answer is option 'E'. Can you explain this answer?
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Many of the students at the International School speak French or German or both. Among the students whospeak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speakGerman do speak French. What fraction of the students speak German?(1) Exactly 60 students speak French and German.(2) Exactly 75 students speak neither French nor German.a)Statement ( 1 ) ALONE is sufficient but statement ( 2 ) alone is not sufficient.b)Statemrnt ( 2 ) ALONE is sufficient but statement ( 1 ) is not sufficientc)Both Stement TOGETHER are sufficient, but Neither statement ALONE is sufficientd)EACH stetement ALONE is sufficiente)Statement ( 1 ) and ( 2 ) TOGETHER are NOT Sufficient.Correct answer is option 'E'. 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 Many of the students at the International School speak French or German or both. Among the students whospeak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speakGerman do speak French. What fraction of the students speak German?(1) Exactly 60 students speak French and German.(2) Exactly 75 students speak neither French nor German.a)Statement ( 1 ) ALONE is sufficient but statement ( 2 ) alone is not sufficient.b)Statemrnt ( 2 ) ALONE is sufficient but statement ( 1 ) is not sufficientc)Both Stement TOGETHER are sufficient, but Neither statement ALONE is sufficientd)EACH stetement ALONE is sufficiente)Statement ( 1 ) and ( 2 ) TOGETHER are NOT Sufficient.Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Many of the students at the International School speak French or German or both. Among the students whospeak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speakGerman do speak French. What fraction of the students speak German?(1) Exactly 60 students speak French and German.(2) Exactly 75 students speak neither French nor German.a)Statement ( 1 ) ALONE is sufficient but statement ( 2 ) alone is not sufficient.b)Statemrnt ( 2 ) ALONE is sufficient but statement ( 1 ) is not sufficientc)Both Stement TOGETHER are sufficient, but Neither statement ALONE is sufficientd)EACH stetement ALONE is sufficiente)Statement ( 1 ) and ( 2 ) TOGETHER are NOT Sufficient.Correct answer is option 'E'. Can you explain this answer?.
Many of the students at the International School speak French or German or both. Among the students whospeak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speakGerman do speak French. What fraction of the students speak German?(1) Exactly 60 students speak French and German.(2) Exactly 75 students speak neither French nor German.a)Statement ( 1 ) ALONE is sufficient but statement ( 2 ) alone is not sufficient.b)Statemrnt ( 2 ) ALONE is sufficient but statement ( 1 ) is not sufficientc)Both Stement TOGETHER are sufficient, but Neither statement ALONE is sufficientd)EACH stetement ALONE is sufficiente)Statement ( 1 ) and ( 2 ) TOGETHER are NOT Sufficient.Correct answer is option 'E'. 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 Many of the students at the International School speak French or German or both. Among the students whospeak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speakGerman do speak French. What fraction of the students speak German?(1) Exactly 60 students speak French and German.(2) Exactly 75 students speak neither French nor German.a)Statement ( 1 ) ALONE is sufficient but statement ( 2 ) alone is not sufficient.b)Statemrnt ( 2 ) ALONE is sufficient but statement ( 1 ) is not sufficientc)Both Stement TOGETHER are sufficient, but Neither statement ALONE is sufficientd)EACH stetement ALONE is sufficiente)Statement ( 1 ) and ( 2 ) TOGETHER are NOT Sufficient.Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Many of the students at the International School speak French or German or both. Among the students whospeak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speakGerman do speak French. What fraction of the students speak German?(1) Exactly 60 students speak French and German.(2) Exactly 75 students speak neither French nor German.a)Statement ( 1 ) ALONE is sufficient but statement ( 2 ) alone is not sufficient.b)Statemrnt ( 2 ) ALONE is sufficient but statement ( 1 ) is not sufficientc)Both Stement TOGETHER are sufficient, but Neither statement ALONE is sufficientd)EACH stetement ALONE is sufficiente)Statement ( 1 ) and ( 2 ) TOGETHER are NOT Sufficient.Correct answer is option 'E'. Can you explain this answer?.
Solutions for Many of the students at the International School speak French or German or both. Among the students whospeak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speakGerman do speak French. What fraction of the students speak German?(1) Exactly 60 students speak French and German.(2) Exactly 75 students speak neither French nor German.a)Statement ( 1 ) ALONE is sufficient but statement ( 2 ) alone is not sufficient.b)Statemrnt ( 2 ) ALONE is sufficient but statement ( 1 ) is not sufficientc)Both Stement TOGETHER are sufficient, but Neither statement ALONE is sufficientd)EACH stetement ALONE is sufficiente)Statement ( 1 ) and ( 2 ) TOGETHER are NOT Sufficient.Correct answer is option 'E'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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ample number of questions to practice Many of the students at the International School speak French or German or both. Among the students whospeak French, four times as many speak German as don't. In addition, 1/6 of the students who don't speakGerman do speak French. What fraction of the students speak German?(1) Exactly 60 students speak French and German.(2) Exactly 75 students speak neither French nor German.a)Statement ( 1 ) ALONE is sufficient but statement ( 2 ) alone is not sufficient.b)Statemrnt ( 2 ) ALONE is sufficient but statement ( 1 ) is not sufficientc)Both Stement TOGETHER are sufficient, but Neither statement ALONE is sufficientd)EACH stetement ALONE is sufficiente)Statement ( 1 ) and ( 2 ) TOGETHER are NOT Sufficient.Correct answer is option 'E'. Can you explain this answer? tests, examples and also practice GMAT tests.
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