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A teacher took a pre-announced test in a class 3/4th. of the students had not prepared for the test. Of the students who had prepared for the test, 2/3rd passed the test. If only 25 percent of the class passed the test, what fraction of the students who had not prepared for the test, failed the test?
- a)1/12
- b)1/9
- c)1/2
- d)2/3
- e)(8over 9)
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
A teacher took a pre-announced test in a class 3/4th. of the students ...
Given:
- Number of students who did not prepare for the test =3/4 of the total student
- Number of students who prepared for the test = 1/4 of the total student
- Number of students who prepared and passed the test = 2/3of the students who prepared for the test
- Number of students who passed the test = 25% of the total students
- Number of students who failed the test = 75% of the total students
- Number of students who failed the test = 75% of the total students
To Find: fraction of the students who had not prepared for the test and failed the test?
Approach:
- Required Fraction =
- So, we need to either find the values of both “Number of students who did not prepare and failed the test” and “Number of students who did not prepare for the test” or express both of them in terms of a common variable
- As we are not given any information about the number of students, we will try to express both of them in terms of a common variable
- Number of students who did not prepare for the test
- Let’s assume the total number of students in the class be x.
As we know that Number of students who did not prepare for the test = 3/4 of the total student, we can find the number of students who did not prepare for the test in terms of x. - Also that would give us the number of students who prepared for the test in terms of x.
- Let’s assume the total number of students in the class be x.
- Number of students who did not prepare for the test and failed the test
- We know that number of students who failed the test = 75% of the total students
- Also, number of students who failed the test = Number of students who prepared and failed the test + Number of students who did not prepare and failed the test
- Now, we know that Number of students who prepared and passed the test =2/3 of the students who prepared for the test.
- So, number of students who prepared and failed the test = (Number of students who prepared) – (number of students who prepared and passed the test)
- Using the above relation, we can find the number of students who prepared and failed the test in terms of x.
Working out:
- Number of students who did not prepare for the test = 3/4 of the total student =
- So, number of students who prepared for the test =
2. Number of students who failed the test = 75% of x = 3/4
3. Also, number of students who failed the test = Number of students who prepared and failed the test + Number of students who did not prepare and failed the test
- 3/4 = Number of students who prepared and failed the test + Number of students who did not prepare and failed the test.
- Now, we are given that Number of students who prepared and passed the test = 2/3 of the students who prepared for the test =
- So, number of students who prepared and failed the test =
- Using (3.a), (3.b) and (3.c), we can write
Number of students who did not prepare and failed the test, which gives us the number of students who did not prepare and failed the test = 2/3
Answer E
Most Upvoted Answer
A teacher took a pre-announced test in a class 3/4th. of the students ...
To solve this problem, we can break it down into smaller parts and use fractions to represent the different groups of students.
Let's assume that there are a total of 100 students in the class.
1. Students who did not prepare for the test:
Since 3/4th of the students did not prepare for the test, the fraction of students who did not prepare is 3/4 * 100 = 75 students.
2. Students who prepared for the test:
The remaining students who prepared for the test would be 100 - 75 = 25 students.
3. Students who passed the test:
Given that 25% of the class passed the test, the number of students who passed is 25% * 100 = 25 students.
4. Students who prepared and passed the test:
Since 2/3rd of the students who prepared for the test passed, the fraction of students who prepared and passed is 2/3 * 25 = 50/3 ≈ 16.67 students.
Now, let's find the fraction of students who did not prepare and failed the test.
5. Students who prepared and failed the test:
The number of students who prepared and failed the test would be the difference between the total number of students who prepared (25) and the number of students who prepared and passed (16.67).
So, the number of students who prepared and failed the test is 25 - 16.67 = 8.33 students.
6. Students who did not prepare and failed the test:
Since the total number of students who failed the test is 100 - 25 = 75 students, and we know that 8.33 students who prepared failed, the remaining students who failed must be the students who did not prepare.
So, the number of students who did not prepare and failed the test is 75 - 8.33 = 66.67 students.
Finally, let's express the fraction of students who did not prepare and failed the test.
7. Fraction of students who did not prepare and failed the test:
The fraction of students who did not prepare and failed the test would be 66.67 students out of the total number of students who did not prepare (75).
So, the fraction is 66.67/75 = 8/9.
Therefore, the fraction of students who had not prepared for the test and failed the test is 8/9, which corresponds to option 'E'.
Let's assume that there are a total of 100 students in the class.
1. Students who did not prepare for the test:
Since 3/4th of the students did not prepare for the test, the fraction of students who did not prepare is 3/4 * 100 = 75 students.
2. Students who prepared for the test:
The remaining students who prepared for the test would be 100 - 75 = 25 students.
3. Students who passed the test:
Given that 25% of the class passed the test, the number of students who passed is 25% * 100 = 25 students.
4. Students who prepared and passed the test:
Since 2/3rd of the students who prepared for the test passed, the fraction of students who prepared and passed is 2/3 * 25 = 50/3 ≈ 16.67 students.
Now, let's find the fraction of students who did not prepare and failed the test.
5. Students who prepared and failed the test:
The number of students who prepared and failed the test would be the difference between the total number of students who prepared (25) and the number of students who prepared and passed (16.67).
So, the number of students who prepared and failed the test is 25 - 16.67 = 8.33 students.
6. Students who did not prepare and failed the test:
Since the total number of students who failed the test is 100 - 25 = 75 students, and we know that 8.33 students who prepared failed, the remaining students who failed must be the students who did not prepare.
So, the number of students who did not prepare and failed the test is 75 - 8.33 = 66.67 students.
Finally, let's express the fraction of students who did not prepare and failed the test.
7. Fraction of students who did not prepare and failed the test:
The fraction of students who did not prepare and failed the test would be 66.67 students out of the total number of students who did not prepare (75).
So, the fraction is 66.67/75 = 8/9.
Therefore, the fraction of students who had not prepared for the test and failed the test is 8/9, which corresponds to option 'E'.
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A teacher took a pre-announced test in a class 3/4th. of the students had not prepared for the test. Of the students who had prepared for the test, 2/3rdpassed the test. If only 25 percent of the class passed the test, what fraction of the students who had not prepared for the test, failed the test?a)1/12b)1/9c)1/2d)2/3e)(8over 9)Correct answer is option 'E'. Can you explain this answer?
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A teacher took a pre-announced test in a class 3/4th. of the students had not prepared for the test. Of the students who had prepared for the test, 2/3rdpassed the test. If only 25 percent of the class passed the test, what fraction of the students who had not prepared for the test, failed the test?a)1/12b)1/9c)1/2d)2/3e)(8over 9)Correct answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A teacher took a pre-announced test in a class 3/4th. of the students had not prepared for the test. Of the students who had prepared for the test, 2/3rdpassed the test. If only 25 percent of the class passed the test, what fraction of the students who had not prepared for the test, failed the test?a)1/12b)1/9c)1/2d)2/3e)(8over 9)Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A teacher took a pre-announced test in a class 3/4th. of the students had not prepared for the test. Of the students who had prepared for the test, 2/3rdpassed the test. If only 25 percent of the class passed the test, what fraction of the students who had not prepared for the test, failed the test?a)1/12b)1/9c)1/2d)2/3e)(8over 9)Correct answer is option 'E'. Can you explain this answer?.
A teacher took a pre-announced test in a class 3/4th. of the students had not prepared for the test. Of the students who had prepared for the test, 2/3rdpassed the test. If only 25 percent of the class passed the test, what fraction of the students who had not prepared for the test, failed the test?a)1/12b)1/9c)1/2d)2/3e)(8over 9)Correct answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A teacher took a pre-announced test in a class 3/4th. of the students had not prepared for the test. Of the students who had prepared for the test, 2/3rdpassed the test. If only 25 percent of the class passed the test, what fraction of the students who had not prepared for the test, failed the test?a)1/12b)1/9c)1/2d)2/3e)(8over 9)Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A teacher took a pre-announced test in a class 3/4th. of the students had not prepared for the test. Of the students who had prepared for the test, 2/3rdpassed the test. If only 25 percent of the class passed the test, what fraction of the students who had not prepared for the test, failed the test?a)1/12b)1/9c)1/2d)2/3e)(8over 9)Correct answer is option 'E'. Can you explain this answer?.
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