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Question Stats:
83% (01:33) correct
17%
(02:56)
wrong
based on 20
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Three teaching assistants—Mike, Rafael, and Joanna—wrote all the questions for the class midterm. If Mike wrote 1/3 of the questions, what is the number of questions that the three teaching assistants wrote for the midterm?
(1) Joanna and Rafael wrote a total of 30 questions.
(2) Joanna wrote 3/2 the number of questions that Rafael wrote.
The OA will be automatically revealed on Saturday 30th of May 2026 12:06:15 PM Pacific Time Zone
(1) Joanna and Rafael wrote a total of 30 questions.
(2) Joanna wrote 3/2 the number of questions that Rafael wrote.
The OA will be automatically revealed on Saturday 30th of May 2026 12:06:15 PM Pacific Time Zone
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28 May 2026, 12:07
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Three teaching assistants—Mike, Rafael, and Joanna—wrote all the questions for the class midterm. If Mike wrote 1/3 of the questions, what is the number of questions that the three teaching assistants wrote for the midterm?
Since Mike wrote 1/3 of the questions, Joanna and Rafael together wrote the remaining 2/3.
(1) Joanna and Rafael wrote a total of 30 questions.
So 2/3 of the total = 30
Total = 45
Sufficient.
(2) Joanna wrote 3/2 the number of questions that Rafael wrote.
This gives only the ratio between Joanna’s and Rafael’s numbers. It does not give the actual total number of questions.
Not sufficient.
Answer: A.
Since Mike wrote 1/3 of the questions, Joanna and Rafael together wrote the remaining 2/3.
(1) Joanna and Rafael wrote a total of 30 questions.
So 2/3 of the total = 30
Total = 45
Sufficient.
(2) Joanna wrote 3/2 the number of questions that Rafael wrote.
This gives only the ratio between Joanna’s and Rafael’s numbers. It does not give the actual total number of questions.
Not sufficient.
Answer: A.
29 May 2026, 00:09
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We know that Mike wrote 1/3 of the questions. Therefore, Joanna and Rafael together must have written the remaining 2/3 of the questions.
We need to determine the total number of questions on the midterm.
Analyzing Statement (1)
Joanna and Rafael together wrote 30 questions.
Since Joanna and Rafael together account for 2/3 of the total questions:
2/3 × Total = 30
So the total number of questions is 45
The total can be uniquely determined.
Therefore, statement (1) alone is sufficient.
Analyzing Statement (2)
Joanna wrote 3/2 times the number of questions that Rafael wrote.
This only gives a ratio between Joanna’s and Rafael’s questions. Although we know together they wrote 2/3 of the total questions, we still do not know the actual number of questions written.
So the total number of questions cannot be determined.
Therefore, statement (2) alone is insufficient.
Since statement (1) alone is sufficient and statement (2) alone is not sufficient:
Correct Answer: A
We need to determine the total number of questions on the midterm.
Analyzing Statement (1)
Joanna and Rafael together wrote 30 questions.
Since Joanna and Rafael together account for 2/3 of the total questions:
2/3 × Total = 30
So the total number of questions is 45
The total can be uniquely determined.
Therefore, statement (1) alone is sufficient.
Analyzing Statement (2)
Joanna wrote 3/2 times the number of questions that Rafael wrote.
This only gives a ratio between Joanna’s and Rafael’s questions. Although we know together they wrote 2/3 of the total questions, we still do not know the actual number of questions written.
So the total number of questions cannot be determined.
Therefore, statement (2) alone is insufficient.
Since statement (1) alone is sufficient and statement (2) alone is not sufficient:
Correct Answer: A
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