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04 Mar 2025, 01:30
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All of the students in a certain class took a test consisting of 20 questions. Did at least two students have the same number of correct answers on the test?
(1) Each student answered an even number of questions correctly.
(2) There are more than 11 students in the class.
(1) Each student answered an even number of questions correctly.
(2) There are more than 11 students in the class.
04 Mar 2025, 01:50
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Total Q = 20
Total Students = S
Statement 1
Each student answered even number of questions correctly.
We have 11 possible values 0,2,4,....,20
If S> 11, then answer is Yes else No
Without knowing the number of students, we cannot say if 2 students have the same number of correct answers
Insufficient
Statement 2
S >11
The possible number of correct answers for each of them could be anything
1,2,3,4,5,...,11 OR All 20
Insufficient
Combined, we know the answer is Yes as S > 11 and this was the missing piece in Statement 1 to answer the prompt. Answer C
Total Students = S
Statement 1
Each student answered even number of questions correctly.
We have 11 possible values 0,2,4,....,20
If S> 11, then answer is Yes else No
Without knowing the number of students, we cannot say if 2 students have the same number of correct answers
Insufficient
Statement 2
S >11
The possible number of correct answers for each of them could be anything
1,2,3,4,5,...,11 OR All 20
Insufficient
Combined, we know the answer is Yes as S > 11 and this was the missing piece in Statement 1 to answer the prompt. Answer C
Bunuel
04 Mar 2025, 02:55
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Question: Did atleast two students have the same number of correct answers?
Given: Total Questions = 20
Statement 1: Each student answered an even number of questions correctly.
i.e. Correct answers of students are {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} [10 possibilities]
But the number of students is unknown where as we know that there could be only 10 possible different response outcomes as mentioned above hence
NOT SUFFICIENT
Statement 2: There are more than 11 students in the class.
For 12 students their correct number of questions could be {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}i.e. NO to question
For 12 students their correct number of questions could be {1, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} i.e. YES to question
NOT SUFFICIENT
Combining the statements
As per statement-1, there can be only 10 possible outcomes of number of correct
Since the number of students is greater than 11 (statetemtn2) therefore atleast two students MUST have same number of correct hence
SUFFICIENT
Answer: Option C
Related Video:
[b]
Given: Total Questions = 20
Statement 1: Each student answered an even number of questions correctly.
i.e. Correct answers of students are {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} [10 possibilities]
But the number of students is unknown where as we know that there could be only 10 possible different response outcomes as mentioned above hence
NOT SUFFICIENT
Statement 2: There are more than 11 students in the class.
For 12 students their correct number of questions could be {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}i.e. NO to question
For 12 students their correct number of questions could be {1, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} i.e. YES to question
NOT SUFFICIENT
Combining the statements
As per statement-1, there can be only 10 possible outcomes of number of correct
Since the number of students is greater than 11 (statetemtn2) therefore atleast two students MUST have same number of correct hence
SUFFICIENT
Answer: Option C
Related Video:
[b]
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Bunuel
