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To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?
- a)30,000
- b)2,70,000
- c)3,90,000
- d)4,20,000
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
To pass a test, a candidate needs to answer at least 2 out of 3 questi...
Given Information:
- Total number of candidates appeared for the test = 6,30,000
- Number of candidates who answered Question A correctly = 3,30,000
- Number of candidates who answered Question B correctly = 2,50,000
- Number of candidates who answered Question C correctly = 2,60,000
- Number of candidates who answered both questions A and B correctly = 1,00,000
- Number of candidates who answered both questions B and C correctly = 90,000
- Number of candidates who answered both questions A and C correctly = 80,000
- Number of candidates who answered all questions correctly = Number of candidates answering none (unknown)
Approach:
To find the number of candidates who failed to clear the test, we need to determine the number of candidates who answered exactly one question correctly and the number of candidates who answered none of the questions correctly.
Solution:
Let's calculate the number of candidates who answered exactly one question correctly.
Number of candidates who answered exactly one question correctly:
To calculate the number of candidates who answered exactly one question correctly, we can use the principle of inclusion-exclusion.
We'll add the number of candidates who answered each question correctly and subtract the number of candidates who answered multiple questions correctly.
Number of candidates who answered exactly question A correctly = Number of candidates who answered question A correctly - Number of candidates who answered both questions A and B correctly - Number of candidates who answered both questions A and C correctly + Number of candidates who answered all questions correctly
= 3,30,000 - 1,00,000 - 80,000 + Number of candidates who answered all questions correctly (unknown)
Similarly, we can calculate the number of candidates who answered exactly question B correctly and exactly question C correctly.
Number of candidates who answered exactly question B correctly = Number of candidates who answered question B correctly - Number of candidates who answered both questions A and B correctly - Number of candidates who answered both questions B and C correctly + Number of candidates who answered all questions correctly (unknown)
= 2,50,000 - 1,00,000 - 90,000 + Number of candidates who answered all questions correctly (unknown)
Number of candidates who answered exactly question C correctly = Number of candidates who answered question C correctly - Number of candidates who answered both questions A and C correctly - Number of candidates who answered both questions B and C correctly + Number of candidates who answered all questions correctly (unknown)
= 2,60,000 - 80,000 - 90,000 + Number of candidates who answered all questions correctly (unknown)
Number of candidates who answered none of the questions correctly:
Given that the number of candidates who answered all questions correctly is the same as the number answering none, let's denote this common value as 'x'.
Therefore, the number of candidates who answered none of the questions correctly = x
Number of candidates who failed to clear the test:
The candidates who failed to clear the test are those who either answered exactly one question correctly or answered none of the questions correctly.
Number of candidates who failed to clear the test = Number of candidates who answered exactly one question correctly + Number of candidates who answered none of the questions correctly
= (Number of candidates who answered exactly question A correctly + Number of candidates who answered exactly question
- Total number of candidates appeared for the test = 6,30,000
- Number of candidates who answered Question A correctly = 3,30,000
- Number of candidates who answered Question B correctly = 2,50,000
- Number of candidates who answered Question C correctly = 2,60,000
- Number of candidates who answered both questions A and B correctly = 1,00,000
- Number of candidates who answered both questions B and C correctly = 90,000
- Number of candidates who answered both questions A and C correctly = 80,000
- Number of candidates who answered all questions correctly = Number of candidates answering none (unknown)
Approach:
To find the number of candidates who failed to clear the test, we need to determine the number of candidates who answered exactly one question correctly and the number of candidates who answered none of the questions correctly.
Solution:
Let's calculate the number of candidates who answered exactly one question correctly.
Number of candidates who answered exactly one question correctly:
To calculate the number of candidates who answered exactly one question correctly, we can use the principle of inclusion-exclusion.
We'll add the number of candidates who answered each question correctly and subtract the number of candidates who answered multiple questions correctly.
Number of candidates who answered exactly question A correctly = Number of candidates who answered question A correctly - Number of candidates who answered both questions A and B correctly - Number of candidates who answered both questions A and C correctly + Number of candidates who answered all questions correctly
= 3,30,000 - 1,00,000 - 80,000 + Number of candidates who answered all questions correctly (unknown)
Similarly, we can calculate the number of candidates who answered exactly question B correctly and exactly question C correctly.
Number of candidates who answered exactly question B correctly = Number of candidates who answered question B correctly - Number of candidates who answered both questions A and B correctly - Number of candidates who answered both questions B and C correctly + Number of candidates who answered all questions correctly (unknown)
= 2,50,000 - 1,00,000 - 90,000 + Number of candidates who answered all questions correctly (unknown)
Number of candidates who answered exactly question C correctly = Number of candidates who answered question C correctly - Number of candidates who answered both questions A and C correctly - Number of candidates who answered both questions B and C correctly + Number of candidates who answered all questions correctly (unknown)
= 2,60,000 - 80,000 - 90,000 + Number of candidates who answered all questions correctly (unknown)
Number of candidates who answered none of the questions correctly:
Given that the number of candidates who answered all questions correctly is the same as the number answering none, let's denote this common value as 'x'.
Therefore, the number of candidates who answered none of the questions correctly = x
Number of candidates who failed to clear the test:
The candidates who failed to clear the test are those who either answered exactly one question correctly or answered none of the questions correctly.
Number of candidates who failed to clear the test = Number of candidates who answered exactly one question correctly + Number of candidates who answered none of the questions correctly
= (Number of candidates who answered exactly question A correctly + Number of candidates who answered exactly question
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To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?a)30,000b)2,70,000c)3,90,000d)4,20,000Correct answer is option 'D'. Can you explain this answer?
Question Description
To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?a)30,000b)2,70,000c)3,90,000d)4,20,000Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?a)30,000b)2,70,000c)3,90,000d)4,20,000Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?a)30,000b)2,70,000c)3,90,000d)4,20,000Correct answer is option 'D'. Can you explain this answer?.
To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?a)30,000b)2,70,000c)3,90,000d)4,20,000Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?a)30,000b)2,70,000c)3,90,000d)4,20,000Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?a)30,000b)2,70,000c)3,90,000d)4,20,000Correct answer is option 'D'. Can you explain this answer?.
Solutions for To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?a)30,000b)2,70,000c)3,90,000d)4,20,000Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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ample number of questions to practice To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000 candidates. Question B was answered correctly by 2,50,000 candidates. Question C was answered correctly by 2,60,000 candidates. Both questions A and B were answered correctly by 1,00,000 candidates. Both questions B and C were answered correctly by 90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates. If the number of students answering all questions correctly is the same as the number answering none, how many candidates failed to clear the test?a)30,000b)2,70,000c)3,90,000d)4,20,000Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GATE tests.
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