To pass a test a candidate need to answer at least 2 out of 3 question correctly .A total of 630000 candidate appeared for the test. Question A was correctly answered by 330000 candidate. Question B was answered correctly by 250000 candidates. Questions C was answer correctly by 260000 candidates. Both questions A and B were answer correctly by 100000 candidates. Both questions B and C where answered correctly by 90000 candidates. Both questions A and C were answered correctly by 80000 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 ?
Answers
Answer: 30,000
Step-by-step explanation:
Total number of candidate that appears the exam = 630000
Let the candidates that pass all the exam = x
⇒ The candidate that can not pass any of the exam = x
By the below Venn diagram,
The number of candidates that pass only Exam A = 330000-100000-80000-x = 150000-x
The number of candidates that pass only Exam B = 250000-100000-90000-x = 60000-x
The number of candidates that pass only Exam C = 260000-100000-70000-x = 90000-x
Thus, the total candidate = 150000-x + 60000-x + 90000-x + 100000+80000+x+90000 + x = 630000
570000 - x = 630000
⇒ - x = - 60000
⇒ x = 60000
Therefore, the candidates that passed to clear the test = 100000+80000+90000+60000=330000
Hence, the candidate that failed the exam = 630000-33000 = 30,0000
