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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?

  1. $30,000$
  2. $2,70,000$
  3. $3,90,000$
  4. $4,20,000$
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