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 answered correctly 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 3 questions correctly is 60,000, how many candidates failed the test? A. 4,20,000 B. 2,10,000 C. 3,90,000 D. 4,20,000

GATE 2018 · General Aptitude · Counting · medium

Answer: 4,20,000 candidates failed the test. Answer: D.

1. Count candidates who answered at least 2 questions correctly: Candidates answering at least 2 correctly = |A^B| + |B^C| + |A^C| - 2|A^B^C| = 1,00,000 + 90,000 + 80,000 - 2*60,000 = 2,70,000 - 1,20,000 = 2,10,000.
2. Compute the number who failed: Failed = Total - Passed = 6,30,000 - 2,10,000 = 4,20,000.