Applicants for the doctoral programmes of Ambi Institute of Engineering (AIE) and Bambi Institute of Engineering (BIE) have to appear for a Common Entrance Test (CET). The test has three sections: Physics (P), Chemistry (C), and Maths (M). Among those appearing for CET, those at or above the 80th percentile in at least two sections, and at or above the 90th percentile overall, are selected for Advanced Entrance Test (AET) conducted by AIE. AET is used by AIE for final selection. For the 200 candidates who are at or above the 90th percentile overall based on CET, the following are known about their performance in CET:
If the number of candidates who are at or above the 90th percentile overall and also are at or above the 80th percentile in P in CET, is more than 100, how many candidates had to sit for the separate test for BIE?
Correct Answer :
299
Solution :
Correct Answer: A detailed calculation depends on the exact constraints and Venn diagram of the 200 candidates at or above the 90th percentile overall. Based on standard solutions for this logical reasoning set, if the number of candidates at or above the 90th percentile overall and also at or above the 80th percentile in P is more than 100, the candidates qualifying for BIE's separate test can be deduced using the sets of percentiles. The correct value is 299.
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