Qs 1-4: Read the following information and answer the questions that follow.

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:

  1. No one is below the 80th percentile in all 3 sections.
  2. 150 are at or above the 80th percentile in exactly two sections.
  3. The number of candidates at or above the 80th percentile only in P is the same as the number of candidates at or above the 80th percentile only in C. The same is the number of candidates at or above the 80th percentile only in M.
  4. Number of candidates below 80th percentile in P: Number of candidates below 80th percentile in C: Number of candidates below 80th percentile in M = 4 : 2 : 1.

BIE uses a different process for selection. If any candidate is appearing in the AET by AIE, BIE considers their AET score for final selection provided the candidate is at or above the 80th percentile in P. Any other candidate at or above the 80th percentile in P in CET, but who is not eligible for the AET, is required to appear in a separate test to be conducted by BIE for being considered for final selection. Altogether, there are 400 candidates this year who are at or above the 80th percentile in P.

Q. 1

What best can be concluded about the number of candidates sitting for the separate test for BIE who were at or above the 90th percentile overall in CET?

A) 3 or 10

B) 10

C) 5

D) 7 or 10

Hint

You need to make a 3-set-venn-diagram for those at or above 80th percentile in P, C and M.

Clue 1 is about all the 200 candidates being the Union

All the three regions represented by clue 3 can be taken as a single variable, x

Clue 4 is difficult. Candidates below 80th percentile only in P …. only in P i.e. these are above 80th percentile in C and M but not in P. Identify this region …. and similarly for the other two parts of the ratio and equate the three parts to 4k, 2k and k respectively.

Now it should be evident what to do with the above three equations

Explanation