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  • 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:

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 CM). 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 ATE. AET is used by ATE for final selection.
For the 200 candidates who are at or above the 9oth 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 V Number of candidates below 8oth 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 ATE, 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 STE for being considered for final selection. Altogether, there are 400 candidates this year who are at or above the 80th percentile in P. 

Question : If the number of candidates who are at or above the 90th percentile overall and also at or above the 80th percentile in all three sections in CET is actually a multiple of 5, then how many candidates were shortlisted for the AET for AIE? 

Option: 1

170


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

200 candidates scored above the 90th percentile in CET.

The Venn diagram represents the number of candidates who scored above the 80th percentile in each of the three sections.

To solve the problem, let's consider the given information:

From (1), we know that n = 0.

From (2), the sum of d, e, and f is 150.

From (3), a, b, and c are equal.

There are a total of 200 candidates.

By analyzing the conditions, we can deduce:

The sum of a, b, c, and g is equal to 50 (as 200 - 150 = 50).

The equation 3a + g = 50 holds, indicating that a is less than 17.

From (4), the ratio of (b + f + c) to (a + d + b) to (a + e + c) is 4 : 2: 1.

Simplifying further, we have (2a + f) : (2a + d) : (2a + e) = 4 : 2 : 1.

Combining these equations, we get 6a + (d + e + f) = 7x, where x is a multiple of 24 or 30.

Solving for a, we find that it can be either 3 or 10.

Now, let's consider the possibilities:

If a = 3, x = 24, and 2a + e = 24, we find e = 18.

If a = 10, x = 30, and 2a + e = 30, we find e = 10.

Similarly, we can calculate the values of d, f, and g for each case.

Among the candidates who scored above the 90th percentile, those who scored above the 80th percentile in at least two sections are selected for AET. This means that the candidates represented by d, e, f, and g are chosen for AET.

BIE considers candidates appearing for AET and scoring above the 80th percentile in P. Therefore, BIE will consider the candidates represented by d, e, and g, which can be either 104 or 80.

For the remaining students who scored above the 80th percentile in P, BIE conducts a separate test. Given that there are a total of 400 candidates meeting this criterion and either 104 or 80 candidates who scored above the 80th percentile in P and above the 90th percentile overall, we can deduce that there must be 296 or 320 candidates who scored above the 80th percentile in P but below the 90th percentile overall.

Based on this analysis, we can conclude that the correct answer is 170, representing the number of candidates shortlisted for AET.

Therefore, the solution shows that 170 candidates fulfill the given criteria.

Posted by

manish

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