Discussion

Explanation:

Using the information given in the question let us represent it in the Venn diagram shown below. The diagram depicts the number of candidates getting 80 percentile and above in at least one or more of the subjects amongst students getting 90 percentile overall.

The number of candidates scoring 80 percentile and above in only Physics, only Chemistry and only Math is the same. Let this be ‘d’

Let ‘a’ – number of candidates scoring 80 percentile and above only in Physics and Math.

Let ‘b’ – number of candidates scoring 80 percentile above only in Physics and Chemistry.

Let ‘c’ – number of candidates scoring 80 percentile and above in Chemistry and Math.

Let ‘e’ – number of candidates scoring 80 percentile and above in all 3 subjects.

a + b + c = 150

Also a + b + c + 3d + e = 200

⇒ 3d + e = 50

Given that (2d + c) : (2d + a) : (2d + b) = 4 : 2 : 1

This implies 6d + a + b + c is a multiple of 7. We already know that a + b + c = 150. So 6d + 150 is a multiple of 7. This implies that 6d + 3 will also be a multiple of 7. So d will be 3, 10, 17. But as 3d + e = 50, it implies that d < 17. So d will be either 3 or 10.

The number of students who scored 90 percentile and above and scored at least 80 percentile in Physics (but not in Chemistry and Math) will be eligible for the BIE entrance test. This is equal to d which is either 3 or 10.

Hence, option (a).

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