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In a class, among the boys B is taller than 10 boys, but shorter than 13 others. Among girls, G is taller than 6 girls, but shorter than 8 others. Two
Question

In a class, among the boys B is taller than 10 boys, but shorter than 13 others. Among girls, G is taller than 6 girls, but shorter than 8 others. Two boys and three girls are shorter than B, but taller than G. If no two persons have the same height, then in the entire class, B is

A.

taller than 21, but shorter than 18 others

B.

taller than 20, but shorter than 18 others

C.

taller than 20, but shorter than 19 others

D.

taller than 19, but shorter than 19 others

Correct option is B

Solution:

B is taller than 10 boys and B is shorter than 13 boys.

Therefore, there are a total of 10 + 1 + 13 = 24 boys in the class (including B).

G is taller than 6 girls and G is shorter than 8 girls.

Therefore, there are a total of 6 + 1 + 8 = 15  girls in the class (including G).

Two boys and three girls are shorter than B, but taller than G.

If B is taller than 10 boys, then B's position among the boys is11th in height order

(since B is taller than 10 boys, but shorter than 13).

Among the girls, there are 15 girls, and we know two boys and three girls are shorter than B.

Therefore, 5 students (2 boys + 3 girls) are shorter than B overall.

Total Number of Students:

There are 24 boys and 15 girls, so the total number of students is 39 

Since B is taller than 10 boys, and there are 2 boys and 3 girls shorter than B,

B must be taller than 10 +1 + 3 +  6= 20 students.

Therefore, B is taller than 20 students and shorter than  39 - 20-1 = 18 others.

Thus, the correct option is Option b.

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