BTGModeratorVI wrote: ↑

Wed Mar 25, 2020 6:27 am

In a certain class, 1/5 of the boys are shorter than the shortest girl in the class, and 1/3 of the girls are taller than the tallest boy in the class. If there are 16 stu­dents in the class and no two people have the same height, what percent of the students are taller than the shortest girl and shorter than the tallest boy?

A. 25%
B. 50%
C. 62.5%
D. 66.7%
E. 75%

Answer: C
Source: Manhattan Prep

GIVEN: There are 16 students and 1/5 of them are boys.
This means the number of boys must be a multiple of 5.
There are 3 possible cases:
i) 5 boys and 11 girls
ii) 10 boys and 6 girls
iii) 15 boys and 1 girl

GIVEN: There are 16 students and 1/3 of them are girls.
This means the number of girls must be a multiple of 3.
When we check the three possible cases above, we see that only one case (case ii) is such that the number of girls is divisible by 3.

So we now know that there are 10 boys and 6 girls

Let A, B, C, D, E, F represent the heights of the 6 girls arranged in ASCENDING order
Let Q, R, S, T, U, V, W, X, Y, Z represent the heights of the 10 boys arranged in ASCENDING order

1/5 of the boys are shorter than the shortest girl in the class
1/5 of 10 = 2
So, 2 boys are shorter than the shortest girl in the class
We have: Q, R, A [ these 3 heights must be arranged in ascending order]


1/3 of the girls are taller than the tallest boy in the class
1/3 of 2 = 2
So, 2 girls are taller than the tallest boy in the class
We have: Z, E, F [ these 3 heights must be arranged in ascending order]

NOTE: The remaining students must lie BETWEEN A and Z, however there is no way to determine the relationships between each boy and each girl within this range.

So one possible configuration is as follows: Q, R, A, S, T, U, V, W, X, Y, B, C, D, Z, E, F


What percent of the students are taller than the shortest girl and shorter than the tallest boy?
Shortest girl is A and the tallest boy is Z
As we can see from the above diagram, there are 10 such students

10/16 = 5/8 = 62.5%

Answer: C

Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Mar 25, 2020 6:27 am

In a certain class, 1/5 of the boys are shorter than the shortest girl in the class, and 1/3 of the girls are taller than the tallest boy in the class. If there are 16 stu­dents in the class and no two people have the same height, what percent of the students are taller than the shortest girl and shorter than the tallest boy?

A. 25%
B. 50%
C. 62.5%
D. 66.7%
E. 75%

Answer: C
Source: Manhattan Prep

First, we need to determine the number of boys and girls in the class. We see that the number of boys must be a multiple of 5, and the number of girls must be a multiple of 3. Since the total number of students in the class is 16, the number of boys must be 10 and the number of girls must be 6.

Therefore, 2 boys are shorter than the shortest girl and 2 girls are taller than the tallest boy. Because we are asked to find the percent of the students that are taller than the shortest girl and shorter than the tallest boy, we cannot count those two students. Thus, the number of students between those two students is 16 - 4 - 2 = 10. The percent of students satisfying the criterion is 10/16 = ⅝ = 62.5%.

Answer: C