Carcass wrote:
In a certain class, \(\frac{1}{5}\) of the boys are shorter than the shortest girl in the class, and \(\frac{1}{3}\) 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%
NOTE: I'm probably over explaining things here, but I want the solution to be absolutely clear.
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 girlsLet
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 class1/5 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 class1/3 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, FWhat 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
ZAs we can see from the above diagram, there are 10 such students
10/16 = 5/8 = 62.5%
Answer: C
Cheers,
Brent
Thank you so much.