Given: The ratio of the number of boys to the number of girls in Washington High School is 5:3.
Asked: What is the number of teachers in the school?
(1) In the same school, the ratio of the number of girls to the number of teachers is 4:17
Ratio of the number of boys to the number of girls to the number of teachers = 20:12:51
Number of teachers is a multiple of 51.
Number of teachers may be 51, 102,....
NOT SUFFICIENT
(2) There are less than 55 teachers in the school
Since there is no other information about number of teachers in the school
Number of teachers may be 1,2,3,.....or 54
NOT SUFFICIENT
(1) + (2)
(1) In the same school, the ratio of the number of girls to the number of teachers is 4:17
Ratio of the number of boys to the number of girls to the number of teachers = 20:12:51
Number of teachers is a multiple of 51.
(2) There are less than 55 teachers in the school
Number of teachers in the school = 51
Since any other multiple of 51 is greater than 55.
SUFFICIENT
IMO C
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com