The ratio of the number of boys to the number of girls in Washington

Given, B/G = 5/3

Stat1: In the same school, the ratio of the number of girls to the number of teachers is 4:17
And, G/T = 4/17, But we don't know the common multiplier in two ratios. Not sufficient

Stat2: There are less than 55 teachers in the school
No idea about, the nos. of teachers. Not sufficient

Combining both, We can say for minimum values, B/G = 20/12 and G/T = 12/51 and T <55
So, T = 51. Sufficient.

So, I think C.

Solution:

Given, the ratio of Boys: Girls = 5:3.

St(1):-In the same school, the ratio of the number of girls to the number of teachers is 4:17

Using information from Question stem and statement we have,

=>Boys: Girls = 5:3 = 20:12

=>Girls: Teachers = 4:17 = 12:51

=>Boys :Girls: Teachers = 20:12:51

=>Number of teachers must be a multiple of 51

We cannot determine the exact number of teachers.(Insufficient)

St(2):-There are less than 55 teachers in the school

No information provided to find the number of teachers

Combining both we have,

The smallest positive multiple of 51 less than 55 is 51,

=>There are 51 teachers. Sufficient.(option c)

Devmitra Sen
GMAT SME

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