Question 1040489
you need to test each one out to see which ones are possible.


if the total is 20, and 2/3 are girls, then the number of girls is 20 * 2/3 = 13 and 1/3 which is not possible, so it can't be 20.


if the total is 30, and 2/3 are girls, then the number of girls is 20 which is possible.   
if 2/5 of those are seniors, then the number of girl seniors is 2/5 * 20 = 40/5 = 8 which is possible.  
if 1/3 of the senior girls passed the test, then the number of girl seniors that passed the test is 1/3 * 8 = 8/3 which is equal to 2 and 2/3 which is not possible, so it can't be 30.


if the total is 45, and 2/3 are girls, then the number of girls is 30 which is possible.
if 2/5 of those are seniors, then the number of girl seniors is 2/5 * 30 = 12 which is possible.
if 1/3 of the senior girls passed the test, then the number of girl seniors that passed the test is 1/3 * 12 = 4 which is possible, so a total of 45 is possible.


if the total is 60, and 2/3 are girls, then the number of girls is 40 which is possible.
if 2/5 of those are seniors, then the number of girl seniors is 2/5 * 40 = 16 which is possible.
if 1/3 of the senior girls passed the test, then the number of girl seniors that passed the test is 1/3 * 16 = 5 and 1/3 which is not possible.


the only possible number of students is therefore 45.


you could also have done this algebraically as follows:


let g = number of girls.
let t = total number of students.
2/3 of the students are girls.
you get g = 2/3 * t.


2/5 of the girls are seniors.
let s = number of seniors.
you get 2/5 * g = s
since g = 2/3 * t, you get 2/5 * 2/3 * t = s
simplify to get 4/15 * t = s


let p = number of senior girls who passed the final
you get p = 1/3 * s
since s = 4/15 * t, you get 1/3 * 4/15 * t = p
simplify to get 4/45 * t = p


you can use this last formula to determine what the number of t could be.


if t = 20, then 4/45 * 20 = p which results in p = 1.78 which is not possible.


if t = 30, then 4/45 * 30 = p which result in p = 2.67 which is not possible.


if t = 45, then 4/45 * 45 = 4 which is possible *****


if t = 60, then 4/45 * 60 = 5.33 which is not possible.


the only possible situation that results in p being equal to an integer is when the total number of student = 45, so that has to be your solution.