Are you familiar with double entry table?
Here is a step by step guide to solve this problem:
Step 1: Construct a table similar to the one attached but without any entry except for the titles (Boy, Girl, Travel, No Travel)
Step 2: Let y be the total number of students who did not travel.
Step 3: From the given, #of students who didn't travel is 105 less than #of students who did, so in the
table fill number of students who did travel with y+105 (y being the number of students who didnt travel)
Step 3: Total number of students is #Travel + #No Travel = y+(y+105)=2y+105
Step 4: According to the given 45% of the students are girl so #of girls = 0.45*(2y+105)
and #of boys is 0.55(2y+105)
Step 5: According to the given 25% of the students who did not travel are girls and 75% are boys
so Girls who did not travel= 0.75y and boys who did not travel=0.25y
Step 6: Boys who did travel=0.75(y+105) and girls who did travel= 0.25(y+105)
Now you have your table set up.
Use the first column of the table to get the following equation:
0.75(y+105)+0.25y=0.55(2y+105)
Solve for y.
y=210
Total number of students=2y+105=2*210+105=525
Hope that helped
Cheers
The GMAT can be destroyed.
