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

Arent those calculations a bit cumbersome? i.e 0.25 x 105

Is there a simpler way to make the calculations faster?

Brent@GMATPrepNow wrote:

faraz_jeddah wrote:Aren't those calculations a bit cumbersome? i.e 0.25 x 105

Is there a simpler way to make the calculations faster?

The important thing to recognize is that we don't need to perform any big calculations.
For example, all we need to do is see that we could solve the equation 0.75(y+105)+0.25y=0.55(2y+105) for y, which means we could determine the total number of students, in which case the statement is sufficient.

Remember that, for Data Sufficiency questions, our goal is not to answer the target question; our goal is to determine whether or not the statements provide sufficient information to answer the target question.

Performing more calculations than are necessary is covered in our free video titled "Avoiding Common Mistakes - Part I": https://www.gmatprepnow.com/module/gmat- ... cy?id=1098

Cheers,
Brent

Thanks Brent but I only asked because the original question is not in the DS format.