To make our lives easier, let's go ahead and assume there are 20 students in the class.
Statement 1
This doesn't tell us much. 1) We don't know how many girls are in the class. There could be 18 girls in the class, and 9 could be holding a popsicle, or there could be 2 girls in the class, and 1 could be holding a popsicle. 2) We don't know what fraction of the boys in the class are holding a popsicle - half of them? all of them? none of them? Insufficient.
Statement 2
This has the exact same problem as statement 1: we don't know how many boys are in the class, and we don't know what fraction of the girls are holding a popsicles. Insufficient.
Both
If half of the girls AND half of the boys are holding a popsicle, this means that half (or 50%) of the class is holding a popsicle, no matter how many girls and boys there are. We can prove that with a couple examples. Say there are 4 girls and 16 boys. Then 2 girls and 8 boys are holding a popsicle. That's 10 children, or half of the class. Say there are 12 girls and 8 boys. Then 6 girls and 4 boys are holding a popsicle. That's 10 children again. Sufficient.
Note: this wouldn't have worked if both groups didn't have the same fraction. So say if 25% of the girls and 50% of the boys were holding popsicles, we couldn't solve the problem without knowing how many of the students were girls/boys.
Remember: if you can't conceptualize a problem (super common with percents, fractions, and ratios), plug in easy numbers!
