problems from GMAT disclosed edition 55

I'm not sure how to set up equations for these three problems. I managed to solve two of them through backsolving. Can you help, pls? 1) If x dollars is invested at 10% for one year and y dollars is invested at 8% for one year, the annual income from the 10% investment will exceed the annual income ...

OA is E, all solutions are useful and particularly the shortcut. thanks

thanks a lot, all. I totally understand it now.

ratio of stamps

The number of stamps that Kaye and Alberto had were in the ratio 5:3, respectively. After Kaye gave Alberto 10 of her stamps, the ratio of the number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto? 20 30 40 60 90 Simple enough? I tried to set up a ratio but...

understand. My issue is to understand from weighted average perspective? - what am i doing wrong in weighted average ? 1/2(30) + 1/2(60) = 45 it seems you are following a different formula should be ----> total distance/total time; in this case total distance=30+30=60 total time=1+1/2=3/2 so 60/3/2...

I've recently been given this solution:

t/s*(-1/root(3)) = -1 ---> since lines OP and OQ are perpendicular

also let
s^2+t^2=r^2=3+1=4 ---> (since P lies on the same circle and O is origin)

solve for s

s^2+3s^2=4 => s=+/-1

OA is A. Any ideas about the other two questions??