Hi All,
Ratio questions such as these can certainly be solved with Algebra, and in many cases can be solved by TESTing THE ANSWERS. Here, since the numbers involved are relatively small, we can "brute force" the solution and focus on the basic Arithmetic involved:
We're told a number of Facts about the number of coins that Lana and Brad had:
1) To start, the ratio of coins was 5:2
2) After Lana gave Brad 8 coins, the ratio became 3:2
The question asks how many MORE coins Lana had than Brad AFTER she gave him the 8 coins.
From the initial ratio, we know that Lana had a multiple of 5 coins and Brad had an equivalent multiple of 2 coins. Since Lana gave Brad 8 coins, she clearly had to START with MORE than 8 coins. The smallest multiple of 5 that "fits" is 10, so we'll start there:
IF....
Lana = 10 coins; Brad = 4 coins
After 8 coins are given....
Lana = 2 coins; Brad = 12 coins
This does NOT match the 3:2 ratio. Lana needs to start off with LOTS more coins....
IF....
Lana = 30 coins; Brad = 12 coins
After 8 coins are given....
Lana = 22 coins; Brad = 20 coins
This does NOT match the 3:2 ratio
IF....
Lana = 40 coins; Brad = 16 coins
After 8 coins are given....
Lana = 32 coins; Brad = 24 coins
This does NOT match the 3:2 ratio, but it's getting close....
IF....
Lana = 50 coins; Brad = 20 coins
After 8 coins are given....
Lana = 42 coins; Brad = 28 coins
This MATCHES the 3:2 ratio
After the 8 coins are given, Lana has 42-28 = 14 more coins than Brad.
Final Answer:
GMAT assassins aren't born, they're made,
Rich