BTGModeratorVI wrote: ↑Sun Sep 27, 2020 7:10 am
If Carla, Nora, and Wanda have a total of $48, how much money does Carla have?
(1) The positive difference between the amounts of money that Carla and Nora have is $12.
(2) Nora and Wanda have the same amount of money.
Answer:
E
Source: GMAT hacks
Target question: How much money does Carla have?
Given: Carla, Nora, and Wanda have a total of $48
Statement 1: The positive difference between the amounts of money that Carla and Nora have is $12
So, EITHER Carla has $12 more than Nora OR Carla has $12 less than Nora.
This certainly doesn't seem very helpful.
ALSO, there's no information about Wanda.
Statement 1 is clearly NOT SUFFICIENT
Statement 2: Nora and Wanda have the same amount of money.
No information about Carla.
Statement 2 is clearly NOT SUFFICIENT
Statements 1 and 2 combined
Let's examine the 2 possible cases from statement 1 in conjunction with statement 2.
Case a: Carla has $12 more than Nora
Let x = the $ Nora has
This means that x+12 = the $ Carla has
And x = the $ Wanda has (since Nora and Wanda have the same amount of money)
Since the TOTAL = $48, we can write: x + (x+12) + x = 48
Simplify: 3x + 12 = 48
Solve: x = 12
Since x+12 = the $ Carla has, we can conclude that 12+12 = Carla's money.
In other words,
Carla has $24
Case b: Carla has $12 less than Nora
Let x = the $ Carla has
This means that x+12 = the $ Nora has
And x+12 = the $ Wanda has (since Nora and Wanda have the same amount of money)
Since the TOTAL = $48, we can write: x + (x+12) + (x+12) = 48
Simplify: 3x + 24 = 48
Solve: x = 8
In other words,
Carla has $8
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
