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If Carla, Nora, and Wanda have a total of $48, how much money does Car

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If Carla, Nora, and Wanda have a total of $48, how much money does Car  [#permalink]

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New post Updated on: 14 Oct 2018, 08:31
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Question Stats:

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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.

Difficulty Level: 700

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Originally posted by SajjadAhmad on 26 May 2017, 10:03.
Last edited by SajjadAhmad on 14 Oct 2018, 08:31, edited 1 time in total.
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Re: If Carla, Nora, and Wanda have a total of $48, how much money does Car  [#permalink]

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New post 26 May 2017, 10:28
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SajjadAhmad wrote:
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.


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:

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Re: If Carla, Nora, and Wanda have a total of $48, how much money does Car  [#permalink]

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New post 14 Oct 2018, 07:06
Twisted language in Statement 1.

Actually it is saying that absolute value of C-N= 12
So here are two cases.
C-N= 12
or
N-C =12

Nice learning from this question.
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Re: If Carla, Nora, and Wanda have a total of $48, how much money does Car   [#permalink] 14 Oct 2018, 07:06
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If Carla, Nora, and Wanda have a total of $48, how much money does Car

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