AbeNeedsAnswers wrote:Three children inherited a total of X dollars. If the oldest child inherited $7,000 more than the youngest child, and the youngest child inherited $9,000 less than the middle child, what is the value of X ?

(1) The middle child inherited $27,000.
(2) The youngest child and the middle child together inherited a total of $45,000.

D

Source: Official Guide 2020

Given: Three children inherited a total of X dollars. The oldest child inherited $7,000 more than the youngest child, and the youngest child inherited $9,000 less than the middle child
Let y = the amount the YOUNGEST child received
So, y + 7000 = the amount the OLDEST child received
And y + 9000 = the amount the MIDDLE child received

We can write: y + (y + 7000) + (y + 9000) = X
Simplify: 3y + 16,000 = X

Target question: What is the value of X?

Statement 1: The middle child inherited $27,000.
y + 9000 = the amount the MIDDLE child received
We can write: y + 9,000 = 27,000
Solve to get: y = 18,000
Since we already know that 3y + 16,000 = X, we can replace y with 18,000
We get: 3(18,000) + 16,000 = X
Evaluate to get: X = 70,000
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The youngest child and the middle child together inherited a total of $45,000.
We can write: y + (y + 9,000) = 45,000
Simplify: 2y + 9,000 = 45,000
So, 2y = 36,000
Solve: y = 18,000
Since we already know that 3y + 16,000 = X, we can replace y with 18,000
We get: 3(18,000) + 16,000 = X
Evaluate to get: X = 70,000
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

Hi All,

We're told that three children inherited a TOTAL of X dollars, the oldest child inherited $7,000 MORE than the youngest child and the youngest child inherited $9,000 LESS than the middle child. We're asked for the value of X. This question is built around some basic Arithmetic and Algebra.

(1) The middle child inherited $27,000.

With the information in Fact 1, we can determine the exact amount of money that each child inherited, so we CAN figure out the exact value of X. If you recognize that the relationships among the various numbers, then you don't actually have to do any math here. However, you can quickly calculate the individual values involved:

-Since the youngest child inherited $9,000 LESS than the middle child, then the youngest received $27,000 - $9,000 = $18,000
-The oldest child inherited $7,000 MORE than the youngest child, so the oldest received $18,000 + $7,000 = $25,000
-Thus, the value of X is 27,000 + 18,000 + 25,000 = $70,000
Fact 1 is SUFFICIENT

(2) The youngest child and the middle child together inherited a total of $45,000.

With the information in Fact2, we can create the following equation...
Y + M = 45,000

...and with the information in the prompt, we can create another equation using these 2 variables:
Y = M - 9000

Here, we have a 'System' of equations: 2 variables and 2 unique equations - which means that we can solve for the exact values of Y and M (they would be Y = 18,000 and M = 27,000). With those values, we can then determine the amount of money that the oldest child received and the value of X.
Fact 2 is SUFFICIENT

Final Answer: D

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