BTGModeratorVI wrote: ↑

Sun Sep 27, 2020 7:07 am

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.


Answer: D
Source: Official guide

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