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(2) The youngest child and the middle child together inherited a total of $45,000. D Source: Official Guide 2020 ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12991 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 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 _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 496 members Upvotes: 2867 GMAT Score: 800 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

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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