Three children inherited a total of X dollars. If the oldest child inh

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Youngest = \(y\)
Middle = \(y + 9000\)
Oldest = \(y + 7000\)
Total \(X = y + y + 9000 + y + 7000 = 3y + 16000\). Thus figuring out \(y\) is enough to find \(X\).

1. The middle child inherited \(27000\).
So \(y + 9000 = 27000\). \(y = 18000\)
Sufficient

2. The youngest child and the middle child together inherited a total of \(45000\).
So \(y + y + 9000 = 45000\). \(y = 18000\)
Sufficient

The answer is D

We can let the amounts inherited by the youngest, middle, and oldest children = a, b, and c,respectively. We can create the equations:

c = 7,000 + a

and

a = b - 9,000

Thus:

c = 7,000 + b - 9,000

c = b - 2,000

Statement One Alone:

The middle child inherited $27,000.

Thus, b = 27,000, so we can determine a and c as follows:

a = 27,000 - 9,000 = 18,000

and

c = 27,000 - 2,000 = 25,000

So X = 18,000 + 27,000 + 25,000 = 99,000.

Statement one alone is sufficient to answer the question.

StatemenTwo Alone:

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

Thus:

45,000 = a + b

From the given information, we have:

a = b - 9,000

9,000 = b - a

Adding the equations together, we have:

54,000 = 2b

27,000 = b

Since we have the value of b, from the work we did in statement one, we see we have enough information to determine X.

Statement two alone is sufficient to answer the question.

Answer: D

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

• Three children inherited a total of X dollars.
• The oldest child inherited $7000 more than the youngest child.
• The youngest child inherited $9000 less than the middle child.

We need to determine

• The value of X, that is, the total amount inherited.

If we assume that the amount inherited by the middle child is m, then

• The amount inherited by the youngest child = m – 9000
• The amount inherited by the oldest child = m – 9000 + 7000 = m – 2000
• Therefore, the total inherited amount = X = m + (m – 9000) + (m – 2000) = 3m – 11000

Hence, to determine X, we need to know the amount inherited by any one of the three children.
With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1

As per the information given in statement 1, the middle child inherited $27000.

• Or, m = 27000

As we know the value of m, we can determine the value of X.
Hence, statement 1 is sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, the youngest child and the middle child together inherited a total of $45000.

• Or, m – 9000 + m = 45000
Or, 2m = 54000
Or, m = 27000

As we know the value of m, we can determine the value of X.
Hence, statement 2 is sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from either of the statements individually, this step is not required.
Hence, the correct answer choice is option D.

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:

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

Answer: Option D

Video solution by GMATinsight

Video solution from Quant Reasoning:
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We know how much each child earned, relative to the youngest child (the oldest received $7k more, and the middle received $9k more), so we only have one unknown, and any other relevant relationship will let us solve for everything here. Statement 1 is clearly sufficient, because then the youngest child received $9k less than $27k, or $18,000. Statement 2 tells us the youngest and middle sum to $45,000. It might be clear we'll be able to solve because we have two different linear equations in two unknowns (m + y = 45,000 and m - y = 9000). Or without algebra: they received an average of 45,000/2 = 22,500 each. That average is halfway between what they each received. So if their amounts differ by 9000, one is 4500 above average, the other 4500 below, and they received 18,000 and 27,000 dollars.

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