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?
- The middle child inherited $27,000.
- The youngest child and the middle child together inherited a total of $45,000.
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.
