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

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Three children inherited a total of X dollars. If the oldest child inh  [#permalink]

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New post 26 Apr 2019, 02:04
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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.


DS90602.01
OG2020 NEW QUESTION

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Re: Three children inherited a total of X dollars. If the oldest child inh  [#permalink]

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New post 26 Apr 2019, 14:21
Bunuel 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.


DS90602.01
OG2020 NEW QUESTION


We'll translate our question into equations to make it easier to SEE the logic. This is a Precise approach.
Labeling the 3 children as old, middle, young we have:
old + middle + young = x
old = 7000 + young
young = middle - 9000

This is 3 equations with 4 variables, so to solve for x we need one more equation.
Both (1) and (2) give us an additional equation so both are sufficient.

(D) is our answer.
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Re: Three children inherited a total of X dollars. If the oldest child inh  [#permalink]

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New post 27 Apr 2019, 08:46
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Bunuel 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.


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

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Re: Three children inherited a total of X dollars. If the oldest child inh  [#permalink]

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New post 29 Apr 2019, 02:05
Bunuel 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.


DS90602.01
OG2020 NEW QUESTION



Hola amigos :cool:

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
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Re: Three children inherited a total of X dollars. If the oldest child inh  [#permalink]

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New post 06 May 2019, 20:00
Bunuel 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.


DS90602.01
OG2020 NEW QUESTION


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
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Three children inherited a total of X dollars. If the oldest child inh  [#permalink]

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New post 14 May 2019, 05:54

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.

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Re: Three children inherited a total of X dollars. If the oldest child inh  [#permalink]

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New post 20 May 2019, 13:51
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:

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Re: Three children inherited a total of X dollars. If the oldest child inh   [#permalink] 20 May 2019, 13:51
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