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Math Expert V
Joined: 02 Sep 2009
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Three children inherited a total of X dollars. If the oldest child inh  [#permalink]

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Difficulty:   5% (low)

Question Stats: 86% (01:23) correct 14% (01:45) wrong based on 355 sessions

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

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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.

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.

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

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Top Contributor
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

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

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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.

DS90602.01
OG2020 NEW QUESTION

Hola amigos 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

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

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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.

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.

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e-GMAT Representative V
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Three children inherited a total of X dollars. If the oldest child inh  [#permalink]

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