Jones has worked at Firm X twice as many years as Green, and Green has

Given: Jones has worked at Firm X twice as many years as Green, and Green has worked at Firm X four years longer than Smith.
Let G = the number of years Green worked at Firm X
So, G - 4 = the number of years Smith worked at Firm X (since we're indirectly told Smith worked 4 years less than Green)
And 2G = the number of years Jones worked at Firm X (since we're told Jones has worked at Firm X twice as many years as Green)

Target question: How many years has Green worked at Firm X?
In other words, "What is the value of G?"

Statement 1: Jones has worked at Firm X 9 years longer than Smith.
In other words, (Jones' years) = (Smith's years) + 9
Replace values to get: 2G = (G - 4) + 9
Simplify: 2G = G + 5
Solve: G = 5
The answer to the target question is Green worked at Firm X for 5 years
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Green has worked at Firm X 5 years less than Jones.
In other words, (Green's years) = (Jones' years) - 5
Replace values to get: G = (2G) - 5
Solve: G = 5
The answer to the target question is Green worked at Firm X for 5 years
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

Hi All,

We're told that Jones has worked at Firm X TWICE as many years as Green, and Green has worked at Firm X four years LONGER than Smith. We're asked for the number of years that Green has worked at Firm X. This question can be approached in a couple of different ways, but there's a built-in Algebra 'shortcut' that we can take advantage of. From the given information, we can create a couple of equations - and that should get you thinking about "System Math" (re: 2 variables and 2 unique equations, 3 variables and 3 unique equations, etc.).

To start, we'll use the variables J, G and S for Jones, Green and Smith, respectively. We can then create 2 equations:
J = 2G
G = S + 4

We're asked to find the value of G. Right now, we have 3 variables, but just 2 equations. If we can get one more UNIQUE equation involving some combination of these three variables, then we'll have a System of equations - and can solve for all 3 variables.

(1) Jones has worked at Firm X 9 years longer than Smith.

With the information in Fact 1, we can create the following equation:
J = S + 9
We now have a third unique equation, so we could solve for all 3 variables - including G. The shortcut is that we don't actually have to do that math; having the necessary equations to do it proves that we COULD get the one value of G that exists to answer the question.
Fact 1 is SUFFICIENT

(2) Green has worked at Firm X 5 years less than Jones.

With the information in Fact 2, we can create the following equation:
G = J - 5
Again, we have a third unique equation, so we could solve for all 3 variables - including G. The shortcut is that we don't actually have to do that math; having the necessary equations to do it proves that we COULD get the one value of G that exists to answer the question.
Fact 2 is SUFFICIENT

Final Answer:

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

We can let the number of years Jones, Green, and Smith worked = J, G, and S respectively.

Since Jones has worked at Firm X twice as many years as Green:

J = 2G

Since Green has worked at Firm X four years longer than Smith:

G = S + 4

We see that we have two unique equations, and three total variables, so if we can create one more unique equation with those variables, we can determine G.

Statement One Alone:

Jones has worked at Firm X 9 years longer than Smith.

We can create the equation:

J = 9 + S

Since we have our 3rd equation, statement one is sufficient to determine G.

Statement Two Alone:

Green has worked at Firm X 5 years less than Jones.

We can create the equation:

G = 5 + J

Since we have our 3rd equation, statement two is sufficient to determine G.

Answer: D

The above solutions are too complicated. The question can be solved with one variable only
S=x
G=4+x
J=8+2x

I) 8+2x=x+9 –> x=1
II) 4+x=3+2x –> x=1

Video solution from Quant Reasoning:
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Answer: Option D

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