## OG 2020: Question No. 327

Jones has worked at Firm X twice as many years as Green, and Green has worked at Firm X four years longer than Smith. How many years has Green worked at Firm X?

- Jones has worked at Firm X 9 years longer than Smith.
- Green has worked at Firm X 5 years less than Jones.

Source | OG 2020 |

Type | Data Sufficiency |

Topic | Algebra/Word Problems |

Sub-Topic | Linear Equations |

Difficulty | Easy – Medium |

### Solution

__Steps 1 & 2: Understand Question and Draw Inferences__

__Steps 1 & 2: Understand Question and Draw Inferences__

In this question, we are given

- Jones has worked at Firm X twice as many years as Green.
- Green has worked at Firm X four years longer than Smith.

We need to determine

- The number of years for which Green has worked at firm X.

Let us assume that the number of years for which Smith has worked for firm X is n.

- Therefore, number of years for which Green has worked = (n + 4) years
- And, the number of years for which Jones has worked = 2(n + 4) years

Hence, to determine the value of (n + 4), we need to know the value of n.

With this understanding, let us now analyse the individual statements.

__Step 3: Analyse Statement 1__

__Step 3: Analyse Statement 1__

As per the information given in statement 1, jones has worked at Firm X 9 years longer than Smith.

In terms of n, we can write this as

- 2(n + 4) – n = 9

Or, 2n + 8 – n = 9

Or, n = 1

As we can determine the value of n, we can also determine the value of (n + 4).

Hence, statement 1 is sufficient to answer the question.

__Step 4: Analyse Statement 2__

__Step 4: Analyse Statement 2__

As per the information given in statement 2, Green has worked at Firm X 5 years less than Jones.

In terms of n, we can write this as

- 2(n + 4) – (n + 4) = 5

Or, n + 4 = 5

Or, n = 1

As we can determine the value of n, we can also determine the value of (n + 4).

Hence, statement 2 is sufficient to answer the question.

__Step 5: Combine Both Statements Together (If Needed)__

__Step 5: Combine Both Statements Together (If Needed)__

Since we could determine the answer from either of the statements individually, this step is not required.

Hence, the correct answer is option D.

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