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## 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?

1. Jones has worked at Firm X 9 years longer than Smith.
2. 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

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

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

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)

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

Hence, the correct answer is option D. Payal Tandon
Co-founder, e-GMAT
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