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## OGQR 2020: Question No. 208

How old is Jane?

1. Ten years ago, she was one-third as old as she is now.
2. In 15 years, she will be twice as old as she is now.
 Source OGQR 2020 Type Data Sufficiency Topic Algebra Sub-Topic Linear Equations Difficulty Easy

### Solution

#### Steps 1 & 2: Understand Question and Draw Inferences

We need to find the age of Jane.

• Let us assume that the present age of Jane is x years.
• Hence, we need to find the value of x.

As we do not have any relevant information to infer from, let us now analyse the individual statements.

#### Step 3: Analyse Statement 1

“Ten years ago, she was one-third as old as she is now.”

• Age of Jane ten years ago = 1/3 (Present age of Jane)
• Ten years ago, the age of Jane was = x – 10 years.

Hence, x – 10 =  x/3

• 3x – 30 = x
• From this equation, we can easily find the value of x.

Thus, statement 1 is sufficient to answer the question.

#### Step 4: Analyse Statement 2

“In 15 years, she will be twice as old as she is now.”

• Age of Jane 15 years after Now = 2 × Present age of Jane
• After 15 years, age of Jane will be = x + 15
• x + 15 = 2x
• From this equation, we can easily find the value of x.

Thus, 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.

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