How old is Jane? (1) Ten years ago she was one-third as old as she is

Target question: How old is Jane?

Statement 1: Ten years ago she was one-third as old as she is now.
Let x = Jane's PRESENT age
So, x - 10 = Jane's age TEN YEARS AGO

We can write: x - 10 = x/3
Multiply both sides by 3 to get: 3x - 30 = x
Subtract 3x from both sides: -30 = -2x
Solve: x = 15
The answer to the target question is Jane is 15 years old
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: In 15 years, she will be twice as old as she is now
Let x = Jane's PRESENT age
So, x + 15 = Jane's age FIFTEEN YEARS FROM NOW

We can write: 2x = x + 15
Subtract x from both sides: x = 15
The answer to the target question is Jane is 15 years old
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

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 = (Present age of Jane)/3
• 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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Either statement is independently sufficient. D

(1) j-10 = (1/3)*j

(2) j+15 = (2)*j

Jane is now x years old

(1) \(x-10=1/3x; 3x-30=x; 2x=30; x=15; \ sufficient. \)

(2)\( x+15=2x;x=15; \ Sufficient. \)

The answer is \(D\)
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