If James is currently 1/3 as old as his mother, how old is James?

Statement 1
- \(\frac{(J+10)}{(3J+10)} = \frac{1}{2}\) --> \(2J+20 = 3J+10\) --> \(-J=-10\), thus J=10 years old.
- SUFFICIENT

Statement 2
- \((J-5)*2 = J\) --> \(2J-10=J\), thus J=10 years old
- SUFFICIENT

D.

Hi,
Solution follows:

James is currently 1/3 as old as his mother => J=M/3 => M=3J
Question asks: J=??

Statement 1: In 10 years, James will be half as old as his mother will be then => J+10 = M+10/2 (substitute M=3J) on solving we get J=10 (Sufficient)

Statement 2: James is now twice as old as he was 5 years ago => J=2(J-5) => J=10 (Sufficient)

Answer: D

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We can let James’ current age = j and James’ mother's current age = m.

We have the following equation:

j = (1/3)m

3j = m

Statement One Alone:

In 10 years, James will be half as old as his mother will be then.

In 10 years, James will be (j + 10) and his mother will be (m + 10). The relationship between those two ages is that James will be ½ his mother’s age. We can create the following equation:

j + 10 = (m + 10)(1/2)

2j + 20 = m + 10

2j + 10 = m

Since 3j = m:

2j + 10 = 3j

j = 10

Statement one is sufficient to answer the question.

Statement Two Alone:

James is now twice as old as he was 5 years ago.

We can create the following equation:

j = 2(j - 5)

j = 2j - 10

j = 10

Statement two is sufficient to answer the question.

Answer: D