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

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If James is currently 1/3 as old as his mother, how old is James? [#permalink]

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New post 28 Aug 2017, 01:36
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If James is currently 1/3 as old as his mother, how old is James?

(1) In 10 years, James will be half as old as his mother will be then.
(2) James is now twice as old as he was 5 years ago.
[Reveal] Spoiler: OA

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Re: If James is currently 1/3 as old as his mother, how old is James? [#permalink]

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New post 28 Aug 2017, 01:37
Bunuel wrote:
If James is currently 1/3 as old as his mother, how old is James?

(1) In 10 years, James will be half as old as his mother will be then.
(2) James is now twice as old as he was 5 years ago.


Check other Age Problems in our Special Questions Directory.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If James is currently 1/3 as old as his mother, how old is James? [#permalink]

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New post 28 Aug 2017, 01:49
LET JAMES BE J YEARS OLD AND HIS MOTHER IS M
3J=M

1) (J+10)= 0.5(M+10) AND ALSO 3J=M, GIVES J=10 AND M=30
2) J= 2(J-5) , GIVES J=10 AND WE KNOW M=3J =30
THEREFORE BOTH ARE SUFFICIENT

D IS THE ANSWER
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If James is currently 1/3 as old as his mother, how old is James? [#permalink]

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New post 28 Aug 2017, 01:54
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Bunuel wrote:
If James is currently 1/3 as old as his mother, how old is James?

(1) In 10 years, James will be half as old as his mother will be then.
(2) James is now twice as old as he was 5 years ago.


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.
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If James is currently 1/3 as old as his mother, how old is James? [#permalink]

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New post 12 Oct 2017, 08:46
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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Re: If James is currently 1/3 as old as his mother, how old is James? [#permalink]

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New post 27 Nov 2017, 18:17
Bunuel wrote:
If James is currently 1/3 as old as his mother, how old is James?

(1) In 10 years, James will be half as old as his mother will be then.
(2) James is now twice as old as he was 5 years ago.


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
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Re: If James is currently 1/3 as old as his mother, how old is James?   [#permalink] 27 Nov 2017, 18:17
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