Age Word Problem -- How to approach it?

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alexdu: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Aug 24, 2010 4:23 pm

by alexdu » Mon Aug 22, 2011 11:25 am

I'm working on a word problem that I can't seem to wrap my head around. Can someone please breakdown how to solve this? Thanks!

1. Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Four years ago, Jim was 4 times as old as Sam. How old is Jim now?

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Source: Beat The GMAT — Problem Solving | Mon Aug 22, 2011 11:25 am

vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 amFollowed by: 34 members; Thanked: 156 times; GMAT Score:720

by vineeshp » Mon Aug 22, 2011 12:05 pm

Today Jim is twice as old as Fred

J = 2F

Sam is 2 years younger than Fred

S = F-2

Four years ago, Jim was 4 times as old as Sam

Jim 4 years ago = J - 4.
Sam 4 years ago, S - 4.
Equation:
J-4 = 4 (S-4)

3 equations and 3 unknowns. Must be solvable.

Vineesh,
Just telling you what I know and think. I am not the expert.

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Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Mon Aug 22, 2011 12:22 pm

alexdu wrote:I'm working on a word problem that I can't seem to wrap my head around. Can someone please breakdown how to solve this? Thanks!

1. Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Four years ago, Jim was 4 times as old as Sam. How old is Jim now?

Alternative solution method, requiring the answer choices: start with the answer choices and work backwards. The right answer is 20, and for that answer, and only for that answer, everything will check out.

The question asks "how old is Jim". Let's say that Jim is 20, and work through th problem under that assumption. If Jim is 20 now, then Fred is 10 (half of 20) and sam is 8 (two years younger). Four years ago Jim was 20-4=16 and sam was 8-4=4, and 16 is indeed 4 times 4, so this answer choice satisfies the second sentence as well. Thus, it's the right answer choice.

For other answer choices, Jim's age 4 years ago won't align with 4 times Sam's age 4 years ago. No ned to check all of them though - you can stop when you check 20 and see that it works, as there can;t be more than one right answer choice.

Geva
Senior Instructor
Master GMAT
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https://www.mastergmat.com

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BlindVision: Master | Next Rank: 500 Posts; Posts: 253; Joined: Fri Dec 26, 2008 8:39 pmFollowed by: 1 member; Thanked: 8 times

by BlindVision » Mon Aug 22, 2011 4:13 pm

vineeshp wrote:
Today Jim is twice as old as Fred
J = 2F

Sam is 2 years younger than Fred
S = F-2

Four years ago, Jim was 4 times as old as Sam
Jim 4 years ago = J - 4.
Sam 4 years ago, S - 4.
Equation:
J-4 = 4 (S-4)

3 equations and 3 unknowns. Must be solvable.

Using the formulas above:

J - 4 = 4(S - 4)
J - 4 = 4S - 16
J = 4S - 12

Substitute F - 2 = S for the above:

J = 4(F - 2) - 12
J = 4F - 8 - 12
J = 4F - 20

Substitute J = 2F for the above:

2F = 4F - 20
20 - 2F
10 = F

Since Today Jim is twice as old as Fred

J = 20

Life is a Test

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naveenchandra kv: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Aug 21, 2011 8:41 pm; Thanked: 5 times

by naveenchandra kv » Mon Aug 22, 2011 8:08 pm

Hi,

You can solve this using two ways.
1. Back solving using answer options
2. Traditional substitution method

for first method, just try with the available options from E to A.

I will show you how to use the second method;

As per the given first statement, we get J=2F AND F=S+2;
4 Years ago, i.e J-4=4(S-4)
Substituting for J AND S in the above,
2F-4=4(F-2-4)
2F-4=4F-8-16
2F=20
F=10; HENCE J=20;

HOPE YOU GOT IT.

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