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?
Age Word Problem  How to approach it?
This topic has expert replies
 vineeshp
 Legendary Member
 Posts: 965
 Joined: 28 Jan 2010
 Thanked: 156 times
 Followed by:34 members
 GMAT Score:720
J = 2FToday Jim is twice as old as Fred
S = F2Sam is 2 years younger than Fred
Jim 4 years ago = J  4.Four years ago, Jim was 4 times as old as Sam
Sam 4 years ago, S  4.
Equation:
J4 = 4 (S4)
3 equations and 3 unknowns. Must be solvable.
Vineesh,
Just telling you what I know and think. I am not the expert.
Just telling you what I know and think. I am not the expert.
 Geva@EconomistGMAT
 GMAT Instructor
 Posts: 905
 Joined: 12 Sep 2010
 Thanked: 378 times
 Followed by:123 members
 GMAT Score:760
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.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?
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 204=16 and sam was 84=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.
 BlindVision
 Master  Next Rank: 500 Posts
 Posts: 253
 Joined: 26 Dec 2008
 Thanked: 8 times
 Followed by:1 members
Using the formulas above:vineeshp wrote:J = 2FToday Jim is twice as old as Fred
S = F2Sam is 2 years younger than Fred
Jim 4 years ago = J  4.Four years ago, Jim was 4 times as old as Sam
Sam 4 years ago, S  4.
Equation:
J4 = 4 (S4)
3 equations and 3 unknowns. Must be solvable.
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

 Junior  Next Rank: 30 Posts
 Posts: 24
 Joined: 21 Aug 2011
 Thanked: 5 times
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 J4=4(S4)
Substituting for J AND S in the above,
2F4=4(F24)
2F4=4F816
2F=20
F=10; HENCE J=20;
HOPE YOU GOT IT.
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 J4=4(S4)
Substituting for J AND S in the above,
2F4=4(F24)
2F4=4F816
2F=20
F=10; HENCE J=20;
HOPE YOU GOT IT.