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PS: Jim is twice as old as Fred...

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PS: Jim is twice as old as Fred...

by Alpha800 » Mon Aug 04, 2008 2:32 pm
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?

8
12
16
20
24

Princeton Review used this problem to illustrate their example of "plugging in the answers" to solve it. But how do you solve it algebraically? I've been trying to solve this for the past half an hour and it's driving me nuts. How do you setup the formula to solve it algebraically?

Thanks in advance!
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by dbart06 » Mon Aug 04, 2008 2:59 pm
IMO 12. if this is correct, here's how.

write 3 equations:

1)j=2f
2)s=f-2
3)j-4=4s
Sub equation 1 & 2 into 3 to get 2f-4=4(f-2) & solve for f to get 2. Now this is how old f is 4 yrs ago because we solved for the 4 yrs ago equation.

If f=2 4 yrs ago then f=6 now. plug that 6 into equation 1 to get j =12
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by Ian Stewart » Mon Aug 04, 2008 3:06 pm
dbart06 wrote: 3)j-4=4s
This is the trap on most age problems. Four years ago, Jim and Sam were both four years younger- the equation needs to be:

j-4 = 4(s-4)

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?

I'd bypass Fred altogether (using that s+2 = f):
today: j = 2(s+2)
four years ago: j-4 = 4(s-4)

we get 2 eqns, 2 unknowns:

j = 2s + 4
j = 4s - 12
0 = 2s - 16
8 = s
20 = j
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by Alpha800 » Mon Aug 04, 2008 3:06 pm
dbart06 wrote:IMO 12. if this is correct, here's how.

write 3 equations:

1)j=2f
2)s=f-2
3)j-4=4s
Sub equation 1 & 2 into 3 to get 2f-4=4(f-2) & solve for f to get 2. Now this is how old f is 4 yrs ago because we solved for the 4 yrs ago equation.

If f=2 4 yrs ago then f=6 now. plug that 6 into equation 1 to get j =12
Thanks for replying. Sorry I left out the supposed correct answer. Princeton claims the answer is (D - 20). The method they used was to plug in all the answers to see which one worked.

I'm going to go over your algebra now and see if it works.
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by Alpha800 » Mon Aug 04, 2008 3:09 pm
Eureka!!! Thanks so much Ian. that's the stupid part that I couldn't figure out. You have to subtract 4 to both ages. I kept on only subtracting 4 to Jim. Thanks a million Ian. It makes sense now! :D
Ian Stewart wrote:
dbart06 wrote: 3)j-4=4s
This is the trap on most age problems. Four years ago, Jim and Sam were both four years younger- the equation needs to be:

j-4 = 4(s-4)

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?

I'd bypass Fred altogether (using that s+2 = f):
today: j = 2(s+2)
four years ago: j-4 = 4(s-4)

we get 2 eqns, 2 unknowns:

j = 2s + 4
j = 4s - 12
0 = 2s - 16
8 = s
20 = j
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by Alpha800 » Mon Aug 04, 2008 3:14 pm
dbart06 wrote:IMO 12. if this is correct, here's how.

write 3 equations:

1)j=2f
2)s=f-2
3)j-4=4s
Sub equation 1 & 2 into 3 to get 2f-4=4(f-2) & solve for f to get 2. Now this is how old f is 4 yrs ago because we solved for the 4 yrs ago equation.

If f=2 4 yrs ago then f=6 now. plug that 6 into equation 1 to get j =12
Ok, having looked over your math, it is exactly as how I set up the problem as well. However, as Ian pointed out, we both missed the -4 to Sam's age four years ago. That's what kept on tripping up my answer. :o

Thanks for posting dbart06.
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by Alpha800 » Mon Aug 04, 2008 3:17 pm
Ian Stewart wrote: I'd bypass Fred altogether (using that s+2 = f):
today: j = 2(s+2)
four years ago: j-4 = 4(s-4)

we get 2 eqns, 2 unknowns:

j = 2s + 4
j = 4s - 12
0 = 2s - 16
8 = s
20 = j
Ian, one followup please:

How do I remember to setup the equation as j-4 = 4(s-4) and not j-4 = 4s-4
I am tempted to subtract 4 years from 4s. :(

Thanks!
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by Ian Stewart » Mon Aug 04, 2008 3:54 pm
Alpha800 wrote:
Ian Stewart wrote: we get 2 eqns, 2 unknowns:

j = 2s + 4
j = 4s - 12
0 = 2s - 16
8 = s
20 = j
Ian, two followups please:
1) how did you get 0 = 2s - 16.
Where did you extract that info from?

2) how do I remember to setup the equation as j-4 = 4(s-4) and not j-4 = 4s-4
I am tempted to subtract 4 years from 4s. :(

Thanks!
1) I was solving the 2 equations, 2 unknowns- I subtracted the first equation from the second. So really, I was thinking of the two equations like this:

j = 4s - 12
j = 2s + 4

and subtracting. Of course, since j is equal both to 4s - 12 and to 2s + 4, you could also simply solve:

4s - 12 = 2s + 4
2s = 16
s = 8

2) It is easy to make such mistakes on these kinds of questions. I ask myself 'what quantity is equal to 4 times what quantity?'
--> 'Jim's age four years ago (j-4) is equal to 4 times Sam's age four years ago (s-4)', so

(j-4) = 4(s-4)

Hope that helps!
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by Alpha800 » Mon Aug 04, 2008 4:07 pm
Ian Stewart wrote: 1) I was solving the 2 equations, 2 unknowns- I subtracted the first equation from the second. So really, I was thinking of the two equations like this:

j = 4s - 12
j = 2s + 4

and subtracting. Of course, since j is equal both to 4s - 12 and to 2s + 4, you could also simply solve:

4s - 12 = 2s + 4
2s = 16
s = 8
Thanks very much Ian. It's been a long time since I've done some extensive algebra--I just started seriously prepping for the GMAT last week--so I totally forgot a lot of methods used to solve for equations. After I asked my question, I was able to figure out what you did and I started remembering what one does when there's two equations to solve. LOL.. It's funny how things start to come back as you think about it more. But thanks for taking the time to answer my question. :)
2) It is easy to make such mistakes on these kinds of questions. I ask myself 'what quantity is equal to 4 times what quantity?'
--> 'Jim's age four years ago (j-4) is equal to 4 times Sam's age four years ago (s-4)', so

(j-4) = 4(s-4)

Hope that helps!
Ok. That helps. I'll try to remember to think along this route. Thanks!
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Re: PS: Jim is twice as old as Fred...

by Ian Stewart » Mon Aug 04, 2008 4:12 pm
Alpha800 wrote:
Princeton Review used this problem to illustrate their example of "plugging in the answers" to solve it.
I should add that it's a very good idea to learn how to do this question algebraically, and I think your efforts here are worthwhile. As they've presented the question, plugging in answers is fairly quick, and perhaps less prone to error. But the question could instead have asked: Now, Jim is what percent older than Sam? It's much harder, in this case, to test answer choices like 125% or 150% to see if they're correct- you'd be best off doing the algebra. I don't much like when books illustrate problem solving for certain question types only via 'plugging in answers', because it's invariably easy for GMAT test-writers to modify their questions to foil the strategy.
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Re: PS: Jim is twice as old as Fred...

by Alpha800 » Mon Aug 04, 2008 4:20 pm
Ian Stewart wrote:
Alpha800 wrote:
Princeton Review used this problem to illustrate their example of "plugging in the answers" to solve it.
I should add that it's a very good idea to learn how to do this question algebraically, and I think your efforts here are worthwhile. As they've presented the question, plugging in answers is fairly quick, and perhaps less prone to error. But the question could instead have asked: Now, Jim is what percent older than Sam? It's much harder, in this case, to test answer choices like 125% or 150% to see if they're correct- you'd be best off doing the algebra. I don't much like when books illustrate problem solving for certain question types only via 'plugging in answers', because it's invariably easy for GMAT test-writers to modify their questions to foil the strategy.
Absolutely Ian. I agree with you 100%. I'm trying to score 800! :) (700+ realistically) I want to know the math (algebra) behind the questions. I don't like their idea of plugging in so frequently so I'm trying to learn/re-learn/remember how to solve these problems using actual math, and not a gimmick.

Cracking the GMAT with Princeton is just my first book to give me a quick and easy review. After this I go onto Kaplan then Kaplan 800. So I'm certainly not planning on only using Princeton to score my 700+. A lot of their tips and suggestions really are targeted towards 550-650 scores, not 700+ scores.

Thanks again for your help and tips. Much appreciated!
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by dbart06 » Mon Aug 04, 2008 6:52 pm
Thank Ian.

I realized I messed up the equation about the 4 yrs ago.
The simple things get me every time.
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by shalen78 » Thu Sep 11, 2008 2:43 am
There is one other way to do this, although very similar:
J = 2F (Equation 1)
S= F-2

J-4=4(F-2-4)
J-4=4F-8-16
J-4=4F-24
J=4F-20 (Equation 2)

Set the two equations equal

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

Plug F=10 into first equation
2F = J
2(10) = J
20 = J
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