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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
This is the trap on most age problems. Four years ago, Jim and Sam were both four years younger- the equation needs to be:dbart06 wrote: 3)j-4=4s
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.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
Ian Stewart wrote:This is the trap on most age problems. Four years ago, Jim and Sam were both four years younger- the equation needs to be:dbart06 wrote: 3)j-4=4s
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
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.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
Ian, one followup please: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
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:Alpha800 wrote:Ian, two followups please:Ian Stewart wrote: we get 2 eqns, 2 unknowns:
j = 2s + 4
j = 4s - 12
0 = 2s - 16
8 = s
20 = j
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!
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.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
Ok. That helps. I'll try to remember to think along this route. Thanks!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!
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.Alpha800 wrote:
Princeton Review used this problem to illustrate their example of "plugging in the answers" to solve it.
Absolutely Ian. I agree with you 100%. I'm trying to score 800!Ian Stewart wrote: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.Alpha800 wrote:
Princeton Review used this problem to illustrate their example of "plugging in the answers" to solve it.
(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.New here Create free account
