Problem Solving

I'm trying to learn to guess on problems I know how to solve , following the advice I read here. But, I can't find a way to guess on such a problem. How would you tackle it. I need an example for how this strategy works.

On Sunday, Bill ran 4 more miles than he ran on Saturday. Julia did not run on Saturday, but she ran twice the number of miles on Sunday that Bill ran on Sunday. If Bill and Julia ran a total of 24 miles on Saturday and Sunday, how many miles did Bill run on Sunday?

choices are : 5,6,7,8,9



Thank you,

Fadi

Hi!

Let X represent number of miles that Bill ran on Saturday
Bill ran on Sunday X + 4 miles
Julia ran on Sunday 2(X + 4) miles
Total 24 miles
24 = X + X + 4 + 2(X + 4)
24 = 4X + 12
X = 3
X + 4 = 7
Bill ran on Sunday 7 miles

Hope it helps!
Best,
Maciek

Hey Fadi,

Interesting question...I guess you could go one of two ways with it, so hopefully one of these is what you're thinking:

1) You have 20 seconds or less left and have to just guess without any time to really think.

Read the question and get a feel for how they'd set up the answer choices so that you can strategically rule out the likely "trap" answers. Since they're asking about Bill's Sunday run, we can tell that:

It's longer than his Saturday run
It's shorter than Julia's run

There's a good chance that the GMAT would set up answer choices that would correspond with the Saturday run or Julia's run, so you're looking for a number toward the middle of the range of answer choices (the biggest number may well be Julia's, the smallest may well be Saturday).

Now...that's a pretty low-percentage "get it right" strategy, but definitely not a bad "give yourself a significantly better than 20% blind guess" strategy. Picking a number toward the middle helped you get close to that correct answer of 7, but neither Saturday's nor Julia's run was an answer choice, so the strategy didn't really work as planned.


2) You want to backsolve (not really guess) using the answer choices.

Here, the strategy is to start with a middle number, plug it back into the word problem, and determine whether it's:

Correct (you're done)
Too small (you can eliminate it and anything smaller)
Too big (you can eliminate it and anything bigger)

If you start exactly in the middle, you can plug in C:

7 is the Sunday run, 7*2 = 14 is Julia's run, and 7-4 = 3 is the Saturday run. 7 + 14 + 3 = 24 so that's correct.

However, if C is not right, you have to do one more problem to get it right (say C were too small, you'd have to check D, and either that would be right or if not it's E).

Therefore, if you have a feeling that you need a larger number or a smaller number (say they were asking about the Saturday run, you'd have a good inkling that the trap answers could be the larger numbers for Sunday and Julia), then you can pick B or D to backsolve, with the added benefit that if B is too big, only A is left as a possible choice. This way, you're more likely to have the correct answer in just one step.




All that said, if you find a question relatively straightforward using the algebra, why guess or backsolve? You may well be at the point where the algebra is faster than trying to find a "faster" way...

Thank you, but to make it clear I know how to solve it directly but I would like to know how people think when trying to guess on this problem which I understand

Thank you

Thanks Brian that is what I was looking for. I'm asking because I read on the articles here to try to find the guessing strategy for problems I solved right so that I can use it on harder problems that I might not be able to solve. But that.s theoretical I needed an example of how to think about it in practice.

Thank you again for clearing that up

Note: the previous post was posted before brian answered, but it was marked as spam and delayed.