Picking numbers is generally faster for all but the simplest problems. I advise my students to try both approaches while practicing. Over time they will recognize which approach is faster for them for which type of problem. Also, once you have mastered both approaches, you have twice as many tools at your command on test day. That means that if you get stuck with one approach, you can try the other.

Tani Wolff - Kaplan wrote:Picking numbers is generally faster for all but the simplest problems. I advise my students to try both approaches while practicing. Over time they will recognize which approach is faster for them for which type of problem. Also, once you have mastered both approaches, you have twice as many tools at your command on test day. That means that if you get stuck with one approach, you can try the other.

Completely agree with Tani above. While not necessarily faster (though it can be), plugging in is usually a safer way to avoid those trap answer choices set by the ACT question writers specifically to lure in test-takers who are set on using algebra. Our instructors and stronger students have grown to respect the power of plugging in, and report using it as the first tool whenever possible, reverting to algebra only if plugging in turns not to be the best way for a particular problem. However, to reach that stage, you must first try out plugging in until you are confident that it works. I suggest you force yourself to find opportunities to plug in, or solve questions in both ways until you are confident of the method.

Hey Kyle,

Well, someone needs to play devil's advocate, right? I may actually agree a little with you about plugging in numbers having the potential to become time-consuming. While it's certainly a valid way to solve problems and something that everyone should have in his arsenal, I have a hard time looking a problem like the one below knowing that I'm committed to doing 6 arithmetic problems by plugging in those numbers:

If a taxi driver charges x cents for the first quarter-mile of a trip and x/5 cents for
each additional quarter-mile, what is the charge, in cents, for a trip whose distance in miles is the whole number y?

A) (x+xy)/125
B) (4x+4xy)/5
C) (4x+xy)/500
D) (4x +xy)/5
E) xy/25

Granted, some of the arithmetic is going to be replicated in each step, but I like using what I'll call the "Hybrid Method" for problems like these, in which I plug in a few numbers just to get the algebra started, then go right back to the algebra.

HYBRID METHOD

For this problem, it may be tough to set things up using just pure algebra, but you'd do it quite easily if you had numbers. Say that it were a 3-mile trip and that the cab charged 50 cents for the first quarter-mile and then 10 cents for each additional. You'd have:

x = 50
x/5 = 10
y = 3

How would you calculate the charge? You'd start with the 50 cents for the first quarter, and there would be 10 cents for each remaining quarter mile, of which there are 111, so you'd have 50 + 10*11.

Now, here's where I think it's often advantageous to convert right back to algebra. I know what the setup is now - it's:

50 + 10 * 11
x + x/5 * (11 is the number of quarter miles left), so:

x + x/5 * (4y-1) ---> (4y-1 is how we mathematically got to 11 by subtracting the one quarter-mile)

Now we find common denominators so that we can get to one term as in the solutions:

5x/5 + x(4y-1)/5

Then distribute the multiplication and keep it all over the common denominator 5:

(5x + 5xy - x)/5

Then combine like terms:

(4x + 5xy)/5 --> Choice B



Now, I should add that one reason I do the algebra is that I'm very comfortable with algebra, but I would hope that anyone looking for a high score on the GMAT is working on getting toward that point. What I like about the hybrid method is:

-The answer choices give you an algebraic goal (in this case, all one fraction with one common denominator) so once you're set up the steps should seem somewhat clear
-The use of numbers helps you to reason out the algebra clearer than keeping it all completely theoretical
-You avoid that potential of having multiple answer choices work out based on the values that you picked, and you avoid having to do multiple arithmetic calculations

As the others on this thread have mentioned, number picking can be a very useful strategy, but I also worry that relying solely on number picking is often a crutch for those who fear algebra. A healthy percentage of hard GMAT problems are algebra-based, so I'd strongly advise having multiple tools for these questions - plugging in, hybrid, and some pure algebra - at your disposal and practicing some with each, as ultimately having flexibility on test day and the skill base of having practiced with algebra in multiple ways will be instrumental in your success.

Thanks a lot for your help!