# Beat The GMAT Team's Featured Posts for 2010 - Problem Solving

by Beat The GMAT, Dec 27, 2010

2010 has been a special year for the Beat The GMAT community. This fall we celebrated our 100,000th member and this important milestone reminded us all that we are, first and foremost, a community built by our members for our members. We wanted to thank all of our members, both regular test takers and experts, by featuring some of our favorite threads from our forums. Your wonderful contributions are much appreciated by MBA hopefuls everywhere!

Problem Solving is the most active subforum in our community. Here, members post questions on the most diverse of topics, ranging from number properties to geometry, from statistics to combinatorics. Each post in this forum is worth a read, because you never know when youre going to stumble upon that shortcut that saves you 3 minutes on the real test. We particularly like the fact that youll sometimes get two or more different approaches to solving a given problem, which allows you to find the best way that works for you.

## Divisors on the GMAT

praveen_gmat was looking for a quick way to figure out the number of divisors of a certain number. Should you really spend time listing all the factors of [pmath]36^2[/pmath]? After all, 36 already has quite a few divisors: 1, 2, 3, 4, 6 and so on. Squaring this number and trying to list all its divisors is certainly a good way to waste 10 minutes. Brent Hanneson provided one of our favorite shortcuts in GMAT quant, though:

In general, we can say that if [pmath]N = (p^a)(q^b)(r^c)[/pmath]..., where p, q, r etc are prime numbers, then the total number of positive divisors of N is equal to [pmath](a+1)(b+1)(c+1)[/pmath]...

Check out the thread here. Also, be sure to watch Brents series on Data Sufficiency!

## Solving an overlapping sets question without calculations?

As weve mentioned before, we love to see more than one solution to a question. ikaplan posted a question involving overlapping sets, a type youll surely see on test day. shovan85 and [email protected] both provided answers using straightforward calculations, but we also really liked Stuart Kovinskys way of solving the problem:

If we understand the concept of weighted averages, and keep an eye on the choices, we can solve this with 0 calculations.

If the men's average were 18, then the women and men would be equally weighted. Accordingly, the men's average must be more than 18. Only (D) fits the bill - done!

You can read the thread by clicking here.

## Stepping on an escalator

Sometimes one answer inspires another, which seeds discussion in our community. This is exactly what happened when goyalsau posted a question about stepping on an escalator. limestone provided an answer, which then inspired fskilnik to come up with a fast and easy to understand solution. He even created a similar question, in case you want to practice what youve learned. Try answering this question:

M. Poirot and Miss Marple walk into a turned-off escalator to realize that he is able to walk 3 steps during the time she needs to walk only 2. When the escalator is turned-on (and is already working at constant speed), M. Poirot enters again the escalator to realize he needs to take 25 steps to go through it, while Miss Marple realizes she needs only 20 steps to reach its end (at the very same conditions). How many steps are there in the escalator ?