Prep - GMAT Advanced Quant

Chapters deal specifically with DS issues.

This chapter outlines broad principles for solving advanced PS problems. You've already seen very basic versions of the first three principles in the Introduction, in the dialogues between the Top-Down and the Bottom-Up brain.

As mentioned earlier, these principles draw on the work of George Polya, who was a brilliant mathematician and teacher of mathematics. Polya was teaching future mathematicians, not GMAT test-takers, but what he said still applies. His little book How To Solve It has never been out of print since 1945it's worth getting a copy.

In the meantime, keep reading!

Principle #1: Understand the Basics

Slow down on difficult problems. Keep three broad activities in mind while trying to Understand the problem:

Glance Read Jot

Glance at the entire problem: is it PS or DS? If it's PS, glance at the answer choices to see what form they're in. If it's DS, glance at the statements: is most of the complexity in the question stem or in the statements?

Polya recommended that you ask yourself a few simple questions as you Read a problem. We whole-heartedly agree. Here are some great Polya-style questions that can help you Understand:

• What exactly is the problem asking for?
• What are the quantities I care about? These are often the unknowns.
• What do I know? This could be about certain quantities or about the situation more generally.
• Whatdon'tI know?
  • Sometimes you care about something you don't know. This could be an intermediate unknown quantity that you didn't think of earlier.
  • Other times, you don't know something, and you don't care. For instance, if a problem includes the quantity 11! (11 factorial), you will practically never need to know the exact value of that quantity.
• What is this problem testing? In other words, why is this problem on the GMAT? What aspect of math are they testing? What kind of reasoning do they want me to demonstrate?

Don't forget to Jot down any given numbers or formulas on your scrap paper.

The Understand the Basics principle applies later on as well. If you get stuck, go back to basics. Re-read the problem and ask yourself these questions again (within a reasonable amount of time, of course).

Start the following problem by trying to Understand what's going on.

Try-It #1-1

x = 910 317 and is an integer. If n is a positive integer that has exactly two factors, how many different values for n are possible?

Glance. This is a PS problem. The answers are numbers but in written form; this format is reserved for questions that ask for the number of numbers or number of possibilities for something. The numbers are small.

Read. Dive into the text. Here are some possible answers to the Polya questions.

You can ask these questions in whatever order is most helpful for the problem. For instance, you might not look at what the problem is asking for until you've understood the given information.

Jot. As you decide that a piece of information is important, jot it down on your scrap paper. At this point, your scrap paper might look something like this:

= int n = prime
x = 910 317

Principle #2: Build a Plan

Next, think about how you will solve the problem.

Reflect Organize

Reflect. Here are some Polya questions that help you think about what you know and come up with a Plan.

Organize. For the Try-It #1-1 problem, some of the information is already rephrased (re-organized). Go further now, combining information and simplifying the question.

You need the prime factorization of x. Notice that n is not even in the question anymore. The variable n just gave you a way to ask this underlying question.

Consider the other given fact: x = 910 317. It can be helpful initially to put certain complicated facts to the side. At this stage, however, you know that you need the prime factors of x. So now you have the beginning of a plan: factor this expression into its primes.

Principle #3: Solveand Put Pen to Paper

The third step is to do the work: Solve.

Work