### Number Properties in GMATPrep

What are number properties? This concept covers things that we often call basic “ topics that we learned in middle school (or earlier): divisibility, factors and multiples, odds and evens, positives and negatives, and so on. It’s also true, though, that this material can become quite complex. For example, fundamental counting principles are included in number properties, and the more complex problems of this typeare something called Combinatorics which most of us hate. = ) In addition, we’ve all come up against very challenging problems testing a supposedly “simple” concept, such as divisibility.

We face two big challenges in dealing with number properties:

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### Translating Words into Math

I’ve spoken with several students recently who are struggling with translating wordy quant problems into the actual math necessary to set up and solve the problem. Some people make too many mistakes when doing this, and others find that, though generally accurate, they take more time than they can afford. In the next two articles (this is part 1!), we’re going to talk about how to translate efficiently and effectively.

We’re going to do this by example: I’ll provide short excerpts from OG or GMATPrep problems, and then we’ll discuss how to know what to do, how to do the actual translation, and how to do so efficiently. Note that I’m not going to provide the full text of problems “ and, therefore, we’re not going to solve fully. That’s not our goal today.

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### Challenge Problem Showdown – February 26th, 2012

We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!

Here is this week’s problem:

How much greater is the square of the sum of three different positive integers than the sum of their squares?

(1) The sum of the products of all possible pairs of two different integers out of the original set of three is 61.

(2) The largest of the three integers, 7, is equal to the sum of the two smaller integers.

### Disguising – and Decoding – Quant Problems

How can the GMAT disguise a prime number (or any other) problem? That’s exactly what we’re going to discuss today! We’re going to use the concept of prime to describe this, but the general process of disguising “ and studying how to decode “ problems is applicable to a great number of problems on the test. Pay particular attention to the end of the article; you can use these concepts when studying a number of different GMAT content areas. Read more

### Challenge Problem Showdown – February 21st, 2012

We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!

Two integers between 1 and 100, inclusive, each randomly and independently chosen, are either added or multiplied, with an equal chance of either operation. What is the probability that the result is even?

### Tackling a GMATPrep Critical Reasoning Weaken Problem

This week, we’re going to discuss one of the most common critical reasoning problem types: Weaken the Conclusion. If you haven’t yet, read this article before we try our GMATPrep problem. Then set your timer for 2 minutes and go!

* Tiger sharks are common in the waters surrounding Tenare Island. Usually tiger sharks feed on smaller sharks, but sometimes they have attacked tourists swimming and surfing at Tenare’s beaches. This has hurt Tenare’s tourism industry, which is second only to its fishing industry in annual revenues. In order to help the economy, therefore, the mayor of the island has proposed an ongoing program to kill any tiger sharks within a mile of the beaches.

Which of the following, if true, most strongly calls into question the likelihood that implementation of the mayor’s proposal will have the desired consequences?

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### Challenge Problem Showdown – February 13th, 2012

We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!

Here is this week’s problem:

Standing on the origin of an

xy-coordinate plane, John takes a 1-unit step at random in one of the following 4 directions: up, down, left, or right. If he takes 3 more steps under the same random conditions, what is the probability that he winds up at the origin again?

### Inequalities

Today we’ve got an inequalities data sufficiency question on tap from GMATPrep. Set your timer for 2 minutes and go!

Is

m+z> 0?(1)

m“ 3z> 0

(2) 4z“m> 0

This is a yes/no data sufficiency question. I’m just going to remind myself of the rules: an always yes answer to a statement is sufficient, an always no answer is also sufficient, and a maybe or sometimes yes / sometimes no answer is *not* sufficient.

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### Challenge Problem Showdown – February 6th, 2012

We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!

Here is this week’s problem:

Each of three investments has a 20% of becoming worthless within a year of purchase, independently of what happens to the other two investments. If Simone invests an equal sum in each of these three investments on January 1, the approximate chance that by the end of the year, she loses no more than 1/3 of her original investment is