Consider the following scenario. Suppose you solve for all the numbers in a Venn Diagram, in a scenario in which 200 students are taking AP Chemistry, AP Literature, both, or neither. Here are the results you find. OK, from this solved Venn diagram, there’s a ton we know: total in AP Chemistry = 50 + […]

## Counting Practice Problems for the GMAT

1) A librarian has 4 identical copies of Hamlet, 3 identical copies of Macbeth, 2 identical copies of Romeo and Juliet, and one copy of Midsummer’s Night Dream. In how many distinct arrangements can these ten books be put in order on a shelf? (A) 720 (B) 1,512 (C) 2,520 (D) 6,400 (E) 12,600 […]

## One More RTD Table Problem: Average Rates Part 2

If you haven’t been following our series on RTD tables, take a few minutes to catch up: Using Diagrams to Solve Rate Problems: Part 1 Using Diagrams to Solve Rate Problems: Part 2 A Different Use of the RTD Table: Part 1 A Different Use of the RTD Table: Part 2 Using the RTD Table […]

## One More RTD Table Problem: Average Rates Part 1

My last several posts have been devoted to the use of a table to answer rate problems. Today’s post will assume familiarity with that table, so please take a look back at these posts is you’re not already familiar with the RTD table: Using Diagrams to Solve Rate Problems: Part 1 Using Diagrams to Solve […]

## Using the RTD Table for a Complicated Problem

My last few blog posts have involved rate problems about simultaneous movement. In each of these problems we discovered exactly two travelers who either (1) moved at their own constant rates for the entire time period covered by the story, or (2) moved at their own constant rates and started and stopped simultaneously. If you’d […]

## A Different Use of the RTD Table: Part 2

Let’s recap where we left off yesterday. We were working with this diagram: We wanted to solve for Mary’s time, t. In every row the relationship among rate, time, and distance is the same: RT=D. In this diagram the bottom row looks the most promising, since it alone contains only the variable for which we’re […]

## A Different Use of the RTD Table: Part 1

In my last couple of posts (Using Diagrams to Solve GMAT Rate Problems Part 1 and Part 2) I used a Rate-Time-Distance table, (or RTD table) to solve the most common sort of rate problem: a combined-rate problem in which two travelers move in opposite directions simultaneously. (If you haven’t read those posts and aren’t […]

## Using Diagrams to Solve GMAT Rate Problems: Part 2

In Part 1 we used what is called an RTD table to solve a fairly typical rate problem. Today I want to revisit the problem in Part 1 to make a simple point: There’s more than one correct way to use the table. If you keep in mind a few simple truth about the […]

## Using Diagrams to Solve GMAT Rate Problems: Part 1

Diagrams are great! Like all types of scratch-work, diagrams can forestall cognitive fatigue because working a problem out on paper is much less demanding than doing all the work in your head. Diagrams can also help you to visualize relationships, and can make problems more concrete. Generally though, we use diagrams to generate equations, which […]

## GMAT Practice Problems: Variables in the Answer Choices

1) Jennifer can buy watches at a price of B dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of T by selling N watches, then in terms of B and T and N, what is the percent of the markup from her buy price […]

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