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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 […]
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 […]
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 […]
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 […]
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 […]
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 […]
Here are four practice problems involving similar figures. 1) In the figure, KLMN is a square, and angle KJN = 45°. Find the area of figure JKLMN. 2) In the diagram, HJLM is a square, and GH = 10. Find the area of trapezoid GHJK. 3) In the diagram, BD = 5, CD = 10, […]
1) The line shown passes through the point (A, 30). Which of the following is closest to the value of A? (A) 58 (B) 59 (C) 60 (D) 61 (E) 62 2) Line A has a slope of and passes through the point (–2, 7). What is the x-intercept of Line A? 3) Line J […]
Here are twelve challenging problems related to the topic of exponents & roots. Remember, no calculator. (A) 17 (B) 19 (C) 21 (D) 23 (E) 27 4) Rank the following quantities in order, from smallest to biggest. (A) I, II, III (B) I, III, II (C) II, I, III (D) III, I, II (E) III, […]
Here are eight practice problems on Sequences. 14, 23, 32, 41, 50, 59, … 1) In the sequence above, each term is 9 more than the previous term. What is the 40th term of the sequence? (A) 360 (B) 365 (C) 369 (D) 374 (E) 383 2) What is the difference […]
Here are four reasonably challenging problems about sets. 1) At a certain school of 200 students, the students can study French, Spanish, both or neither. Just as many study both as study neither. One quarter of those who study Spanish also study French. The total number who study French is 10 fewer than those who […]
Here are ten reasonably challenging problems on powers and roots. Solutions follow the problems. Remember, no calculator! Statement #1: x < 1 Statement #2: x > –1 4 8 14 28 42 5) If A is an integer, what is the value of A? 11 30 45 75 225 Powers & roots This is […]
Here are ten problems on fractions and decimals, some of which are quite challenging. Remember, no calculator! (A) 0.1 (B) 1 (C) 10 (D) 100 (E) 1000 6) Suppose you have access to a large vat of distilled water, several gallons large. You have two precise measuring pipettes, one to measure exactly 1/3 of an […]
Hello! 🙂 This week, I’m solving a tough challenge question that you might have seen on our blog if you visit often! This challenge question draws on a whole host of geometry concepts and formulas, so it’s a great test for how much of geometry you really know. And just in case the board […]
