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Lines on the GMAT: The Basics of Coordinate Geometry

By posted September 16, 2011

MBA admissions, and life in general, doesn’t always seem to follow a straight line. However in math, lines are one of the most fundamental building blocks and vital to practicing for the GMAT. In Euclidean geometry, a line is defined as having only one dimension: length. Lines appear on the GMAT in coordinate geometry in several ways, and various linear equations must be understood and applied on your GMAT practice questions to get even the most basic Geometry questions correct. It’s comforting to know that while MBA applications may be circuitous, the fundamentals of GMAT stay the same. Here are the need-to-know equations for better scores in GMAT Geometry!

Test your GMAT skills with this GMAT problem solving practice question!

The general equation for a line is: ax + by + c = 0 for all values (x,y) that are on that line. In this form, the slope is –a/b and the y-intercept is –c/b.

The most common equation for a line is called slope-intercept form: y = mx + b, for all values (x, y) on the line. Here m is the slope and b is the y-intercept.

A modified version of slope-intercept form is called point-slope form: y – y1 = m (x – x1) + b. This equation is helpful if you are given two points on the line, (x, y) and (x1, y1).

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GMAT Quant: 3 Great Tips for Interpreting Graphs & Tables

By posted September 8, 2011

Data Analysis is not heavily tested on the GMAT, but you will likely see at least 2 or 3 test questions that require you to understand a graph or a table and answer relevant questions. (After all, you’ll need to analyze a lot of information in business school, so it makes sense that the best business schools want MBA candidates to start now.) Make sure to take note of DA questions on your GMAT practice tests and on the various GMAT online resources. It will help you improve your GMAT practice if you review this specific type of GMAT practice question in a set, emphasizing applying this strategy to your Test Prep.

Check out this GMAT graph question for more GMAT practice!

1. Analyze the data first. Don’t jump to the question and then go back to the data to look for an answer. Read all of the labels on the presented graph or table. What is in each column? What is in each row? What is the range of values? Does the data have a direct or indirect relationship? Do the lines have positive or negative slopes? Where was there the most change or growth? Where was there the least?  With this kind of discipline, you will already understand what is being presented. The question becomes almost an afterthought, and you’ll know exactly where to look for the correct information.

2. Ask yourself: what data do I need to solve? Graphs and tables often give us extraneous information. You will not need everything to solve. Chances are the correct answer hinges on just 1 or  2 numbers from the data. Most people get Data Interpretation questions wrong because they do not know what data to use to solve, not because the Math involved is difficult. You will likely only be performing calculations as simple and easy as addition, subtraction, multiplication and division.

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3 Ways of Looking at Profit (with 3 Harder Questions)

By posted August 31, 2011

As someone who is about to shell out hundreds of dollars in MBA application fees, you know that money makes the GMAT-world go round. Profit is an essential concept for any aspiring MBA admissions applicant. The GMAT tests this concept in both Problem Solving and Data Sufficiency questions in three main ways. Let’s examine the need-to-know formulas with three GMAT practice questions.

  1. A firm increases its revenues by 10% between 2008 and 2009. The firm’s costs increase by 8% during this same time. What is the firm’s percent increase in profits over this period, if profits are defined as revenues minus costs?(1) The firm’s initial profit is $200,000.(2) The firm’s initial revenues are 1.5 times its initial costs.

In this question from Grockit, we can start with our most basic Profit formula:

Profit = Revenue – Cost

Try this GMAT problem solving question for more GMAT practice!

Using Statement (1), we can say that 200,000 = R – C.

(1.1)r – (1.08)c = 200,000(1 + x), where x equals the amount of the increase. We still do not know R and C so we can’t find x. Insufficient.

Using Statement (2), 1.5c – c = p and (1.1)(1.5)c – (1.08)c = (1 + x)P. Here we can simplify.

.5c = p

.57c = (1 + x)p

Without continuing to solve, we can see that we can solve for x using substitution. .57c = (1 + x)(.5c), and dividing both sides by c will cancel out that variable and allow us to isolate x. Statement 2 is sufficient. Now to a more challenging question!

  1. A store purchased 20 coats that each cost an equal amount and then sold each of the 20 coats at an equal price. What was the stores gross profit on the 20 coats?

Statement 1. If the selling price per coat had been twice as much, the store’s gross profit on the 20 coats would have been $2400.
Statement 2. If the selling price per coat had been $2 more, the store’s gross profit on the 20 coats would have been $440.

This GMAT Prep question asks about gross profit.

Gross Profit = Selling price – Cost

For the value Data Sufficiency question, we need to know the price of each coat and the selling price of each coat. From the given information, we can use our known formula to set us the equation: P = 20 (s – c). So either we’ll need a value for s and a value for c, or we’ll need the value of (s – c).

Statement (1) tells us that $2400 = (20(2s – c)) or 2400 = 40s – 20c. We can divide both sides by 20 and simplify it to: 120 = 2s – c.  We still don’t know s and c. Insufficient.

Statement (2) tells us that 440 = 20(s + 2 – c). Let’s simplify: 440 = 20s + 40 – 20c.  400 = 20s – 20c.  400 = 20 (s – c). 20 = s – c. Sufficient. Even though we didn’t solve for s and c separately, we were able to find the value of (s – c). Sometimes DS will surprise you!

  1. If the cost price of 20 articles is equal to the selling price of 25 articles, what is the % profit or loss made by the merchant?A. 25% loss
    B. 25% profit
    C. 20% loss
    D. 20% profit
    E. 5% profit

Profit/Loss % = (Sales Price – Cost Price) / Cost Price x 100

The question asks about % profit or loss. It tells us that 20c = 25s, or 4c = 5s. So the ratio of the sales price to the cost price is 4/5.

Let’s simplify our Profit/Loss % formula by dividing each term by the cost price:

Profit/Loss % = (S/C – C/C) x 100

P/L% = (S/C – 1) x 100

We know that S/C = 4/5 for this problem. So we can plug in and solve:

P/L% = (4/5 – 1) x 100

P/L% = (-1/5) x 100

P/L% = -20%.   The answer is a 20% loss.

Find out how you can collaborate with your peers to reinforce your knowledge and theirs on Grockit today.

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GMAT Basics: Simplifying Algebraic Expressions

By posted August 29, 2011

The GMAT contains a lot of algebra. Don’t feel guilty is you can’t recall the difference between an “integer” and a “whole number” or if your Quant understanding is limited. The GMAT won’t test your knowledge of definitions, per se, but a good grasp of the basics of algebra is essential for a good GMAT score and for achieving your MBA.  Let’s start with the basics! An algebraic expression is a mathematical statement which often uses constants and variables. For example: 10x – 14.

PEMDAS is an acronym for the order of operations, which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Always start with what is inside the parentheses then address any exponents to simplify an expression. Next, move left to right, doing all division and multiplication. Finally, again moving from left to right, do any addition or subtraction.  PEMDAS is important to memorize as it will tell you how to simplify expressions correctly.

Try this GMAT problem solving question for more GMAT practice today!

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When is the GMAT offered?

By posted August 3, 2011

During your GMAT test prep, you’ll need to schedule your actual GMAT test. The GMAT test is offered year round at testing centers around the world. Check with the admission deadlines for the business schools you will be applying to and choose the best test date. Keep in mind that GMAT scores can take up to 4 weeks before being released. Also remember to register early enough as available spots may vary at each GMAT testing location.

If you need disability accommodations you must fill out a request form and send to Pearson VUE.

Check out your data sufficiency skills on this question! Good luck!

Visit mba.com or call 800-717-GMAT to register to take the GMAT test.

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GMAT Quantitative: Distance Problems

By posted July 21, 2011

The “distance problem” on the GMAT depends on one basic formula you may still remember from high school: distance=rate x time, or d=rt. Generally, a distance problem must utilize this formula to solve for one or more of these possible variables. In other words, you will either have to calculate a distance, a rate (such as miles per hour or kilometers per hour), or the length of time it takes to traverse such a distance at a certain rate. As with all formula problems, you should become comfortable with manipulating the formula in every possible way:

Distance = rate x time

Rate = distance / time

Time = distance / rate

Let’s check out an example to start learning the strategies for distance problems.

Need to study GMAT on the go? Check out Grockit’s GMAT mobile app.

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GMAT Geometry Basics: Parallel Lines

By posted June 23, 2011

We can say that two lines are “parallel” if they never intersect and get neither closer nor farther away from one another. || is the symbol for parallel lines. In coordinate geometry, parallel lines have the same slope, but different x-intercepts.

Try this GMAT geometry practice question and test your skills today!

Parallel lines can be tested in either Problem Solving or Data Sufficiency and though the concept itself is relatively simple, the test questions presented can appear somewhat complex. Don’t make assumptions about lines that look parallel but may in fact not be. Let’s look at an example of how the “eyes can deceive” from GMATPrep:

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3 Tips for Confusing Function Questions on the GMAT

By posted June 14, 2011

1. Look for the new definition. In symbol functions, the test makers choose a new symbol, something that you probably haven’t seen before, and give it a new definition. You aren’t supposed to already know the meaning of the new symbol in the same way you know common math symbols like +, -, x and ÷. The question will tell you exactly how the new symbol functions.

Let z € y be defined by the equation z € y = z2 – 1/y. What is the value of 3 € 1?

Check out Grockit’s GMAT video and MBA school admissions course today!

Here we plug in 3 for z and 1 for y to solve.

3² – 1/1

9 – 1

8

2. Replace abstracts with numbers. For questions with functions in the answer choices, use the given definitions to substitute in for x.

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Beat the Coordinate Geometry Blues! – Part 2

By posted May 3, 2011

The standard equation for a parabola is y = ax2 + bx + c. In this equation c represents the y-intercept. A standard equation in which a variable is squared will never make a straight line.

Based on the figure, is this is the correct graph for the equation:  y = (x3 + x)/x ?


For a question like this, don’t get nervous if the equation given does not match the standard equation for a parabola. This equation simplifies to y = x2 + 1. We can see from the graph that the y-intercept is indeed 1. When we plug in the x-coordinates of the other two given points, we know this must be the correct equation. When in doubt, plug in!

The x-intercepts are also called the “roots” or “solutions” of a parabola. On the GMAT, parabolas will often be referred to as “functions” interchangeably. The x-intercepts can be found using the quadratic formula:

To find the number of x-intercepts a given parabola has, calculate what is called the discriminant:  or the information underneath the radical in the quadratic formula.

If the discriminant is positive, the parabola has two intercepts with x-axis; if it is negative there are no intercepts with the x-axis, and if the discriminant is equal to zero there is one intercept with the x-axis.

The vertex represents the maximum (or minimum) value of the function. Think of it as the starting point of the function.


The vertex of the parabola is located at point  for the standard equation. If you are given the standard equation, you can find the vertex and the x-intercepts.

The standard equation of a circle is (x – h)2 + (y – k)2 = r2 where (h, k) is the center point of the circle and r is the radius. For example, on test day you might see a circle plotted on a graph like so:

The question will ask you to find the equation of the circle. All we have to find is the center point (0, 4) and the radius (4), and then plug it into our equation.

(x – h)2 + (y – k)2 = r2

(x – 0)2 + (y – 4)2 = 42

(x)2 + (y – 4)2 = 16

Need more Coordinate Geometry help? Schedule a 1-hour lesson with one of Grockit’s GMAT tutors to focus only on coordinate geometry questions from the Grockit GMAT question bank, or check out the Coordinate Geometry questions in Grockit’s Academy, SAT, ACT, or GRE question banks for even more practice!

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Going the ‘Distance’: Averages and Rates Problems – Part 2

By posted April 30, 2011

Now that we’re on our way to better scores with our solid grasp of distance question basics, let’s look at two more challenging GMAT questions.

QUESTION #3: Tracey ran to the top of a steep hill at an average pace of 6 miles per hour. She took the exact same trail back down. To her relief, the descent was much faster; her average speed rose to 14 miles per hour. If the entire run took Tracey exactly one hour to complete and she did not make any stops, how many miles is the trail one way?

ANSWER: For the way up the hill, we know that D = 6mph x T.

For the way down the hill, we know that D = 14mph x T.  Since we went know that the distance up the hill was the same as the distance down the hill, we can pick a number for D. Let’s choose “84″ since it is a multiple of both 6 and 14.  If 84 = 6mph x T, then we know that T = 14 hours. If 84 = 14mph x T, then we know that T  = 6 hours.

Now we can use another formula, the Average Rate formula, to find the average speed for the WHOLE trip. Average Rate = Total Distance / Total Time

Using our Picked Number of 84, we know that the Total Distance traveled would be 168 miles. The Total Time is 14 hours + 6 hours = 20 hours.  So the Average Rate = 168 miles / 20 hours = 8.4 mph.

It doesn’t matter that Tracey didn’t “really” go 168 miles, or that we know she didn’t “really” go 20 hours. We Picked a Number just so that we could find the ratio of the Total Distance to the Total Time in order to calculate the Average Rate of the ENTIRE journey.

Now that we have found the Average Rate for the whole trip, we can plug it in to the “DIRT” formula to find the ACTUAL distance for the entire journey.

D = R x T

D = 8.4mph x 1 hour

We know that T = 1 hour because the problem told us so. Therefore, the actual distance for the entire trip was 8.4 miles. The problem asks how many miles the trail was one way. 8.4 / 2 = 4.2. The answer to the question is 4.2 miles.

You could also solve this problem in other ways, including using a system of equations and substitution, but it’s nice to know that you can pick a number for the Distance traveled and use it to find the Average Rate for the whole journey! Be on the lookout for those trips where the distance there and back is the same!

We’ve joked about it, but let’s actually try one of those “train”  questions:

QUESTION #4: A train runs over a straight route from town A to town D. It is scheduled to depart town A at 7am and arrive at town D at 2pm, with 10 minute stops in towns B and C. The train’s top speed is 60mph. The entire length of the route is 320 miles. Will the train arrive on time?

(1) The train experiences a 30 minute delay in town B in addition to its scheduled stop.

(2) The train travels at its top speed for exactly 75% of the trip.

ANSWER: This is a yes/no data sufficiency. In order to answer yes or no, we need to know the time it takes the train to make its journey. From the question, we can see that the train is supposed to take 7 hours to go from Town A to Town D with two 10-minute stops. Thus, the total travel-time of the train is 7 hours – 20 minutes = 6 hours, 40 minutes, or 6.67 hours. A train that takes the full 6.67 hours to travel 320 miles would need to travel at a speed of approx 48mph or faster to make its timetable. Remember that this is what the train is supposed to do. Let’s see how each statement affects the time-table.

With a 30 minute delay, the train’s travel-time is now 6 hours, 10 minutes, or 6.167 hours. With that delay, the train needs to travel at approx 51mph to make its timetable. However, what is missing from this statement is proof that the train actually did increase its speed to make its timetable. Just because it was possible the train arrived on time, doesn’t mean it did. Statement (1) is insufficient.

Let’s look at Statement (2). 75% of the trip is 240 miles out of the total 320 miles. This means the train has to travel the remaining 80 miles in a little less than 3 hours, an average speed of approximately 25 miles an hour in order to make the timetable. This is clearly within the train’s limits, but we do not know anything about the train’s speed for these remaining 80 miles. Statement (2) is insufficient.

Combining the two statements, we know that the train only has 2 hours and 10 minutes to travel the remaining 80 miles. This requires traveling almost 40 mph. This is possible, but we have no certainty that the train accomplished this. The answer, therefore, is (E).

For more practice with Distance and Rate questions, you can schedule a group study game in the GMAT Lobby on Grockit. Use Grockit’s message system to invite other students with high scores and Grockit GMAT tutors to RSVP. Studying together is more fun than studying alone.

 

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