6 Most-Tested GRE Problem Solving Concepts

Noticing that your scores on your GRE practice test isn’t quite as high as you’d like? One quick way to get better GRE Quantitative scores is to increase your content-knowledge in the most-tested Problem Solving areas. Here are the top seven most-tested GRE Quant concepts to review; get these down and you’ll ace the GRE section!

1. Functions and Symbols. A function is a different way of writing an equation. Instead of y = mx + b, we’d have f(x) = mx + b. It’s helpful to think of a function as simply replacing the “y” with a symbol called “f(x).” The GRE may also present made-up symbol functions; pay attention to any definitions you are given, and expand accordingly.

2. Number Properties. The properties of integers, primes, odds and evens, integers, fractions, positives, and negatives will all appear in various questions on your GRE test. The more comfortable you are with them, the more quickly you will arrive at the correct answer. This concept will bleed over into Quantitative Comparisons as well.

3. Plane and Coordinate Geometry. Not only will you need to know the standard equations for a line, parabola, and circle, but also you will need to memorize the distance formula, the midpoint formula, the slope formula, the relationship between slopes and the different quadrants, properties of parallel, perpendicular, vertical, and horizontal lines, as well as the quadratic formula/discriminant. For Plane Geometry, triangles are tested the most often on the GRE. You should know the Pythagorean Theorem, Triangle Inequality Theorem, the special right triangles: 45-45-90 and 30-60-90, as well as the properties of isosceles and equilateral triangles. Other plane geometry concepts to review include angles, circles, and polygons. Make sure you know how to find the perimeter and area of all shapes, and be comfortable dividing irregular shapes into manageable pieces.

4. Linear & Quadratic Equations. y = mx + b is the standard equation for a straight line, or a linear equation, where m is the slope and b is the y-intercept. You’ll need to know how to graph them and how to find the slope given two points. Quadratic equations look like y = ax2 + bx + c, and make a parabola, or curved line. Quadratics have two factors, and two solutions (also called “roots”). You will need to know how to factor quadratic equations to find the roots, how to find the quadratic if given the roots, and how to graph a quadratic on a grid given the equation.

5. Ratios and Proportions. A ratio is a relationship between two things. Given a ratio and one “real world” number, you can always set up a proportion to solve for the other missing “real world” number. Sometimes you will need to do this for similar triangles in Geometry, and sometimes in algebraic word problems.

6. Data Analysis. Data Analysis questions are like an open-book test. Make sure you read every tiny piece of writing on or near the data, including titles, the labels for the x and y-axes, column names, and even footnotes if there are any. Pay attention to the units of measurement, and notice any trends in the data BEFORE reading the questions.

Two Types of GRE “Averages”: Mean and Rates

The word “average” on the GRE can refer to two concepts: arithmetic mean, and the average speed (or average rate) formula. It’s important not to confuse the two on the Test Day, as they require different formulas to solve.

Mean is the mathematical average. This is defined as the sum of the terms divided by the number of terms. Mean = Sum / # of terms. For a list of consecutive integers or evenly spaced numbers, the mean is equal to the median, or the middle number. For example, the “average” of 3, 5, and 9 is 5.67.

Average Speed or Average Rate is often found in complex word problems. This type of question is one many students are less familiar with so you may not have seen it before. Let’s review two important equations to remember and look at how this concept appears on the GRE.

The first formula to memorize is: D = R x T. This stands for Distance = Rate x Time (referred to as the “DIRT” formula). It is perfectly acceptable to also think of it as Time = Distance / Rate or as Rate = Distance / Time as well. Usually the “Rate” is speed but it could be anything “per” anything. In a word problem, if you see the word “per” you know this is a question involving rates.

The second formula is: Average Rate = Total Distance / Total Time. This is its own special concept and you will notice that it is NOT a simple Average of the Speeds (which would be something like the Sum of the Speeds / the Number of Different Speeds or what we know as the Arithmetic Mean). Average Rate is a completely different concept, so do not let the common word “average” confuse you. Let’s look at a sample question from Grockit’s GRE question bank:

Question 1: The average (arithmetic mean) of four numbers is 30, after one of the numbers is removed, the average of the remaining three numbers is 10. What number was removed?

We know that the four original numbers sum to 30*4 = 120. The new equation becomes:

4*30 – x/3 = 10
120 – x/3 = 10
120 – x = 30 (add an x to each side and subtract a 30)
90 = x

7 Tips for a Perfect GRE Issue Essay

If you get a perfect score on the GRE’s Issue Essay (a 6), it can really boost your graduate school admissions chances! The best schools want good Verbal and Quantitative scores, but also students who are clear, competent writers. Lots of students have excellent transcripts and are good at taking tests – but not everyone can demonstrate impressive writing skills! Here are 7 tips to take your Issue essay to that perfect 6!

1. Write at least three practice essays. Practice makes perfect! You can study for the GRE online by looking up the AWA prompts and practicing writing several of them within the 30 minute guideline. The only way to get comfortable with the time constraints is to practice them, so set up test-like conditions and get to work. You can see the Issue essay prompts here: http://www.ets.org/gre/revised_general/prepare/analytical_writing/issue/pool

2. Don’t waffle. Choose one side of the issue only, and don’t try to “have it both ways.” Even if you don’t believe in the side you choose, you’ll only have time to argue one side effectively. If you take a middle-of-the-road approach you won’t sound as confident or clear. Remember, according to ETS, the “readers are evaluating the skill with which you address the specific instructions and articulate and develop an argument to support your evaluation of the issue.” What exactly you say (what side you choose to defend) is less important than how you defend it!

3. Choose very specific real-world examples. Don’t be general! Every reader would like to see more specific examples: Mitt Romney, the War of 1812, Keynesian economic theory, the mating rituals of octopii, an anecdote about your Uncle Ralph the compulsive gambler, etc. You can have some fun with it, and your examples don’t have to be the most scholarly. What are you an expert on?

4. BUT, make sure your examples are relevant to the topic. You can absolutely choose examples from a wide range of subjects: personal experience, pop culture, history, sports, literature, current events, politics, etc. But make sure you explain HOW your example clearly supports your thesis.

5. Avoid first-person and self-reference. “I think” or “I believe” are obvious. You are the person writing this essay! First-person pronouns should ONLY appear in a body paragraph if you are using personal experience as an example, and telling a story from your own life to support your thesis. Never use “I” in your introductory or concluding paragraph.

6. Make strong, declarative statements. Look for ways to add charged adjectives, adverbs and “because” clauses to make your sentences sound more confident. EX: “The president shouldn’t allow Congress to pass the law.” Or, “It is unacceptable for the president to permit Congress to pass the law because it unconstitutionally overextends Congress’ powers.”

7. Refute the opposing view in your conclusion. Many GRE students wonder what to do in their conclusion. Try introducing the opposing viewpoint, showing that you recognize that in fact some people do not support your position. Then refute their argument in 1-2 sentences, and reinforce the validity of your own thesis.

Learnist: How to Write a Perfect GRE Argument Essay

The GRE’s Argument essay is remarkably straightforward: all you have to do is rephrase, criticize, and suggest improvements for the given argument. Here’s how to earn a perfect 6!

Focus more on conveying your argument succinctly and forcefully than on sounding scholarly. Don’t include long winding sentences that go nowhere in the hopes of sounding more impressive. Simple, clear transitions work well to help you organize your thoughts. Above all, you want the reader to be convinced that the argument is flawed, and they will only be convinced if they can follow and easily understand your points! This video reviews some other style tips, such as avoiding passive voice and wordiness.

Fun fact: ALL of the Argument Essay topics are available for FREE on ETS’ website. You will see one of these official prompts on Test Day, so it’s a good idea to not only read through all of them, but sketch some possible outlines for essays for a number of them.

There’s about 150 topics here, so unfortunately it’s not possible to pre-write an essay for EVERY topic, but you can definitely see common flaws between these topics.

This pdf file from Kaplan describes the basic 6-scale rubric used to score the Argument Essay. Kaplan uses an adjective to describe each “level”:

6 – Outstanding
5 – Strong
4 – Adequate
3 – Limited
2 – Weak
1 – Deficient
0 – Unscorable

An essay would only be considered “unscorable” if it was written using symbols or in a foreign language. Page 46 of this file shows a sample essay, so you can start to get an idea of what a “6” looks like!

Remember that you already know your thesis for ANY possible prompt you’ll see. No matter what the prompt, your thesis is essentially, “the argument is flawed.” There are many ways to say that in a thesis, but that is essentially what the GRE Argument essay boils down to; all you have to do is show why. This blog article reviews a template you can use for any Argument prompt. Just make sure you practice writing at least 3 full practice essays with it so it becomes second nature!

Get more tips on how to write a perfect GRE Argument essay on Learnist!

Where to Find Challenging Text for Non-Native Speakers

If you’re studying for the GRE or GMAT and English is your second (or third) language, you’ll definitely want to get some extra reading in by looking for challenging, high-quality GMAT-like publications.

Here’s a few suggestions free online suggestions!:

– NY Times book review (I really like this article’s description of how to use these articles for practice: http://smartestprep.wordpress.com/2010/08/27/the-new-york-times-exercise-reading-comprehension/)

– Scientific American: http://www.scientificamerican.com/

– The Economist: http://www.economist.com/

– The Spectator: http://www.spectator.co.uk/

– Forbes: http://www.forbes.com/

Keep in mind that the GMAT and GRE RC is not “hard” because of it’s incredibly advanced language. Most of it is readily comprehensible, although it may occasionally use unfamiliar scientific or business terminology. The challenge of RC lies in breaking down the rhetoric of the passage, and grasping not only what the author’s argument is, but HOW he/she makes it. Absolutely seek out tougher study materials, but make sure to apply your RC method to new passages as well!

GRE Quant Question of the Day: Rates!

Try this “rates” question on your own!

A hiker walked for two days. On the second day the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he walked on the first day. If during the two days he walked a total of 64 miles and spent a total of 18 hours walking, what was his average speed on the first day?

(A) 2 mph
(B) 3 mph
(C) 4 mph
(D) 5 mph
(E) 6 mph

First, let’s consider Day 1 and Day 2’s hours.

If x = hours on Day 1, then x + 2 = hours on Day 2. The question said he walked 18 hours total, so we can set up a simple equation:

x + (x + 2) = 18
2x + 2 = 18
2x = 16
x = 8

Therefore he walked 8 hours on Day 1 and 10 hours on Day 2.

We are told he went 1mph FASTER on Day 2. So if Day 1’s mph is y, then Day 2’s mph is y + 1.

Let’s look at the D = R x T formula.

D1 = R1 x T1

D2 = R2 x T2

If we plug in what we know:

D1 = (y) x 8 hrs

D2 = (y + 1) x 10 hrs

We know that D1 + D2 must equal 64, so we can sum the two equations and set them equal to 64.

(y) x 8hrs + (y + 1) x 10hrs = 64


64 = 8y + 10y + 10

64 = 18y + 10

54 = 18y

3 = y

The answer is (B).

How to Get Every Vocab-in-Context Question Correct on the GRE

Every day, we learn something new – from the discovery of the supergiant amphipod to the latest innovative cancer treatments, humans are constantly discovering that there is more to our world than meets the eye. Your GRE test prep might not feel as exciting as some of these other breakthroughs, but Vocab-in-Context questions are good opportunities to discover new vocabulary in your GRE test prep, and like these discoveries, there is also more to this question type than meets the eye. V-in-C questions look simple, but can be deceptively challenging. Don’t you just have to know the definition of the word? Nope! In fact, the common definition is often wrong (but usually one of the answer choices).
Let’s look at how a question might appear on the GRE test.

In line 19, the word fathom means?

You may see this question and think, I know what “fathom” means. It’s like to be able to understand or comprehend. Scanning the answer choices, you’d see the following options:

A. plaintive
B. secondary
C. understandable
D. measure
E. florid

If you did not go back to the context of the word in the passage, you’d likely choose C quickly and move on to the next question, only to find out later that C was incorrect! This is because many words on the GRE have multiple meanings. You don’t have to know all of them, but you DO have to check to make sure the meaning you think is truly how the word is used in context. Remember, the question-type isn’t called “Vocab Definitions,” it’s called “Vocab-in-Context!”

English words often have many meanings, and can change meaning based on what part of speech they are. For example, “a fathom,” used as a noun, is a measurement of six feet. But “to fathom,” used as a verb, means to comprehend or understand. If the word “fathom” was not being used as a verb in the context, then you could guess C was incorrect, even if you did not know another definition for “fathom.”

When you practice GRE reading passages, always be out the look out for the part of speech of vocabulary words, and memorize words that have multiple or uncommon meanings! You may want to keep a notebook to help you organize these new words – add to it every time you practice!