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.

Strategies and Formulas for Tough GRE Sets

For some advanced Data Analysis and Probability questions, it will help you achieve better scores to know the logic and formulas behind set theory. Set theory hinges on two concepts: union and intersection. The union of sets is all elements from all sets. The intersection of sets is only those elements common to all sets.

Let’s call our sets A, B, and C, and use a Venn diagram to express their relationship.

If n = intersection and u = union, then we can describe the relationship between the sets thusly:
P(A u B u C) = P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C)

To find the number of people in exactly one set: P(A) + P(B) + P(C) – 2P(A n B) – 2P(A n C) – 2P(B n C) + 3P(A n B n C)

To find the number of people in exactly two sets: P(A n B) + P(A n C) + P(B n C) – 3P(A n B n C)

To find the number of people in exactly three sets: P(A n B n C)

To find the number of people in two or more sets: P(A n B) + P(A n C) + P(B n C) – 2P(A n B n C)

To find the number of people in at least one set: P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C)

To find the union of all set: (A + B + C + X + Y + Z + O)

Number of people in exactly one set: (A + B + C)

Number of people in exactly two of the sets: (X + Y + Z)

Number of people in exactly three of the sets: O

Number of people in two or more sets: (X + Y + Z + O)

If you’re like me, and formulas like these sometimes seem complicated and intimidating, let’s look at how making a Venn diagram and applying it to a tough GRE question can provide a little relief!

In 1997, N people graduated from college. If 1/3 of them received a degree in the applied sciences, and, of those, 1/4 graduated from a school in one of six northeastern states, which of the following expressions represents the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?

(A) 11N/12
(B) 7N/12
(C) 5N/12
(D) 6N/7
(E) N/7

The key to understanding this question lies in the last sentence:

…who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?

We have two categories to sum: the people who ONLY received a science degree but NOT from one of the 6 schools, and the people who ONLY went to the 6 schools but did NOT receive a science degree. I made up variables for these categories (x and y).

If N = 12, there are 4 applied science students, 1 of which is both. That means x = 3. If 4 students are applied science, then 12-4 = 8 are from one of the six states but NOT applied science. y = 8.

3 + 8 = 11

So we are looking for an answer choice that gives us 11 when N = 12; the answer is A.

You aren’t likely to see many questions at this difficulty level on the actual GRE, but if you continue to challenge yourself, the medium GRE sets questions will soon look easy!

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!