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.

How to Rock Sequences on the GRE

On the GRE, there are two types of sequences to watch out for: arithmetic, and geometric. An arithmetic sequence occurs when there is a constant difference between terms. For example, in a sequence of 3, 5, 7, 9…, then the difference is +2. In a geometric sequence, there is a constant ratio and not a constant difference.

The common ratio is found by dividing the 1st term into the 2nd term. For example, in a sequence of 2, 4, 8, 16…, the ratio is 2, since each term is multiplied by 2 to get the next term.

The concept of sequences is fairly simple, but what to do when a question asks for an impossibly high term, such as the 149th term? There isn’t enough time to write the sequence out that far, so we’d use one of the following formulas:

For Arithmetic: an = a1 + (n – 1)d

For Geometric: an = a1 * r(n-1)

In these equations, an = nth term, a1 = first term in the sequence, d = difference, r = ratio, and n = the number of the term you want to find. For example, if we were asked to find the 33rd term in the geometric sequence above, we would plug in as follows:

an = 2 * 2(33 – 1)
an = 233

Let’s look at a practice question:

1. In the sequence of numbers, a1, a2, a3, a4, a5, each number after the first is 5 times the preceding number. If a4 – a1 is 93, what is the value of a1?
For this question, it is best to choose simple numbers to see the pattern. If a1 is 1, then we know that a2 = 5, a3 = 25 and a4 = 125, so we know that a4 will be 5*5*5 or 125 times the value a1,. No matter what we choose as a1, a4 will always be 125 times greater than a1. We need to find a value such that 125x – x = 93

124x = 93
x = 3/4

How to Solve 1-Blank GRE Sentence Equivalence Questions

In Sentence Equivalence questions on the New GRE, the blank(s) will always have a relationship to the rest of the sentence. We identify keywords because it helps us understand this relationship. Some blanks will have a “defining” relationship, meaning the blank will be defined by the rest of the sentence, so you’ll look for a word to embody the description. Other blanks will have a “contrasting” relationship, and you’ll need to choose the word that provides the best contrast to the describing keywords.

On harder Sentence Equivalence, you will often see a more complex relationship, such as “causation.” Let’s see an example of how we can identify keywords to show us the relationship, and allow us to predict for the blank.

Although appliance manufacturers would have you believe otherwise, items like blenders and toasters are not requirements for the creation of a delicious meal; for centuries, our ancestors cooked without these modern _______.

A) conveniences
B) hindrances
C) requisitions
D) creeds
E) incidents
F) utilities

Let’s pick out the keywords:

Although appliance manufacturers would have you believe otherwise, items like blenders and toasters are not requirements for the creation of a delicious meal; for centuries, our ancestors cooked without these modern _______.

“Although” is a common keyword that introduces a contrast. The manufacturers want you to believe the “blenders and toasters” ARE requirements. The word “these” in the second clause refers back to the “blenders and toasters” in the first clause. The clauses here contrast with each other, but the blank is going to be a word that describes “blenders and toasters.” A good prediction would be a word like “appliances.” Essentially, a word that could describe an tangible object.

Scanning the answer choices, B, C, D, and E do not refer to tangible objects. The correct answers must be A and F. After identifying the keywords and making a prediction, we barely had to consider each answer choices. Process of elimination allows us to identify the correct choices (always two for sentence equivalence questions) quickly and effectively! There’s never a need to re-read the sentence 6 times with each answer choice plugged in.

How to Handle Short Passages on the GRE

One benefit to the Revised GRE test is that there are two short Verbal sections with 20 questions each instead of one long section. Another is that you can now freely move back and forth between questions within a given section. This means that you will be able to answer look at questions and choose the order in which you can answer them.

According to the official GRE website, “reading comprehension passages are drawn from the physical sciences, the biological sciences, the social sciences, the arts and humanities, and everyday topics, and are based on material found in books and periodicals, both academic and nonacademic. The passages range in length from one paragraph to four or five paragraphs.”

So how should your approach change from longer to shorter passages? For longer passages, it makes sense to thoroughly read and take notes on the important information presented (main idea, function of each paragraph, author’s point of view, etc.). Shorter passages, however, will usually only be accompanied by 1-2 questions.

Therefore it makes sense to read the questions first before looking at the passage. Quickly identify the pieces of information you’ll need to find. For example, let’s say the first question asks about the “Main Idea” and the second question asks about the Logic behind the author’s use of a specific detail. You will only have two tasks as you read: find the purpose, and find out why the detail is included. There’s no point in trying to focus on the author’s point of view if it isn’t necessary to answer any of the given questions! Make your job as simple as possible.

Creating these clear tasks for yourself is an effective strategy for shorter passages, since you don’t have as much text to decipher.

Learnist: How to Interpret your GRE Score

In August of 2011, the GRE completely changed its scoring. Here’s everything you need to know about scoring on the GRE before you take the test!

The GRE (as of 2011) consists of four sections:

  • Verbal (2 sections)
  • Quantitative (2 sections)
  • Analytical Writing (2 essays)
  • Experimental (can be Verbal, Quant, or AWA)

The complete exam takes approximately 4 hours, depending on what type of experimental section you see. As this Kaplan video points out, the GRE is definitely a test of endurance!

The first step is to get ahold of your scores after you take the exam is to create your GRE account on ETS’s website. Official scores will be received 10-15 days after the test. On Test Day, you will get your score, but it is technically an “unofficial” score. You can view your official scores a couple weeks later for free online from your account!

The Verbal and Quantitative sections of the GRE are on a 130-170 scale. The scaled score on the GRE is the most noticeable difference between the older GRE and the revised GRE (as of August 2011). The scaled score is in increments of 1 point. (Previously, the GRE scaled score was between 200-800, like the GMAT).

In this Kaplan video, you can see that since the scores are so clustered together over 40 points, tiny incremental improvements in your performance can make a dramatic difference in your score!

Check out more resources about how to interpret your GRE score on Learnist!