# 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.

# Spotting Consistent Ideas in GRE Sentence Equivalence

Sentence Equivalence is one of the newer GRE Verbal question types (replacing the older Sentence Completions). Like Sentence Completions, Sentence Equivalence consists of one sentence with one blank. Unlike Sentence Completions, there are two correct answers and not one, and you must get both to get the question correct.

To solve Sentence Equivalence, you’ll need to know 1) the relationship of the blank to the rest of the sentence, and 2) the meaning of the entire sentence. There are approximately 8 total Sentence Equivalence questions on the GRE, 4 on each Verbal section. These questions should take approximately 1 minute each.

Consistent Ideas is one of the four types of Sentence Equivalence questions. In Consistent Ideas questions, the blank will mirror or extent the logic of the rest of the sentence. Like it sounds, the blank will continue the ideas of the rest of the sentence. You’ll be able to recognize this type because of certain constructions.

Here are common “Consistent Ideas” key words and phrases to look out for: for this reason, again, to reiterate, along with, in addition, for example, to illustrate, thus, likewise, similarly, since, also, and, next, as well as, as a result, to sum up, concluding, additionally, etc.

Let’s look at an example Sentence Equivalence question:

1. As a teacher of creative writing, Mercedes demanded her students’ best work; likewise, her own fiction was often subjected to ———– analysis by those same students.

A. scrupulous
B. equitable
C. reverent
D. spiteful
E. malicious
F. rigorous

We know this is a Sentence Equivalence Consistent Ideas question because of the keyword “likewise.” The semicolon tells us the second half of the sentence will mirror the logic of the first half. The key phrase is “demanded” which explains the relationship. We can predict something like “demanding” for the blank. We need a word that is neither positive nor negative, but shows a strong, exacting demand.

# 4 Steps for Two-Blank Sentence Equivalence Questions

One the Revised GRE, Sentence Equivalence questions contain one, two, or three blanks. Two of the answer choices (out of six presented on the GRE) will be correct, and you will need to understand both the meaning of the sentence/s as a whole and be able to identify the clues in the sentence to find the correct blanks. For better scores on GRE Verbal questions like these, follow these easy tips on your GRE Test Day!

STEP 1: Write down the keywords. As you read the sentence, you will be on the lookout for keywords, words that describe the blank or relate to the overall flow of the sentence (transition words). Write them down! It may seem redundant, but the act of writing them down will slow down your impulses and force your brain to think critically. What do the words tell you about the blank?

STEP 2: Write down a prediction for the easiest blank. Once you’ve analyzed the keywords and punctuation of a sentence, you can come up with a prediction for the blank which seems the most straightforward to you. It doesn’t have to be a great prediction, but make sure you do write something down. Even a simple prediction like, “a negative word” or “something like sad” is great! Don’t let yourself read the answer choices without a written-down prediction. If you don’t write it down, you will likely forget it as you read the answer choices.

STEP 3: Eliminate answer choices based on that prediction. Instead of scanning the answers quickly looking for the correct one, carefully move through the choices from A to F, eliminating the answer choices that could not possible match your prediction. Only worry about scanning the column for the blank you predicted for – don’t even read the other words.

STEP 4: Plug in for the remaining blank, if necessary. If you have more than two answer choices left after eliminating, then plug them into the sentence to see which ones are correct. Remember that for Sentence Equivalence, there will be two correct answers!

# 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: 7 Ways to Rock the GRE’s Quantiative section

Each GRE quantitative section consists of 20 questions to be completed in 35 minutes. Here’s how to get the most points possible!

When you practice for the GRE, avoid using a calculator unless you really need one. Most GRE Quant questions can be solved within 1-3 minutes without one. It’s provided on the GRE and allows for simple calculations, but don’t use it as a crutch. You should only need it for a couple of questions. You’ll save time if you can do simple conversions in your head.

Review the allowable functions here on the GRE’s official website‘s instructions for using the calculator!

Check out more ways to rock the GRE’s Quantitative section on Learnist!