The Brief
A Blog about the LSAT, Law School and Beyond

Geometry, unlike the other mathematical subjects tested on the GRE, has special rules. Basically, these rules prohibit test-takers from just eye-balling the answers based off of the diagrams. So for example, in the following problem:

Example 1
Find the value of x:

You cannot just look at the figure and guess that the mystery leg is the same length as the other leg of the triangle. For if we used the Pythagorean Theorem to calculate the solution:

Answer

So our first rule is:

Rule 1: Shapes and figures are not necessarily drawn to scale.

So in the following problem:

Example 2
Is side B longer than side A?

The correct answer is that it cannot be determined which side is longer.

However, this does not mean that the figures drawn are totally misleading. For we also have:

Rule 2: Shapes and figures do show the relative position of different objects.

What does this mean? It means that if you see something like:

Then you can conclude that the triangle is to the left of the square. Or if you see:

You can conclude that those two points are on that line, and that point a is to the left of point b.

Finally, the rules are different for co-ordinate systems and the number line:

Rule 3: Co-ordinate systems and the number line are to scale.

The main co-ordinate system you will see on the GRE is the xy-plane:

and the number line is just the following diagram:

On such systems, the objects are to scale. So if you see:

you can conclude that the value for b is twice as large as the value for a. Or if you see:

you can conclude that the area of the smaller square is 1/4 of the area of the larger square.

How do you conclude that?

So in short, remember that the proportions of shapes cannot be trusted, but the relative position of shapes can be trusted, and if there is co-ordinate system or a number line, then even the proportions can be trusted.


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This guide covers all the geometry you need for the GRE math section. We will try to make the content fairly intuitive, combining formulas with some explanation of why the formula makes sense. Doing well on geometry problems can make a big difference for your GRE math score since geometry questions make up about 15% of all GRE math questions.

Most geometry questions will ask you to do one of four things:

  1. Find the line length
    Example 1
    In the following figure, find the value of x
  2. Find the angle
    Example 2
    Find the value of \theta:
  3. Find the area (of a 2D shape) or surface area (of a 3D shape), or
    Example 3
    Find the area of the shaded region:
  4. Find the volume (of a 3D shape)
    Example 4
    Find the volume of the rectangular prism below:

But these problems can be difficult because they give you seemingly odd bits of information. For example, they might ask:

Example 5
The area of the following triangle is 20. Find c:

and you will have to figure out a way to use what you know (the area formula for triangles, the Pythagorean Theorem) to figure out the answer:

Answer

There are many little factoids which matter in geometry, and these will be found throughout our guide. Now, the sheer quantity of formulae can get overwhelming, so we will distinguish between must-know formulas like:

Pythagorean Theorem: For any right triangle where a, b are the legs of the triangle and c is the hypotenuse, a^2 + b^2 = c^2.

and the less critical formulas like:

30-60-90 Right Triangle: For any right triangle with angles of 30, 60, and 90 degrees, the side lengths have the following ratio:

The must-know formulas are, well, a must-know if you want to do well on geometry. But if you are okay with missing a few geometry questions on the exam, you can afford to ignore some of the less critical formulas. Each such formula comes up maybe once per test.


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Welcome to Law School Success Stories, where we discuss 7Sage applicants who made the most of their GPA and LSAT score.

👤 Who: “Sanjay,” a recent college grad

  • 📈 Top LSAT: 170
  • 📉 GPA: 2.99

Results

  • 🏆 Accepted at UVA

🔎 Initial Assessment

Sanjay had applied the previous cycle and been accepted to GW and Fordham with substantial scholarships. During the year since applying, he had taken the LSAT two more times (for a total of five attempts), ultimately raising his score from 155 to a whopping 170. This made him determined to take another crack at the T-14, despite having a GPA well below their 25th percentiles.

A phone call with Sanjay revealed that he was not only a finance whiz, but a funny and down-to-earth guy. His low GPA had been due, in large part, to a debilitating skin condition that struck him at the beginning of college. The resulting social anxiety caused him to miss classes frequently during his first and second years. Sanjay saved up enough money to begin a new treatment regimen, and by the fall of his third year, he was earning good grades.

Our task, then, was to convince the admissions committee at a T-14 school that his GPA didn’t reflect his ability to succeed in law school, and that Sanjay was so smart, ambitious, and congenial that they simply could not turn him down. We developed a three-part strategy:

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Once upon a time, the LSAT was the only game in town for law school applicants. Things began to change in 2016, when the University of Arizona Law allowed applicants to apply with a GRE score, followed by Harvard Law the next year. Nearly forty law schools now accept the test.

The Case for Taking the GRE

The GRE has a lot of advantages from the perspective of a test-taker. Available throughout the year and across the world, it’s easier to schedule and more convenient than the LSAT. The GRE will also feel more familiar to anyone who’s taken the SAT or ACT, and most test-takers find it less time-pressured than the LSAT. The test has special advantages for applicants with quantitative skills, who may find it easier than the LSAT, and for anyone applying to dual-degree programs, who may have to take the GRE in any case. Finally, if an applicant decides to cancel her GRE score, the test doesn’t show up on her record. If an LSAT-taker cancels her score, by contrast, the test still shows up on her score report.

Nevertheless, there are some reasons to hesitate before you go all in on the GRE.

We don’t know how GRE applicants actually fare in the admissions process.

Very few law students in the first-year class of 2018 got into law school with a GRE score alone. Let’s look at some examples:

  • In Harvard’s first-year 2018 class, 18 of 566 students were admitted without an LSAT score, or 3.2%.
  • In Northwestern’s first-year 2018 class, 12 of 245 students were admitted without an LSAT score, or 4.9%.
  • In Georgetown’s first-year 2018 class, 18 of 581 students were admitted without an LSAT score, or 3.1%.

(See the full table.)

At every other T-14 school, either zero or one student got into law school without an LSAT score.

Before you give up on the GRE, we should grant that these numbers don’t tell the full story. The most relevant question isn’t “What percentage of law school applicants got accepted with a GRE alone?” but “What percentage of GRE-only applicants got accepted?” In other words, we want to know if GRE applicants had a higher or a lower acceptance rate than LSAT applicants.

At a panel discussion in June of 2019, Alex Feinson, Harvard Law School’s assistant director of admissions, told a group of prelaw advisors that the acceptance rate of GRE-only applicants mirrored the acceptance rate of all applicants, indicating that it was no easier or harder to get into Harvard Law with a GRE score than with an LSAT score. Eulas Boyd, Brooklyn Law School’s dean of admissions, told the same group that GRE-only applicants had a slightly higher acceptance rate than all applicants, but he still didn’t think that it was easier to get into Brooklyn Law with a GRE score. Rather, he thought that the pool of GRE applicants was stronger than the pool of regular applicants.

As for other schools, we just don’t know. All we can say for sure is that admissions deans are moving away from the LSAT cautiously. The validity of the GRE as a predictor of law school success is an open question, even for law schools that have performed their own studies, and admissions offices are still tracking the progress of their GRE admits. We’ve also heard that law school faculty, who often sit on admissions committees, are skeptical of the GRE. And when we asked Rob Schwartz, the assistant dean of admissions at UCLA Law, whether a 95th percentile LSAT score was more compelling than a 95th percentile GRE score, he agreed that it probably was (though he didn't necessarily think everyone should take the LSAT). Thus we have reason to suspect that for most law schools, getting accepted with a GRE score is no easier than getting accepted with an LSAT score, and that it may well be harder.

If you’ve already taken the LSAT, there’s probably no point in taking the GRE.

If you have any valid LSAT scores on file, LSAC will report them when you apply to law school. You don’t have any choice about that.

This is important for two reasons. First, law school admissions officers are more likely to trust your LSAT score than your GRE score. They have been making admissions decisions for years based on LSAT scores, and they've seen for themselves how students with various LSAT scores tend to fare. As we’ve noted, the GRE is uncharted territory.

The second thing to understand is that your LSAT score will probably have a larger effect on a school’s U.S. News & World Report ranking than your GRE score. Per U.S. News’s ranking methodology, a school’s LSAT median and GRE median account for 12.5% of its ranking. But law schools are required to report their LSAT medians. They are not required to disclose their GRE medians, and only sixteen of them—or eight percent—did report those medians to U.S. News for the 2020 rankings. Even for those schools, we don’t know if the GRE median was factored into the ranking proportionally, based on the number of GRE admits, or if it was discounted.

“But wait,” some of you might be thinking. “Won’t a great GRE score still look impressive to admissions officers, even if I already have an LSAT score?”

Well—sure. An applicant with a perfect GRE score and a 150 LSAT is probably better off than an applicant with a 150 alone, all else being equal. But if you’re capable of getting a GRE score that’s much better in terms of percentiles than your current LSAT score, you’re also probably capable of improving your LSAT score. A better GRE score won't replace your current LSAT score, but a better LSAT score will replace your current LSAT score, practically speaking. Almost all law schools use your highest LSAT score.

Alissa Leonard, the assistant dean for admissions and financial aid at the Boston University School of Law, put it best when she said to a group of prelaw advisors in 2019, “I don’t think it makes sense to take the GRE in addition to the LSAT. It doesn’t bring much to the table.”

A few more considerations for those leaning toward the GRE

  • The list of schools that accept the GRE is growing, but we’re a long way from universal adoption.
  • The ETS’s GRE to LSAT converter is not trusted by many admissions deans. For the most part, admissions deans are looking at the percentiles of your GRE section scores.
  • Although the GRE lets you choose which scores to report to which institutions, almost all law schools require you to submit all of your GRE scores within the last five years.
  • There’s no data on whether applicants who get accepted with GRE scores tend to get merit scholarships. If you’re thinking of applying to a law school with a GRE score, you should call the admissions office and ask if they award merit aid to GRE applicants.

Conclusions

You should probably NOT take the GRE if…

  • You already have a valid LSAT score
  • You want to apply to any law school that doesn’t accept the GRE
  • You may be able to achieve the median LSAT score of your target school

Applying to law school with only a GRE score might be the right decision for you if…

  • You think you’ll be better at the GRE than the LSAT (as is sometimes the case with mathematical applicants)
  • You are applying to dual-degree programs, some of which require the GRE
  • You are positive that you can’t achieve the median LSAT score of your target school and feel like you may as well throw a hail mary.

Bottom line: We recommend that you apply to law school with an LSAT score unless you have a specific reason not to.

Schools That Accept the GRE

2020 Rank School GRE Admits* L50 G50
0001 Yale University 0 173 3.92
0003 Harvard University 18 173 3.9
0004 University of Chicago 0 171 3.89
0005 Columbia University 1 172 3.75
0006 New York University 0 170 3.79
0007 University of Pennsylvania 0 170 3.89
0008 University of Virginia 0 169 3.89
0010 Northwestern University 12 169 3.84
0013 Cornell University 0 167 3.82
0014 Georgetown University 18 167 3.8
0015 University of California—Los Angeles 2 168 3.72
0016 University of Texas at Austin 0 167 3.74
0017 University of Southern California 1 166 3.78
0018 Washington University in St. Louis 1 168 3.81
0021 University of Notre Dame 0 165 3.71
0023 Boston University 0 166 3.74
0023 University of California—Irvine 0 163 3.57
0031 University of California—Davis 0 162 3.63
0031 Wake Forest University 4 162 3.58
0039 Brigham Young University 10 164 3.8
0039 University of Arizona 18 161 3.7
0045 George Mason University 1 163 3.76
0048 Florida State University 2 160 3.63
0051 Pepperdine University 0 160 3.63
0052 Yeshiva University (Cardozo) 1 161 3.52
0064 Pennsylvania State - Penn State Law 0 159 3.58
0071 Brooklyn Law School 3 157 3.38
0077 American University 0 158 3.43
0077 St. John's University 4 159 3.61
0083 Texas A&M University 8 157 3.51
0087 Illinois Institute of Technology (Chicago-Kent College of Law) 6 157 3.44
0087 University of New Hampshire 0 156 3.46
0091 Florida International University 0 156 3.63
0091 University of Hawaii 4 154 3.32
0091 University of South Carolina 0 155 3.41
0104 University of Buffalo—SUNY 0 153 3.41
0122 Pace University 0 151 3.3
0143 Suffolk University 0 153 3.36
0RNP John Marshall Law School 4 149 3.18
0RNP University of Dayton 0 149 3.29
Featured image: pexels-photo-261909-2

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https://soundcloud.com/user-737824810/22-getting-into-ucla-law-rob-schwartz-assistant-dean-of-admissions/

On today's episode David Busis, Partner at 7Sage Admissions Consulting, speaks with Rob Schwartz, Assistant Dean of Admissions at UCLA School of Law.

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While an attorney in private practice works for the benefit of an individual or company, a public interest attorney works for the benefit of an organization, a cause, an individual who cannot afford legal representation, or government (federal, local, or state) agencies. Public defenders, local prosecuting attorneys, and attorneys at civil legal services organizations are all public interest attorneys. 

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In previous posts, we’ve discussed how to solve systems of equations. But often, you will not be given a simply list of equations. Rather, you will get a chunk of text asking you to find some particular value. For example,

Example 1
Tom and Liz are baking cookies. Tom can bake 10 cookies in an hour and Liz can bake 5 cookies in an hour. Working together, how long will it take them to bake 40 cookies?

Example 2
Dembe is reading a long book. He finishes a quarter of it, then puts it down to take a walk. After he comes back, he reads another 50 pages. Now, he has finished 30% of the book. How long is the book?

Example 3
Raymond is trying to calculate how much he needs to invest today in order to have $2,000,000 in an account in 18 years. He can guarantee an annual return of 15% on any funds invested. How much does he need to invest?

The key to such problems lies in translating the text to mathematical equations. As we will see, solving the actual equations is generally not the hard part; the trick lies in the translation.

The problems above are each examples of different kinds of problems. The first problem is an example of a rate problem, the second one is an example of a ratio problem and the last one is a compound interest problem.

Solving Example 1

Example

Let’s look at our first problem. To determine how long it takes the pair to bake 40 cookies, we would try first figuring out how quickly they bake cookies. Let’s try to figure out how many cookies they would bake in an hour. Well, during that hour, Tom would bake 10 cookies and Liz would bake 5 cookies. So together, they would bake 15 cookies.

Now, we ask: if someone could bake 15 cookies in an hour, how long would it take them to bake 40 cookies? To answer this, we use an old equation:

    \[d = rt\]

where d is the total number of cookies baked, r is the number of cookies baked each hour, and t is the amount of hours spent baking cookies. Turning to our problem, we know that their combined rate is 15 cookies per hour, and we want to know how long it takes to bake 40 cookies. Therefore, we set up the following equation:

    \[40 = 15t\]

and solve for t. We learn, by dividing both sides by 15, t = \frac{8}{3}. So it takes them \frac{8}{3} hours to do so (or, in other words, 2 hours and 40 minutes).

This kind of problem often involves some kind of task (eg baking cookies) or distance (eg how far one runs). The key is to use what you know about the outcome (d), rate (r), or time (t) to solve for the unknown quantity. In this case, the problem gave us the rate and outcome, and we solved for the time it took to get that outcome.

Solving Example 2

Example

The key here is setting up the right equation. Let’s use our variables. Let p = the number of pages in Dembe’s book. We know that, after reading .25p + 50 pages, Dembe has finished .3p pages (i.e. 30% of the book). Thus, we get

    \[.25p + 50 = .3p\]

Now that we have this equation, it is easy to solve for the value of p. We subtract to get:

    \[50 = .05p\]

    \[p = 1000\]

Thus, we conclude that Dembe’s book was 1,000 pages long.

Solving Example 3

Example

Again, let’s use our variables. Let x = the amount of money Raymond invests today. Then, in 18 years, with an annual rate of 15%, Raymond will have x(1.15)^18 in that account. We want to make that amount equal to 1,000,000. Thus, we get the equation:

    \[x(1.15)^{18} = 1,000,000\]

And now, we can solve for x by dividing by 1.15^{18}:

    \[x \approx 80805.\]

Thus, Raymond needs to invest about $80,805 today.

Now there is no cookie-cutter recipe that will handle all word problems. But in general, thinking about what the words mean and translating them into mathematical formulas carefully will work.

Practice Problems:

  1. Felipe left for his morning jog with a water bottle that was three-quarters full. On his route, he passed by a high-tech water fountain and added precisely 300 milliliters of water to his bottle (the bottle still was not full). Then, he continued on his run. At the end of it, he drank two-thirds of the water then in his bottle before heading home. Let w be the maximum capacity of Felipe’s water bottle (in milliliters). Write an expression for how much water was left in his water bottle when he reached his home. If he had exactly 200 milliliters of water when he reached home, what was the capacity of his water bottle?
    Answer
  2. The kindergarteners are trying to decide which shape is best. Every kindergartener likes only one shape. 3/5 of the class is tall and the rest are short. Of the tall students, 1/6 like circles, 2/3 like squares, and everyone else likes trapezoids. Suppose 1/2 of the class likes circles. What proportion of the short students like circles?
    Answer

  3. Evan is a distance runner. He runs at a constant rate of 10 miles per hour for as many hours as you like. How long will it take him to finish a marathon (26.2 miles)?
    Answer

 


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We’ve talked before about solving systems of linear inequalities. There, we simply graph the relevant equations to find where the shaded regions all intersect. We do the same thing for systems of quadratic inequalities. Let’s look at an example:

    \[\begin{cases} y \geq  & x^2  \\  y \leq  & x^2 + 10 \end{cases}\]

We begin by graphing the two equations:

Then, we shade in the regions where each inequality applies. So, for example, where will y \geq x^2? Clearly this will be true in the region above the curve. (And if you are unsure, you can always just try testing a point on each side of the curve). We do the same for the second equation to get:

And as before, the solutions will be any point in the area where all of the shaded regions intersect.

Now, we can also have systems of inequalities that combine linear and quadratic inequalities:

    \[\begin{cases} y \geq & x^2 \\ y \leq & 2x + 5 \end{cases}\]

We follow the same method, graphing the functions:

Shading the relevant regions:

And identifying where shaded regions intersect:

And that’s how we handle systems of inequalities for quadratic equations.

Practice Problems

For each of the following systems of quadratic inequalities, graph their solutions. (Some may not have any solutions at all).

  1.  

        \[\begin{cases} y <& x^2 - 5 \\ y >& x - 5 \end{cases}\]

    Answer
  2.  

        \[\begin{cases}y <& x^2 + x \\ x >& 5 \\ y <& 5\\ y >& x \end{cases}\]

    Answer
  3.  

        \[\begin{cases}y >& 3x^2\\ y <& 0 \end{cases}\]

    Answer

 


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