Monthly Archive for February, 2011

The Myth of Grad School? What To Think About Before Applying

Seems the servers needed a little nap.

Sorry about the downtime yesterday, folks! The server crashed, and the whole site was down for the entire day while they were restoring from backups. All in all, it could have been a lot worse (this is why you backup your stuff, people!).

So here’s an interesting article I found today that presents an interesting perspective on why one might not want to go to grad school. I don’t want to discourage anyone from going to grad school, but the decision to pursue a graduate degree is not one to be taken lightly!

Continue reading “The Myth of Grad School? What To Think About Before Applying” »

New GRE: Changes to the Verbal Reasoning Section, Part 1

Verbal section changes

Unlike the math section of the new GRE, the verbal reasoning section is undergoing numerous changes (most of which are pretty significant), so I’ll have to split this post into two parts to make it a bit more digestible.

Change #1
No analogies or antonyms on the new GRE.

What It Means
There is a decreased focus on vocabulary on the new GRE. Analogies and antonyms are notoriously vocabulary-oriented questions. Both of these types of questions test not only your knowledge of definitions but also test your ability to understand words conceptually and identify relationships between two words or phrases. Just knowing a definition isn’t always enough — you have to have a solid understanding of the concept that the word represents. On the current test, the vocabulary can get pretty hard pretty quickly, so spending a significant amount of time studying vocabulary is an absolute must. On the new GRE, you will still need to have a decent vocabulary for the text completion questions, but there will be no questions that ask you vocabulary without context.

Change #2
New question type: sentence equivalence

What It Means
Sentence equivalence questions are pretty similar to text/sentence completion problems. Basically, you are given a sentence in which a word is left out, and you have to choose the two answer choices that will give the sentence the same meaning. Vocabulary is important here, but it’s in context, so you’ll have some help figuring out what words do and don’t work. Most of the time, this basically means that you’re looking for two words that have the same definition, but more difficult problems will probably be less straightforward than that. The important thing to remember is that there must be two answer choices that give the sentence the same meaning — regardless of how apposite one answer choice might be or how perfectly it seems to fit, if there isn’t a corresponding answer choice, then it’s not right!

Change #3
(Sort of) new question type: text completion

What It Means
Text completion is the new sentence completion. The idea behind the question hasn’t changed much — you are given between one and five sentences with up to three words left out, and you must glean from the context which of the answer choices would fit best in the blanks. What has changed is how the question is presented. Problems that only have one blank will give you five answer choices to choose from, just like on the old test; however, problems that have two or three blanks will give you three answer choices for each blank, and you must choose one answer choice for each blank that fits best with the text. For questions with three blanks (three answer choices per blank), this means that you now have 27 possible combinations of answers to choose from. Guessing just got a lot harder! Plus, since the words aren’t already paired together (as they are on the current GRE), you have to be able to figure out each blank individually, which is more difficult.

Stay tuned for Part 2 later this week!

GRE Math: Two More Example Geometry Problems and Solutions

Example Geometry Problem #3

Example Geometry Problem #3

The problem states that the triangle depicted is an isosceles triangle. Remember, there are two qualities that define an isosceles triangle:

1) two identical sides
2) two identical angles

If you have one, you will automatically have the other. The other important fact about isosceles triangles that you need to remember for this question is that the sides that are identical are the two sides that are opposite the two angles that are the same (and vice-versa).

OK, so how does this information help us solve the problem? Well, we know that the two bottom angles are equal, because they are both labeled y. This means that the two sides of the triangle (not the bottom side) are equal because they are opposite the two identical angles. Since they’re equal, we can say

2x – 2 = 3x – 8 [subtract 2x from both sides]
-2 = x – 8 [add 8 to both sides]
6 = x

Now we know that x is 6.

The question is asking about the area of the triangle, which is given by the equation

Atriangle = ½bh

where b is the length of the base, and h is the height. From the diagram, we can see that the height is simply x, which we know to be 6. The base is defined to be

3x – 2

so we simply substitute 6 for x, and evaluate.

3x – 2 = 3(6) – 2
3x – 2 = 16

So the base of the triangle is 16, and the height is 6; thus, the area is

Atriangle = ½(16)(6) = 48

The answer is (C).

Example Geometry Problem #4

Example Geometry Problem #4

The area of a circle is given by the equation

Acircle = πr2

So the area of a semicircle is half of this

Asemicircle = ½πr2

The areas of the three semicircles are given in the problem:

A1 = 8π = ½πr12
A2 = 25π/2 = ½πr22
A3 = 18π = ½πr32

So if we solve for the radius in each of these cases, we get

8π = ½πr12
25π/2 = ½πr22
18π = ½πr32
[multiply all three equations by 2 on both sides]

16π = πr12
25π = πr22
36π = πr32
[divide all three equations by π on both sides]

16 = r12
25 = r22
36 = r32
[take the square root of both sides on all three equations]

4 = r1
5 = r2
6 = r3

Now remember, these are the radii, not the diameters! In order to find the perimeter of the triangle, which is what the question is asking for, we need to multiply each of these by 2 to get the diameters of the semicircles (which are also the sides of the triangle). Thus, the perimeter is

Ptriangle = 2(4) + 2(5) + 2(6) = 30

The answer is (D).

Should I Take a Year Off Before Grad School? What a Year Off Did For Me

You wish. Do something useful! This is for when you retire with millions.

A competitive graduate student application should ideally include a high GPA, a competitive GRE score, applied work experience, and professional presentations (e.g. publications). If you are like one of the many applicants that actually had a social life during college, you may be deficient in one or more areas! As a current grad student, I can attest that in my cohort of 10 people, only one person chose this path to grad school.

Continue reading “Should I Take a Year Off Before Grad School? What a Year Off Did For Me” »

Grad School Applications, Part 1: Why I Chose Grad School

Actually, I just really want another cool hat.

I am officially finished with applications! I received a confirmation email last week from the last school I applied to, telling me that they received all the requisite application materials. Huzzah! Now all that’s left to do is hold my breath.

Actually, I’m not quite finished. I have one interview coming up March 1. They gave me the option of doing it in person at the school or doing it over Skype. As much as I would love to actually go to the school, I think I’ll just do it over Skype. Plane tickets cost an arm, a leg, and an internal organ these days. Fortunately for me, Ben posted a nice entry about graduate school interviews last week, which I will be sure to keep in mind as I prepare.

So now that I’m done, I think it would be a good time to reflect on the whole experience.

Honestly, the most difficult part of the application process was deciding to go to graduate school in the first place. There are a variety of reasons to go to graduate school (the subject of a future post, perhaps?), but for me, there are three main reasons:

1. To Learn More
I do love learning, but, actually, my “love for learning” is not what I’m talking about here. One doesn’t have to be in school to fulfill a desire to learn. In fact, from what I’ve heard about graduate school, I doubt that graduate school is really the place to “learn” — I mean the sort of general learning that goes on in undergrad. Graduate school, for most people, is about conducting research and making a contribution of some sort to their fields of study. Even though you’re called a graduate “student,” I suppose you could think of it more as a job (more like an unpaid internship, am I right?) that happens to be in academia. As with any job, learning happens along the way, but it’s only for the sake of performing specific research projects.

What I’m looking to get out of graduate school is not another couple years of academic indulgence — I’m looking to gain a depth of knowledge and expertise in a particular subject that would make me a unique, valuable asset. Programmers generally don’t have that much trouble finding work, but at the same time, there are so many people competing for the best jobs that it’s hard to stand out and convince employers to hire you. A graduate degree is a good way to demonstrate your depth of knowledge in a field.

2. To Get More (Better) Job Opportunities
This is closely related to the above point. There are myriad jobs available to programmers, but the majority of the best jobs require several years experience or some sort of graduate degree. Deciding whether to tough it out and apply to jobs that I didn’t really want just for the experience or invest a significant amount of money in graduate school was definitely one of the biggest decisions I’ve ever had to make. In the end, I decided that going to graduate school would be a better investment. Even if a graduate degree doesn’t quite give me the running start I’m hoping for in the short term, at least I can be relatively certain that having the degree will help me in the long run.

3. To Take Advantage of Timing
If I had started working and then decided that I wanted (or needed) to go to graduate school in the future, it could have been much more complicated. Many people have also told me how difficult it can be to transition from work-mode back to school-mode. Right now, my life is still pretty simple, and I don’t really have much keeping me grounded to one place, so it seemed like a perfect time to take the plunge.

For those of you out there considering graduate school, what are your reasons? Leave a comment below!

New GRE: Changes to the Quantitative Reasoning Section

What's changing on the math section?

The new GRE begins August 1, 2011. If you’re reading this blog, there’s a good chance the question “should I take the new GRE or the old GRE?” has crossed your mind. There are many factors to consider, and as a primer, take a look at our previous post about which GRE you should take.

In order to make this decision, you need to be informed about exactly what the differences between the new GRE and the old GRE are. This (beautiful, elegant, and efficient) diagram gives both a high-level overview of both tests as well as a more detailed explanation of each question type. In this series of posts, we’ll be going over these points in even greater detail, one section at a time, starting with math.

Continue reading “New GRE: Changes to the Quantitative Reasoning Section” »

GRE Math: Two Difficult Example Problems and Solutions

Example Difficult Arithmetic Problem

Example Hard Arithmetic Problem

These problems aren’t difficult because they use particularly complicated mathematical principles — they’re difficult because they’re a little tricky. They require you to think a little beyond what’s given directly to you.

This problem looks a lot like an algebra problem because of the variables, but unfortunately it’s not. With three variables, you would need three equations to solve it, which you don’t have.

So how do you approach this problem? Well, once you realize that it’s not an algebra problem, you should be thinking of how you can arrive at values for x, y, and z without using algebra. You know you need these values because eventually you have to add them together. So let’s look at what you do know from the problem.

3x = 4y = 7z

This means that 3x, 4y, and 7z all equal some number, which we will call n; this also means that

3x = n
4y = n
7z = n

From this, we can see that n must be a multiple of 3, a multiple of 4, and a multiple of 7. What is the smallest number that is a multiple of 3, 4, and 7 (LCM of 3, 4, and 7)? It’s 84! (3 * 4 * 7 = 84)

So if n = 84, then we get the following three equations

3x = 84
4y = 84
7z = 84

Solving for each variable, we get

x = 28
y = 21
z = 12

If we add them together, we get

x + y + z = 28 + 21 + 12 = 61

Thus, the answer is (D).


Example Difficult Geometry Problem

Example Hard Geometry Problem

The goal of this problem is to find the area of the shaded region. There are two ways to do this problem — I’ll go over both.

Method 1: Find the area of the shaded trapezoid
A trapezoid is defined as a quadrilateral with two parallel sides and two non-parallel sides. The shaded region is a trapezoid.

(Brief aside: We know that the shaded region is a trapezoid because both the top line segment (y) and the bottom line segment (x) form right angles with the left line segment (also labeled x). Because both y and x intersect the left line segment at the same angle, they must be parallel.)

So what is the formula for the area of a trapezoid?

Atrapezoid = ½(b1 + b2)h

b1 and b2 are the bases of the trapezoid, which are the two parallel line segments; h is the height of the trapezoid, which is the perpendicular distance from one base to the other base.

What do we already know?

b1 = x
b2 = y

So all we need to know is the height of the trapezoid. Based on the drawing, it sort of looks like the height is simply half of the left segment — but that’s not good enough (and it will lead you to the wrong answer, in this problem)! We should never, ever have to “guess” at a value on the GRE! There must be a way to figure it out.

Notice that both the bottom segment and the left segment have length x. There’s a name for triangles that have two identical sides — isosceles triangles. Isosceles triangles also have two identical angles as well. The angles that are opposite of the identical sides are also identical. Let’s call it a.

We know that the sum of the angles in a triangle is 180º. So the sum of the angles in the whole triangle is

a + a + 90 = 180
2a + 90 = 180
2a = 90
a = 45

Both angles are 45º.

Now let’s examine the smaller triangle (the unshaded portion). The top angle for that triangle is the same — 45º. It also has a right angle, which is 90º, so that means that the remaining angle is also 45º.

Hey, look at that! This triangle is also an isosceles triangle, and the sides that are the same are the bottom (y) and the left segment — which is also y (this concept is called similar triangles).

We know that the entire left segment has length x, and the top part of that segment has length y — this means that the bottom part has length x – y. This bottom part also happens to be the height of our trapezoid!

Let’s plug it all into the area equation now:

Atrapezoid = ½(b1 + b2)h
Atrapezoid = ½(x + y)(x – y)

Note that

(x + y)(x – y) = x2 – y2

Substituting,

Atrapezoid = ½(x2 – y2)

which is answer choice (A) (multiplying by ½ is the same as dividing by 2).

Method 2: Whole Minus Part
The shaded region of the triangle is part of the whole triangle. In order to find the shaded region, we could find the area of the whole triangle and subtract away the area of the smaller triangle (the unshaded region).

The formula for area of a triangle is

Atriangle = ½(bh)

where b is the base of the triangle, and h is the height.

For the large triangle,

Abig_triangle = ½(x*x) = ½x2

For the small triangle, we know the base is y, and from the previous explanation above, we know that the height (the left segment) is also y (because the triangle is isosceles). Thus, the area of the small triangle is

Asmall_triangle = ½(y*y) = ½y2

Subtracting the two, we get

Abig_triangle – Asmall_triangle = ½x2 – ½y2 = ½(x2 – y2)

which is answer choice (A).


Questions? Concerns? Suggestions? Criticisms? Leave a comment below!

The GRE: Looking Back at Test Day, Part 2

Taking the GRE is fun!

Continuing from Part 1

The room is spartan. There are about twenty computers, but only about ten of them are being used right now. Nobody so much as flinches as I enter the room; everyone is totally submerged beneath a thick layer of concentration. The proctor shows me to my seat in the corner, and I take my seat.

Continue reading “The GRE: Looking Back at Test Day, Part 2” »