Questions tagged [gre-exam]

For questions relevant to the general or subject-specific Graduate Record Examination, abbreviated GRE.

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17 votes
2 answers
19k views

Explicitly finding the sum of $\arctan(1/(n^2+n+1))$

This is from a GRE prep book, so I know the solution and process but I thought it was an interesting question: Explicitly evaluate $$\sum_{n=1}^{m}\arctan\left({\frac{1}{{n^2+n+1}}}\right).$$
100 votes
2 answers
52k views

GRE Subject Test - Past Papers, Books, Advice

This is not for the Maths part of the General GRE. This is for the GRE Subject Test in Maths. Feel free to add or comment. How do I know the definition of rings or of anything on the GRE given that ...
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14 votes
4 answers
6k views

What is the greatest integer that divides $p^4-1$ for every prime number $p$ greater than $5$?

What is the greatest integer that divides $p^4-1$ for every prime number $p > 5$? This was on a practice math GRE so it's probably really easy.
  • 3,945
0 votes
2 answers
431 views

Evaluate $\int_{-\pi/4}^{\pi/4}(\cos(t)+\sqrt{1+t^2}\cos(t)^3\sin (t)^3)dt$

Evaluate: $$\int_{-\pi/4}^{\pi/4}(\cos(t)+\sqrt{1+t^2}\cos(t)^3\sin(t)^3)dt$$ I have tried substituting $t=\tan(\theta)$ and breaking up the $\cos(t)^3$ using $\cos(t)^2=1-\sin(t)^2$, but I can't ...
27 votes
2 answers
27k views

recommending books for GRE math subject test

I wonder if anyone could recommend some books (other than Princeton Review) to prepare for the GRE math subject exam. I've heard that the REA books have lots of typos, though it has 6 practice exams. ...
32 votes
2 answers
7k views

Books to study for Math GRE, self-study, have some time.

I just graduated from a regional university in the US with a minor in mathematics. There is a masters program overseas, for economics, that I want to attend but they require applicants to take the ...
  • 321
9 votes
3 answers
2k views

GRE linear algebra question

The following is a question from the sample GRE Mathematics Subject Test found on the ETS website: Let $M$ be a $5\times 5$ real matrix. Exactly four of the following five conditions on $M$ are ...
  • 1,693
2 votes
4 answers
2k views

$\log x =Cx^4$ has only one root. Find C

$\log x =Cx^4$ has only one root. Find C. I don't know how to solve this problem. Do you take derivative on both sides? I am thinking C equals 0. Am I correct on that?
  • 225
17 votes
6 answers
4k views

Math Subject GRE 1268 Question 55

If $a$ and $b$ are positive numbers, what is the value of $\displaystyle \int_0^\infty \frac{e^{ax}-e^{bx}}{(1+e^{ax})(1+e^{bx})}dx$. A: $0$ B: $1$ C: $a-b$ D: $(a-b)\log 2$ E: $\frac{a-b}{ab}\...
4 votes
3 answers
469 views

If $f$ and $f''$ are square integrable is $f'$?

Let $f:[0,\infty)\rightarrow \mathbb{R}$ be twice differentiable. Such that $\int_{0}^{\infty}f(x)^{2}dx<\infty$ and $\int_{0}^{\infty}f''(x)^{2}dx<\infty $, show that $$\int_{0}^{\infty}f'(x)^...
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3 votes
2 answers
3k views

Multivariable Calculus for GRE

This is going to sound strange, but I am a third year math major who never took multivariable calculus (despite having taken courses on Galois and Lebesgue theory, etc). I plan to take the GRE next ...
2 votes
2 answers
761 views

Derive quadratic formula [duplicate]

I cannot understand how quadratic formula to solve for $x$ was derived. On this website, it explains the steps Following I understand but I cannot understand how they got $b/2a$ and why they are ...
  • 403
2 votes
2 answers
281 views

Gre Question Complex Number (plug and chug) [duplicate]

This seems like it should be easy, but I can't seem to simplify it: If $z=e^{i\frac{2\pi}{5}}$, then what is $1+z+z^2+z^3+5z^4+4z^5+4z^6+4z^7+4z^8+5z^9$. The choices are $0, 4e^{i\frac{3\pi}{5}}, 5e^{...
  • 6,017
2 votes
4 answers
2k views

GRE problem involving LCD, prime factorization, and sets.

I think this problem was a bit tricky and I'm trying to better think through this. Here is the problem: Let S be the set of all positive integers n such that $n^2$ is a multiple of both 24 and 108. ...
  • 5,514
2 votes
2 answers
618 views

x minute break in work rate problem

Working alone at their respective constant rate, Audery can complete a certain job in 4 hours, while Ferris can do the same job in 3 hours. Audery and Ferris worked together on the job and completed ...
1 vote
1 answer
3k views

GRE - Probability Question

For a certain probability experiment, the probability that event $A$ will occur is $\displaystyle\frac12$ and the probability that even $B$ will occur is $\displaystyle\frac13$. Which of the following ...
0 votes
1 answer
879 views

At what times before $1{:}30$ in the afternoon do all three doctors schedule their appointments to begin at the same time?

In a certain medical group, Dr. Schwartz schedules appointments to begin $30$ minutes apart, Dr. Ramirez schedules appointments to begin $25$ minutes apart, and Dr. Wu schedules appointments to begin $...
  • 2,233
18 votes
3 answers
49k views

GRE Math Subject Test [closed]

I am studying for GRE Math. I am looking for specific tips. What types of questions usually come up? Does anyone know any tricks (e.g. integration tricks) that might be helpful? Which theorems are ...
  • 9,820
10 votes
3 answers
17k views

Are there 3 or 4 quartiles? 99 or 100 percentiles?

So I understand that a quartile is a quantile where the data is divided into four groups. 1 2 3 ---|---|---|--- And 1, 2, and 3 are the quartiles. The ...
  • 2,065
8 votes
4 answers
702 views

Interesting GRE problem

I found this in a practice GRE problem. I thought I would have a crack at it after being spoiled by the answer At how many points in the xy-plane do the graphs of $y = x^{12}$ and $y = 2^x$ ...
  • 12.2k
7 votes
3 answers
3k views

If p and q are prime which elements are in the subgroup? (GRE question)

I was just doing some practice problems in my abstract algebra book trying to get a warm up this morning, but I found a GRE problem in the problem set and I don't know how to solve it. I've tried to ...
  • 1,284
6 votes
7 answers
30k views

Finding a number given its remainder when divided by other numbers

I have this GRE question that I'd like to know how to solve. I want to solve it in as simple a way as possible, since it is GRE material. In particular, I don't want to use "congruences" or modulo ...
  • 1,359
6 votes
1 answer
982 views

A Calculus problem in GRE math sub test

$$\int_0^{\frac{\pi}{2}} \frac{\sin^3(t)}{\sin^3(t)+\cos^3(t)}$$ I tried to use $x=\tan(t)$ to transform but it's really a mess..
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3 votes
2 answers
559 views

how to solve $\log{x}=cx^4$ for $x$

I was wondering if there is a general solution for this form of equations: $$\log{x}=cx^4$$ Tried: $$ x = e^{cx^4}\\ xe^{-cx^4}=1$$
3 votes
3 answers
385 views

A couple of GRE questions

Look for help with the following GRE questions Question 1. If $C$ is the circle in the complex plane whose equation $|z|=\pi$, oriented counterclockwise, find the value of the integral $\oint_C(\cos ...
  • 700
2 votes
2 answers
15k views

GRE Probability question

How many 3-digit positive integers are odd and do not contain the digit 5 ? My attempt: 100-999 3 -digit integers, 900/2=450 odd numbers. Now how to calculate odd numbers which do not contain digit 5 ...
  • 241
2 votes
1 answer
859 views

What is a good combinatorics text for someone studying for the Math GRE Subject Test?

I have NEVER taken a combinatorics course, outside of what one covers in a calculus-based probability course. I would be interested in knowing what would be a suitable combinatorics text for ...
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2 votes
2 answers
6k views

Finding the possible dimensions of the intersection of subspaces

I read this problem, If $V$ and $W$ are 2-dimensional subspaces of $\mathbb{R}^{4}$ what are the possible dimensions of $V\cap W$? I know the answer is: 0, 1, or 2. But I would like more insight ...
  • 4,937
1 vote
2 answers
2k views

Evaluate the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} (\cos(t)+\sqrt{1+t^2} \cos^3(t)\sin^3(t) )dt$ [duplicate]

Found this problem on the most recent GRE practice booklet by ets. I ended up skipping it because it looked like too much work. Going back through, I still don't know how to evaluate it. To me, this ...
  • 314
1 vote
4 answers
34k views

Minimum area of Inscribed Square

GRE study guide asks The perimeter of square S is 40. Square T is inscribed in square S. What is the least possible area of square T? Choices are 45 48 49 50 52 They say answer is 50. How do ...
  • 403
1 vote
2 answers
788 views

Finding the value of this integral $ \int_{-\pi/4}^{\pi/4}{ (\cos{t} + \sqrt{1 + t^2} }\sin^3{t}\cos^3 {t})dt$? [duplicate]

I stumbled on this problem and I'm stuck. Any hints on how I could approach evaluating this particular integral? $$ \int_{-\pi/4}^{\pi/4}{ (\cos{t} + \sqrt{1 + t^2}\sin^3{t}\cos^3 {t})\,dt}$$ What ...
  • 807
1 vote
1 answer
458 views

Some GRE questions (II) [closed]

Let $F$ be a constant unit force that is parallel to the vector $(1, 0, 1)$ in xyz-space. What is the work done by $F$ on a particle that moves along the path given by $(t, t^2, t^3)$ between time $t=...
  • 700
1 vote
1 answer
200 views

$x \in (a-r,a+r)$ versus $|x-a| < |r-a|$

From the Princeton book for the GRE Subject Test in Maths: That part seems to suggest that if $x \in (a-r,a+r)$ then $f(x) < \frac1q < \varepsilon$ and hence $f$ is continuous at the ...
  • 12.5k
1 vote
0 answers
86 views

Arithmetic question [duplicate]

"In a certain medical group, Dr. Schwartz schedules appointments to begin 30 minutes apart, Dr. Ramirez schedules appointments to begin 25 minutes apart, and Dr. Wu schedules appointments to begin 50 ...
  • 143
1 vote
1 answer
441 views

Lipschitz continuity implies differentiability a.e.? - GRE 9768 #64

GRE 9768 #64 From here How do you prove that? I tried this approach based on a question and solution in the Princeton GRE exam The question: The solution: (Btw, it's supposed to be $f'(y)$ not $f'...
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1 vote
2 answers
629 views

GRE permuation and combination problem 1

Question: The University of Maryland, University of Vermont, and Emory University have each $4$ soccer players. If a team of $9$ is to be formed with an equal number of players from each university, ...
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1 vote
2 answers
560 views

GRE test prep question [LCM and divisors]

Let $S$ be the set of all positive integers $n$ such that $n^2$ is a multiple of both $24$ and $108$. Which of the following integers are divisors of every integer $n$ in $S$ ? Indicate all such ...
  • 737
0 votes
1 answer
154 views

Finding distance using rates of change -- best approach?

The question: A man drives from state $A$ to state $B$ going $60 \frac{miles}{hour}$. Then he returns from state $B$ to state $A$, driving $45 \frac{miles}{hour}$. His total driving time is $2.5 hour$...
  • 3,171
0 votes
2 answers
1k views

Matrix Representation of a Bilinear Form

Let $b : \Bbb{R}^2 \times \Bbb{R}^2 \to \Bbb{R}$ be the bilinear form defined by $$b((x_1,x_2),(y_1,y_2)) = x_1 y_1 - 2x_1 y_2 + x_2 y_1 + 3x_2 y_2.$$ Find the $2 \times 2$ matrix $B$ of $b$ relative ...
  • 7,370
0 votes
1 answer
939 views

angle of inscribed triangle

let us consider following problem: we have inscribed triangle,like this we are asked to determine if given $x$ is acute or obtuse,$O$ is center of circle,as i know if $CB$ would be diameter,...
-2 votes
3 answers
350 views

Limits at infinity of a function and its derivative [closed]

I do not know how to solve this question, could anyone help me please?
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