Questions tagged [gre-exam]

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

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How many 2-digit positive integers are there?

How many 2-digit positive integers are there such that the product of their two digits is 24? The answer given is four. I'm not certain if I understand this question correctly and need some guidance ...
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-1 votes
1 answer
205 views

When to take the math GRE, in my situation. [closed]

I am a technically a freshman mathematics and computer science major at the University of Kentucky. However, I was able to take a lot of math classes in high-school (I was home schooled) at the local ...
3 votes
3 answers
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Whether two quantities are greater, smaller or not possible to determine (GRE Quant)?

The question is taken from a general GRE math quantitative comparison question. Problem: $x>y$ and $xy\ne0$ Quantity A: $ \displaystyle\frac{x^2}{{1+ \frac{1}{y}} }$ Quantity B: $ \displaystyle\...
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3 votes
1 answer
134 views

GRE Practice Question Incorrect?

This is a sample GRE question. The answer claims that we cannot make an inference due to insufficient information. Compare the following quantities: Of the 25 people in Fran’s apartment ...
1 vote
1 answer
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Is there a more intuitive/easier way to solve these combined rate problems?

I am helping my brother study for the GRE and we have come across some problems like this in my old precalculus textbook: 1) Karen and Betty have been hired to pain a house. Working together, they ...
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5 votes
3 answers
141 views

Series representation of $2e$

According to GR9768, problem 37: $$\sum_{k=1}^{+\infty} \frac{k^2}{k!} = 2e$$ Can someone please explain how to get started in showing that?
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3 votes
2 answers
671 views

$n$ by $n$ matrices such that $Ax=0$ implies $Bx=0$, then what can we say about $A$ and $B$?

Ok, this is one of the interesting questions I encountered in my GRE Maths exam 2 weeks ago. Fix an $x\in \mathbb{R}^n$ (doesn't have to be $0$), and $A$, $B$ are $n$ by $n$ matrices such that $Ax=0$ ...
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2 answers
100 views

Show mean of a sequence of sets is zero but mean of countably infinite set is infinity if increasing

Let $\Omega$ be a countably infinite set, and let $F$ consist of all subsets of $\Omega$. Define $\mu(A) = 0$ if $A$ is finite and $\mu(A) = \infty$ if $A$ is infinite. Show that $\Omega$ is the limit ...
1 vote
0 answers
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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 ...
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4 votes
3 answers
411 views

$f(1+x) = f(x)$ for all real $x$, $f$ is a polynomial and $f(5) = 11$. What is $f\large(\frac{15}{2}\large)$?

I was looking through a GRE math subject test practice test (here) and in particular I was confused regarding this question I chose E because I thought that (since the problem didn't specify) it ...
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1 vote
2 answers
898 views

Continuity of a step function

I found the following question in GRE 1268 practice test. I was wondering if you could tell me how to approach this problem since everytime I encounter a similar problem I have troubles solving it. ...
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2 votes
1 answer
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Analysis/calculus question from the GRE practice exam

The following question is from GRE 8767, and I am unsure how to view this question. The solution says that ''In a confusing way, this question is asking us what the approximate total change in $f(x)$...
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1 answer
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Ineqality $\lvert z \rvert \leq 1$ but not considering all values

if $|z| \leq 1$, which of the following statements must be true ? Indicate all such values A. $z^2 \leq 1$ B. $z^2 \leq z$ C. $z^3 \leq z$ The book states its answer A, considering the numbers $\frac{...
2 votes
1 answer
92 views

finding the number of all real zeros of $f(x)=\sec(x)-e^{-x^2}$

How can we find the number of all real zeros of $f(x)=\sec(x)-e^{-x^2}$? This was an exam question of GRE subject. Also I am struggle with sketching the graph $f$ by hand.
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1 vote
1 answer
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GRE Subject question $\log x=c x^4$ [duplicate]

For what positive value of $c$ does the equation $\log x=cx^4$ have exactly one real solution for $x$?. Thank you.
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 votes
1 answer
87 views

GRE question $\lim_{n \to \infty} \inf_{x \in \mathbb R} (e^x-nx)$ [closed]

How would you solve this question? $$\lim_{n \to \infty} \inf_{x \in \mathbb R} (e^x-nx)$$ I found it in a GRE exam but I'm not sure how to solve it.
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1 vote
2 answers
483 views

Transform recursive sequence to direct.

I am taking the GRE General Exam in a few weeks and there are some problems about sequences that I have found a bit difficult, e.g given a sequence in recursive form like $S_{n} = S_{n-1} - 10$ and ...
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 answer
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GRE 1268 #57 - Does $g(0)$ exist if $g$ is uniformly continuous on $(0,1)$?

GRE question: An answer: Above is from here: http://www.math.ucla.edu/~iacoley/gre/Practice%201%20solutions.pdf Other answers: https://drive.google.com/file/d/0B-uVGGkZosoPcGVRcDNPN0d2ZVU/view ...
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0 votes
1 answer
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GRE 8767 - 34 - Graphical explanation

Let the bottom edge of a rectangular mirror on a vertical wall be parallel to and h feet above the level floor. If a person with eyes t feet above the floor is standing erect at a distance d feet from ...
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0 votes
3 answers
962 views

Second derivative of parametric equation at given point.

Let $f(t)=(t^2+2t,3t^4+4t^3), t>0$. Find the value of the second derivative, $\frac{d^2y}{dx^2}$at the point $(8,80)$ This is a past Math subject GRE question, and the usual formula: for second ...
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1 vote
3 answers
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If $a<g(x)<x$ on the interval $(a,b)$, why must $g$ be nonconstant? (GRE question)

I have the following GRE question that I have some trouble seeing. If $g$ is a function defined o the open interval $(a,b)$ such that $a < g(x) < x$ for all $x \in (a,b)$, then $g$ is A) an ...
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2 answers
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Piecewise constant function continuity

In page 291 of "Cracking the GRE Mathematics Subject Test" I came upon the following Topology example: $$f(x) = \begin{cases} -2, \text{ if } x<0 \\ \;\;\; 2,\text{ if } x \geq 0 \end{...
7 votes
2 answers
2k views

Which of the following sets of matrices are dense in the set of square $n \times n$ square matrices over $\mathbb{C}$?

Practicing for the GRE I found this question and I was wondering if anyone had any general tips to approach this type of questions or any literature I could review to approach them. Which of the ...
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0 votes
1 answer
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(GRE Bootcamp Question) Curve dotted with its derivative

I have the following multiple choice question with solution that I would like some clarification on. The question is as follows: Suppose that $\vec{r}:\mathbb{R}\to\mathbb{R}^3$ is a curve given by $...
1 vote
1 answer
144 views

Evaluating $\int_x^0 f(x,t) dt$?

I'm working on reviewing one of the problems in the REA GRE math subject test prep book which is to find the derivative of $$ f(x) = \int_x^0 \frac{\cos(xt)}{t}dt $$ My first thought was to flip the ...
2 votes
1 answer
224 views

Fundamental theorem of calculus question from GRE

This question is motivated from GRE math subject test. Let $f$ and $g$ be functions of a real variable such that for all $x$, $$g(x)=\int\limits_{0}^{x}f(y)(y-x)\,\mathrm{d}y\,.$$ If $g$ is three ...
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1 vote
3 answers
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Question in complex numbers from GRE

This is a question motivated from GRE subgect test exam. if f(x) over the real number has the complex numbers $2+i$ and $1-i$ as roots,then f(x) could be: a) $x^4+6x^3+10$ b) $x^4+7x^2+10$ c) $x^3-x^...
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1 vote
1 answer
319 views

Simple Ratios Question involving Currency

In nation Z, 10 terble coins equal 1 galok. In nation Y, 6 barbar coins equal 1 murb. If a galok is worth 40% more than a murb, what is the raio of the value of 1 terble coin to the value of 1 barbar ...
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2 votes
1 answer
204 views

Silly errors during math exams and effective methods of checking. [closed]

I'm sure this is something that all math students experience many times in their career. I've noticed after completing my exam in the examination room that I would go back upon my paper and find ...
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2 votes
2 answers
582 views

Limit of complex quotient with conjugate

This is from the practice GRE online. Compute $$\lim_{z \to 0} \frac{(\bar{z})^2}{z^2}$$ I let $z = re^{i\theta}$ and computed $$\frac{(\bar{z})^2}{z^2} = \frac{(re^{-i\theta})^2}{(re^{i\theta})^...
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7 votes
3 answers
476 views

GRE question: Evaluate $\int_0^\infty \left \lfloor x \right \rfloor e^{-x} \,\mathrm{d}x$

I have the following GRE question that I have no idea how to solve. Let $\left \lfloor x \right \rfloor$ denote the greatest integer not exceeding $x$. Evaluate $\int_0^\infty \left \lfloor x \...
0 votes
2 answers
245 views

Should we take only positive root i.e. -y or both the roots + or -y?

As in gre, square root symbol means principal square root, what should be the answer in this case? Should we take only positive root i.e., $-y$ or both the roots $+$ or $-y$? If $y < 0$, $\sqrt{-y|...
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1 vote
0 answers
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GRE analysis problem

I am trying to prove the existence of continuous onto function from (0,1) to [0,1]. Well, it was easy, since $\sin(\dfrac1{x(x-1)})$ does what I need. BUT... a slight tweak to the definition of ...
3 votes
2 answers
165 views

Number of roots of $x^4 + x^3 \sin(x) + x^2 \cos(x) = 0$

How many roots do the following polynomial have? $$x^4 + x^3 \sin(x) + x^2 \cos(x)$$ Obviously $0$ is a root. Dividing by $x^2$, I am left with $$x^2 + x\sin(x) + \cos(x)$$ How do I know this ...
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3 votes
1 answer
180 views

GRE eigenvalue question. Do we actually have to find the eigenvalues?

The GRE is this weekend and while working through a practice test I came across this question, and I couldn't see any clever way to work out the answer. Of 2, 3, and 5, which are the eigenvalues of ...
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100 votes
2 answers
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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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2 votes
0 answers
259 views

Limit of the integrand of an improper integral.

I don't have any idea about how to solve the following GRE question. Could anyone give me some tips how to solve this kind of problems? Let $f: (1,\infty) \to [0,\infty)$ be a function, such that the ...
1 vote
2 answers
412 views

Let A be a real 3times 3 matrix. Which of the following conditions does not imply that A is invertible?

Let A be a real $3\times3$ matrix which of the following conditions does not imply that A is invertible? (D) The set of all vectors of the form $Av$, where $v \in \mathbb R^3$, is $\mathbb R^3$. (E) ...
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3 votes
1 answer
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Laurent Series From Cracking the GRE (Mistake?)

The problem asks to find the Laurent series for $f(z)=\frac{1}{z-3}$ in the annulus $|z-4|>1$. I found the answer to be $\sum\limits_{n=0}^{\infty}(-1)^n(z-4)^{-n-1}$. However, the book states that ...
2 votes
2 answers
66 views

Evaluating an indefinite integral with exponents and logarithms

I was taking a GRE practice exam and came across $$ \int_0^{\infty} \frac{e^{ax} - e^{bx}}{(1 + e^{ax})(1 + e^{bx})} dx $$ I noted that this can be expressed as $$ \int_0^{\infty} \frac{1}{(1 + e^...
1 vote
3 answers
141 views

Estimation of probability, 70 particular events from 360

A fair die is tossed 360 times. The probability that a six comes up on 70 or more of the tosses is This is a GRE question.
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2 votes
2 answers
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A question involving implied differentiability

I was working on the following problem: Given: $$ g(x) = \int_0^x f(y) (y - x) dy $$ And $g(x)$ is exactly 3 times continuously differentiable. What is the greatest integer n for which $f$ must be $...
3 votes
1 answer
47 views

Names of absorbing sub-structures

I was taking a math GRE and found a curious property in a question. There exists subsets $M$ of Rings $R$ that are absorbing but are not ideals. A prototypical example (the one from the exam) is if ...
3 votes
4 answers
278 views

GRE math question

I have the following problem in a GRE practice exam, I was wondering if someone could help me figure it out. Suppose $y(t) = y$ solves $y' = (y^2-1)e^{2012y-1}$ with initial condition $y(0)=0$, then ...
4 votes
2 answers
758 views

What is the 30th term of this sequence (math GRE)?

I am studying for the math subject GRE and came across the following problem from a previous exam (Form GR0568, found at "www.math.ucla.edu/~cmarshak/GRE1.pdf", question #25). The problem states: ...
-2 votes
3 answers
86 views

When can $0$ be a dimension of $(V \cap W)$?

GRE 0568 GRE 1268 Why is that $0$ is included in the former but not in the latter? It seems to me we just use the rule: $$\dim(V+W)=\dim(V)+\dim(W)-\dim(V \cap W) \le \dim(\text{Well in this case ...
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5 votes
5 answers
6k views

Why is the distance between two circles/spheres that don't intersect minimised at points that are in the line formed by their centers?

From GRE 0568 From MathematicsGRE.Com: I'm guessing the idea applies to circles also? Is there a way to prove this besides the following non-elegant way? Form a line between centers $C_1$ and $C_2$ ...
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4 votes
3 answers
135 views

If $u(x) = \int_1^x \sin(x-t)t^2 dt$, then $u'' + u -x^2 = 0$

Suppose $u(x) = \int_1^x \sin(x-t)t^2 dt$, verify that $u''+u - x^2 = 0$. I know how to verify the equation but I am curious if there is any faster way of doing this (since this is a practice problem ...
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