Questions tagged [gre-exam]

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

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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}\...
0 votes
2 answers
76 views

GRE - Standard Deviation Question (Quantitative Comparasion)

Each video game that a video game shop sold last year was either for the PS4 or Xbox One. The shop sold new PS4 Games for USD 60 and new Xbox One Games for USD 30. The standard deviation for all of ...
0 votes
2 answers
704 views

Find Area of Similar Right Triangle

Need help to approach following from GRE study guide Here is what I have so far $area = 1/2 bh$ $area CDE = 1/2 bh = 42 = 21 bh$ $AD = 3CD$ Honestly, I'm not sure how to approach. Please give ...
0 votes
1 answer
52 views

Distance and Arc Length (Math GRE)

A circular helix in $xyz$-space has the following parametric equations, where $\theta \in \mathbb{R}$. $x(\theta)= 5\cos(\theta)$ $y(\theta)=5\sin(\theta)$ $z(\theta)=\theta$ Let $L(\theta)$ be the ...
0 votes
1 answer
48 views

Finite sum inequality (math GRE subject)

Which of the following statements are true: There exists a constants $C$ such that $\log x \leq C\sqrt x$ for all $x\geq1$ There exists a constant $C$ such that $\sum_{k=1}^nk^2 \leq Cn^2$ for all ...
0 votes
0 answers
28 views

Approximate Binomial Distribution using normal distribution

When I was reading "cracking the GRE mathematics subject test" 4th edition page 282, there is a formula regarding approximation of binomial distribution: In X ~ Binomial(n, p), when n is ...
0 votes
0 answers
75 views

If $f(x)=p \sin x + q x \cos x + x^2$ and $f(2)=3$, find $f(-2)$

A GRE subject trig question: Let $p,q$ be constants and let $$f(x)=p \sin x + q x \cos x + x^2$$ for all real numbers $x$. If $f(2)=3$, find $f(-2)$. So I plug in and obtain $$3=\phantom{-}p \sin 2 +...
1 vote
3 answers
77 views

Evaluating ${\int_{0}^{1}\sqrt{1+\frac{1}{3x}}\text{ d}x}$ using $\int f^{-1}(x)dx=x f^{-1}(x)-F(f^{-1}(x))+C$

While studying, I countered problem $\text{#}2$ here. $\text{(UCHICAGO REU 2019 - MATH GRE PREP: WEEK 2)}$. I saw this also. But wanted to know if my way is also correct (regardless of the time ...
4 votes
0 answers
98 views

Is this a valid way to compute $\int_{0}^{\infty}\frac{\cos(\alpha x)-\cos(\beta x)}{x}\text{d}x$?

I am not sure if the following way is valid to evaluate $$\int_{0}^{\infty}\frac{\cos(\alpha x)-\cos(\beta x)}{x}\text{d}x$$ SOURCE I saw this and this But I am asking if the following is valid or not?...
1 vote
1 answer
1k views

Average question GRE

The average daily temperature from 9th to 16th January(both inclusive) was 38.6 C and that from the 10th to 17th January(inclusive) was 39.2 C. what was the temperature on 17th January? I am able to ...
0 votes
0 answers
112 views

How $5^{40} < 4^{60} < 27^{30}$, $8^{1/11} < 9^{1/10} < 10^{1/9}$, $e^{e} < \pi^{e} < e^{\pi}$, and $200^{100} < 200! < 100^{200}$?

The following four problems appeared in (UCLA) (University of California, Los Angeles) - GRE Preparation. $\mathbf{Problem} \space \mathbf{11}, \mathbf{Problem} \space \mathbf{12}, \mathbf{Problem} \...
0 votes
0 answers
32 views

Finding relative extrema

For the following problem, we are asked which of the following statements is true for $f(x,y)=x^2-2xy+y^3$ A) $f$ has all its relative extrema on the line $y=x$ B) $f$ has all its relative extrema on ...
2 votes
3 answers
3k views

Derivation of the "Combined Work Formula"

Before I get to my question, some background: Person $A$ can paint a fence at the rate $9 \frac{hour}{fence}$ (or equivalently $\frac{1}{9} \frac{fence}{hour}$) Person $B$ can paint a fence at the ...
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. ...
1 vote
1 answer
121 views

If a $3\times 3$ matrix satisfies $A^3-A^2-A+I=0$, then it is not necessarily diagonalisable.

If a $3\times 3$ matrix satisfies $A^3-A^2-A+I=0$, then it is not necessarily diagonalisable. I have a counterexample $\begin{pmatrix}1&1&0\\0&1&0\\0&0&1\end{pmatrix}$. But I ...
3 votes
1 answer
119 views

Showing that $AB$ is a subgroup.

I was trying to solve this question: Let $G$ be a group and $A,B$ subgroups of $G.$ Define $AB$ as the set of all products $ab,$ where $a \in A$ and $b \in B.$ Prove that $AB$ is a subgroup of $G$ iff ...
0 votes
1 answer
55 views

Matrix in $M_2(\mathbf{R})$ of order $2$ has trace $0$

I found this question in a GRE math subject test from 1987. It's problem 61 at http://web.math.ucsb.edu/~padraic/ucsb_2014_15/math_gre_w2015/GRE_8767_test.pdf. It boils down to the following. Prove ...
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 ...
1 vote
2 answers
264 views

Determining the maximum value of a multivariable function under 4 inequality constraints.(Math GRE subject test 9768 Q.25)

I know that I should use Lagrange multiplier method, but how with the inequality constraints? could anyone help me please?
0 votes
0 answers
33 views

$u=f(x,y)$ and the partial derivatives are themselves differentiable functions of $x$ and $y$ (Typo?)

I am really not sure whether this question can be posted in MSE or not, but hopefully can be. If not, kindly do not downvote, but suggest me to delete it from here and post it somewhere else. While ...
2 votes
1 answer
438 views

Let $h$ be the function defined by $h(x)=\int_{0}^{x^2}e^{x+t}dt$ for all real numbers $x$. Then $h'(1)=\dots$

This question appeared in the GRE MATH SUBJECT TEST (GR$0568$) - Question# $24$: Let $h$ be the function defined by $h(x)=\int_{0}^{x^2}e^{x+t}dt$ for all real numbers $x$. Then $h'(1)=$ (A) $e-1$ (...
1 vote
1 answer
119 views

Possible dimensions of $V \cap W$ in $\mathbb{R}^n$

If $V$ and $W$ are two dimensional subspaces of $\mathbb{R}^n$, what are the possible dimensions of $V \cap W$ if; $V$ and $W$ have the same dimensions? (for example; $\dim(V)=2, \dim(W)=2, n=3$) $V$ ...
1 vote
1 answer
40 views

The order of $C=\sum_{k=0}^{90}(90-k)\cos(k ^{\circ}), S=\sum_{k=0}^{90}(90-k)\sin(k ^{\circ})$, and $T=\sum_{k=0}^{90}(90-k)\tan(k ^{\circ})$.

This is multiple choice questions, where using calculators is not allowed. Candidates have, on average, $2$ minutes $30$ seconds to solve it. MY ATTEMPT: $k ^{\circ} = (\text{positive constant} \...
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. ...
1 vote
2 answers
258 views

Let $P$ be a polynomial with integer coefficients satisfying $P(0)=1, P(1)=3, P'(0)=-1, P'(1)=10$. What is the minimum possible degree of $P$?

I am preparing for GRE MATH SUBJECT TEST, I have reviewed many problems, some of these problems are not in GRE Math Practice books, but they are in some other books. I found the following problem, but ...
2 votes
3 answers
9k views

The possible remainders when a multiple of 4 is divided by 6, and when a multiple of 2 is divided by 3

I'm currently studying for the GRE and a specific type of question has me stumped. I have a two part question, but first here is one problem and my work: "If x is the remainder when a multiple of 4 ...
1 vote
2 answers
956 views

Math Subject GRE 1268 Problem 64 Flux of Vector Field

What is the value of the flux of the vector field F, defined on $R^3$ by $F(x,y,z) = (x,y,z)$ through the surface $z=\sqrt{1-x^2-y^2}$ oriented with upward-pointing normal vector field? $$\begin{...
0 votes
2 answers
139 views

Is $\text{for}\ n\in \mathbb{N},\dfrac{u_{n+1}}{u_n}=q \iff \text{for}\ n\in \mathbb{N},u_{n+1}=q u_n$?

In the correction of bac exams in my country , The Correction Committee ordered us to give the whole point for students who they showed that the sequence $u_n$ is geometric using $u_{n+1}=q u_n$ ...
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.
0 votes
2 answers
161 views

Determining the value of the product of a matrix A with another known matrix without knowing what is the matrix A (math GRE subject test 9768 Q.43)

I have given the entries of the matrix the names $a$,$b$,$c$,$\dots$,$i$, and I multiplied the matrix by the given $2$ matrices. But the problem is that I have for every $3$ entries $2$ equation in $3$...
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 ...
1 vote
1 answer
2k views

Find the limit involving a Riemann sum.

Evaluate the two limits. $$ \lim_{n\to \infty} \left(\frac1n\right)^{15}\sum_{k=1}^nk^{15} \tag{1} $$ $$ \lim_{n\to \infty} \left(\frac1n\right)^{17}\sum_{k=1}^nk^{15} \tag{2}$$ can anyone please ...
2 votes
3 answers
488 views

GRE Practice Question

I need a calculus refresher! This question was one of the lowest percent correct on the practice (27%). A curve in the xy-plane is given by \begin{align*} x &= t^2+2t \\ y &= 3t^4+4t^3 \end{...
0 votes
7 answers
1k views

How to multiply decimal with wholenumber?

How Can I multiply x = (0.35)(80) x = 28 steps by step fastest way I am not going to lie, but it is time for me to take a test without using a calculator. Schools have made me worse by giving us a ...
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?
1 vote
4 answers
465 views

function that preserves compactness

Let S be a compact topological space, let T be a topological space, and let f be a function from S onto T . Which of the following conditions on f is the weakest sufficient condition to guarantee ...
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 ...
0 votes
5 answers
2k views

GRE Reasoning problem time/distance/average speed

David drove to work at an average (arithmetic mean) speed of 45 miles per hour. After work, David drove home at an average speed of 60 miles per hour. If David spent a total of 2 hours commuting to ...
1 vote
2 answers
1k views

Divisiblilty & Prime Problems [GRE]

if j is divisible by 12 and 10, is j divisible by 24? Answer by either saying yes, no , or Can't be determined. I approached this question as follow: First i found the prime factors of both ...
2 votes
3 answers
6k views

Tricky Question from GRE using Ratios

Of two kinds of alloy, silver and copper are contained in the ratio of $5:1$ and the other in $7:2$. What weights of the two alloys should be melted and mixed together so as to makeup a $5$ lb mass ...
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 ...
4 votes
5 answers
36k views

How many 3-digit positive integers are odd and do not contain digit 5?

It is a GRE question. And it has been answered here. But I still want to ask it again, just to know why I am wrong. The correct is 288. My idea is, first I get the total number of 3-digit integers ...
2 votes
4 answers
1k views

Among the following, which is closest to $\sqrt{0.016}$?

Among the following, which is closest in value to $\sqrt{0.016}$? A. $0.4$ B. $0.04$ C. $0.2$ D. $0.02$ E. $0.13$ My Approach: $(\frac{16}{1000})^\frac{1}{2} = (\frac{4}{250})^\frac{1}{2} = \...
0 votes
2 answers
335 views

GRE combination problem $877$.

A computer password must be $5$ characters long. The first character must be a capital letter. The second character must be one of eight specified symbols. Each of the fourth and fifth characters can ...
22 votes
4 answers
5k views

Counting numbers in a sequence - explain "Add $1$ before you're done" rule

I'm studying for the GRE, and my study book uses a rule that it never justifies for counting numbers in a sequence: "Add $1$ before you're done." For example, how many multiples of $3$ are between $...
2 votes
1 answer
1k views

If $A$ is a subset of the real line $\mathbb R$ and $A$ contains each rational number, which of the following must be true?

The question and its answer is given in the following picture: Subject GRE 0568 Exam Q.52 Question 52. If $A$ is a subset of the real line $\mathbb R$ and $A$ contains each rational number, ...
1 vote
3 answers
1k views

GRE Statistics Problem

Matt gets \$1000 commission on a big sale.This commission alone raises his average commission by \$150. if Matt's new average commission is $400, how many sales has Matt made? I feel this question is ...
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 ...
4 votes
3 answers
328 views

Answering a question containing $\sqrt{1.5}$ without using calculator.

Of the following which is the best approximation of $\sqrt{1.5}(266)^{\frac{3}{2}}$? (A)1,000 (B)2,700 (C)3,200 (D)4,100 (E)5,300 How can I answer this without using a calculator and in about 2....
0 votes
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 ...

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