Questions tagged [gre-exam]

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

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Multivariate Chain Rule Question from GRE September 2023 Practice Test - Question 45

This question comes from the recently-released GRE Math Subject Test Form GR3768. The question is as follows: Let $u(x,y)$ and $v(x,y)$ be real-valued differentiable functions that are implicitly ...
Stamp's user avatar
  • 399
3 votes
2 answers
126 views

Given $a,b,c \in \mathbb{R}$, and $x,y,z \in \mathbb{R}$, with $x,y,z$ not all zero. Find $a^2+b^2+c^2+2abc$

This question is to be solved in about $3$ minutes, without a calculator. Let $a,b,c$ be any real numbers. Suppose that $x,y,z$ are real numbers, not all simultaneously zero, such that $$x=cy+bz$$ $$...
Hussain-Alqatari's user avatar
1 vote
4 answers
115 views

Calculate expected number of heads in 10+$\xi$ coin tosses (GRE problem)

This is a problem from a preparatory GRE preparatory GRE test made by guys form University of Chicago. Problem: A man flips $10$ coins. With $H$ the number of heads, and $T$ the number of tails, the ...
Haldot's user avatar
  • 771
15 votes
6 answers
709 views

About $I(a,b)=\int_{a}^{b}\sqrt{1+x+x^2+x^3+x^4}\text{ d}x$

The following is an MCQ question, one should answer it without a calculator, within $3$ minutes. Consider the expression $$I(a,b)=\int_{a}^{b}\sqrt{1+x+x^2+x^3+x^4}\text{ d}x.$$ Which of the ...
Hussain-Alqatari's user avatar
0 votes
1 answer
126 views

If you need 3:2:1 ratio of X,Y,Z to make a something, doesn't that mean you need 6 units:4 units:2 units to make two units of that thing?

Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing. If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of ...
user avatar
12 votes
2 answers
879 views

Is there a mistake in a GRE preparation book?

Preface: I am preparing for the GRE Math subject test, and one of the books that I use is this one by Charles Rambo. I have currently been solving through the “Linear Algebra #1” section of the book, ...
o.spectrum's user avatar
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2 votes
1 answer
120 views

Why did my subtraction/addition manipulation of the answer choices of the work?

A buzzer sounds every $15$ minutes. If the buzzer sounded at $12:40$PM, which of the following could be a time at which the buzzer sounded? A. $4:05$ B. $5:30$ C. $6:45$ D. $7:15$ E. $8:10$ I chose E. ...
user avatar
0 votes
1 answer
55 views

Why does 1950/20 approximately equals 100 implies A and B are eliminated first?

Rachel needs to type up her 1950-word paper by its 5 pm deadline. If she starts at least two hours in advance, her typing speed will be a constant 20 words per minute, but for every two minutes beyond ...
user avatar
4 votes
2 answers
145 views

Possible values of c in the polynomial $x^3+ax^2+bx+c$.

I'm studying for a GRE and this is a question from an old test: Let $p(x)$ be the polynomial $x^3+ax^2+bx+c$, where $a,b,$ and $c$ are real constants. If $p(-3)=p(2)=0$ and $p'(-3)<0$, which of the ...
Ty Perkins's user avatar
1 vote
2 answers
96 views

In a division, why is every common divisor of the divisor and the remainder also a divisor of the dividend? [duplicate]

In the GRE quantitative reasoning exam, I came across the following question: when the positive integer $n$ is divided by $45$, the remainder is $18$. Which of the following must be a divisor of $n$? ...
YOONES MAHDIAN's user avatar
0 votes
0 answers
105 views

What is the largest order of an element in the group of permutations of $n$ objects?

I have a very little knowledge in abstract algebra and want to know what does the problem actually mean. I encountered this question in the official test $\text{Graduate Record Examination - Math ...
Hussain-Alqatari's user avatar
0 votes
2 answers
99 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 ...
jacobian16241's user avatar
0 votes
1 answer
119 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 ...
user8083's user avatar
  • 131
0 votes
1 answer
63 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 ...
user8083's user avatar
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1 vote
3 answers
130 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 ...
Hussain-Alqatari's user avatar
4 votes
0 answers
147 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?...
Hussain-Alqatari's user avatar
1 vote
0 answers
37 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 ...
Hongbo Wang's user avatar
0 votes
0 answers
129 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} \...
Hussain-Alqatari's user avatar
0 votes
0 answers
93 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 +...
homosapien's user avatar
  • 4,173
0 votes
0 answers
36 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 ...
user8083's user avatar
  • 131
1 vote
1 answer
149 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 ...
Dimension Entangled's user avatar
3 votes
1 answer
212 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 ...
Brain's user avatar
  • 1,003
0 votes
1 answer
68 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 ...
subrosar's user avatar
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0 votes
0 answers
44 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 ...
Hussain-Alqatari's user avatar
2 votes
1 answer
767 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) $e-1$ (...
Hussain-Alqatari's user avatar
1 vote
1 answer
228 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; $\dim(V)=2, \dim(W)=2, n=3$) $V$ ...
Hussain-Alqatari's user avatar
1 vote
1 answer
45 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} \...
Hussain-Alqatari's user avatar
1 vote
2 answers
292 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 ...
Hussain-Alqatari's user avatar
0 votes
2 answers
140 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 $u_{n+1}=q u_n$ ...
zeraoulia rafik's user avatar
2 votes
2 answers
328 views

Preimage of Closed Set Under a Continuous Map Isn't Closed?

Problem: In the $xy$-plane, the graph of $x^{\log y} = y^{\log x}$ is (A) Empty (B) A single point (C) A ray in the open first quadrant (D) A closed curve (E) The open first quadrant Here is ...
user193319's user avatar
  • 7,950
2 votes
2 answers
1k views

Integral of the Product of a Function and Its Derivative

Problem: Let $f$ be a function such that the graph of $f$ is a semicircle $S$ with end points $(a,0)$ and $(b,0)$, where $a < b$. The improper integral $\int_{a}^{b} f(x) f'(x) dx$ is (A) ...
user193319's user avatar
  • 7,950
1 vote
2 answers
98 views

For what values of t does the eigenvalues $\lambda_1$,$\lambda_2$ has the value $\lambda_1$+$\lambda_2$ = 1.

Do not know how to solve it, could anyone help me please?
Emptymind's user avatar
  • 2,039
0 votes
2 answers
134 views

Determining the number of gallons of fuel that the car used on the trip.

My answer was (C), where I was thinking while I was solving how the unit could be Gallons only, but the correct answer is (A), I do not know why my answer is wrong and why (A) is the correct answer, ...
Emptymind's user avatar
  • 2,039
2 votes
1 answer
4k views

Is this Enough for the Math Subject GRE? [closed]

I have been studying for the math GRE for quite sometime now. I have been going through the princeton review and old GRE tests, and in fact without much very difficulty at all. As a way of getting ...
user193319's user avatar
  • 7,950
0 votes
2 answers
235 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 $3$...
Emptymind's user avatar
  • 2,039
0 votes
0 answers
166 views

Does the math subject GRE exam contains a graph paper and a calculator or no.

I know that the math subject GRE exam is a paper based test, but does this paper contains a graph paper? I also have read(not sure from the source) that calculators are not allowed on this test, even ...
Emptymind's user avatar
  • 2,039
0 votes
1 answer
98 views

Knowing 3 points of a figure, the fourth point can take how many values so that the given figure form a parallelogram. (GRE exam 9768 Q.42)

I do not know how to solve it, could anyone give me a hint? or tell me if this question How to test whether a set of four points can form a parallelogram is useful in the solution or irrelevant?
Emptymind's user avatar
  • 2,039
0 votes
2 answers
96 views

Determining the relative maximum of a 2 variable function in less than 2.5 minuites.(GRE Exam 9768 Q.41)

I know that I have to calculate the gradient of $f$, equate it to zero to find the critical points, calculate A,B,C,$\vartriangle$, then if $\vartriangle$ < 0 & A < 0 then f has relative(...
Emptymind's user avatar
  • 2,039
3 votes
2 answers
2k views

Closure in the Discrete Topology

If $\tau$ is the discrete topology on the real numbers, find the closure of $(a,b)$ Here is the solution from the back of my book: Since the discrete topology contains all subsets of $\Bbb{R}$, ...
user193319's user avatar
  • 7,950
1 vote
1 answer
432 views

Cauchy Number of a Permutation

Find the Cauchy number for the permutation $(1354)(267)$. I did a google search on the definition of a Cauchy number, but nothing really came up. This is the best I could find, but it is rather ...
user193319's user avatar
  • 7,950
0 votes
3 answers
311 views

Calculating the probability that more of a fair coin tosses will result in heads than in tails.

My thought was the probability is: $\frac{5}{8} + \frac{6}{8} + \frac{7}{8} + 1$ and the sum is $\frac{13}{4}$ but this is not one of the choices. and the correct answer is E. I do not know why my ...
Emptymind's user avatar
  • 2,039
3 votes
1 answer
211 views

Domain of the Function Defined in Terms of a Series

The domain of the function $f(x) = \int (x+2x^2 + 3x^3 + ...)dx$ is... I just want to find out whether the method I used to arrive at the solution is valid. In finding the domain, I first noted that $...
user193319's user avatar
  • 7,950
-1 votes
2 answers
266 views

The greatest value of Riemann sum and integral of a function on the interval [0,10]

My answer was D, but the correct answer is B, I do not no why my answer is wrong and why B is the correct answer and why other answers are wrong. Could anyone explain this for me?
Emptymind's user avatar
  • 2,039
0 votes
2 answers
2k 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 ...
user193319's user avatar
  • 7,950
0 votes
4 answers
117 views

How can I solve this question without using calculator and in only 2.5 minuites.

This is a math subject GRE exam question, that I know how to solve but in more than 2.5 minuets and using a calculator, may be there is some intuition for solving this question that I do not know that ...
Emptymind's user avatar
  • 2,039
2 votes
2 answers
140 views

Solution to Integral Equation

Which of the following is a solution of $u(x) = x + \int_{0}^{x} (t-x)u(t)dt$?? (A) $\sin x$ (B) $x \cos x$ (C) $\ln (x+1)$ (D) $x e^{-x}$ (E) $xe^x$ Since all of the choices are twice differentiable,...
user193319's user avatar
  • 7,950
-1 votes
3 answers
440 views

For how many values of $x$ are the median and the mean are equal? [closed]

I know how to calculate the mean and the median, but I do not know how to solve this. Could anyone help me please?
Emptymind's user avatar
  • 2,039
-1 votes
1 answer
434 views

Calculating the equation of the plane tangent to a given surface in xyz space. [closed]

The solution is written below and I understood all the solution until saying that the value of z is 1, but I do not understand the rest, why z + x = 1, could anyone clarify this for me please ?
Emptymind's user avatar
  • 2,039
-2 votes
3 answers
389 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?
Emptymind's user avatar
  • 2,039
2 votes
3 answers
6k views

Number of integers between 1 and 1000 that are divisible by 30 but not divisible by 16.

I know that the number of integers between 1 and 1000 that are divisible by 30 is 33, and the number of integers between 1 and 1000 that are divisible by 16 is 62, but I do not know how to calculate ...
Emptymind's user avatar
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