Questions tagged [gre-exam]

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

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2 answers
72 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
1 answer
48 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 ...
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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 ...
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1 vote
3 answers
73 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
94 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?...
0 votes
0 answers
26 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 ...
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0 answers
111 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} \...
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0 answers
74 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 +...
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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 ...
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1 vote
1 answer
120 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
112 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 ...
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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 ...
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0 votes
0 answers
30 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
390 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
113 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} \...
1 vote
2 answers
250 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 ...
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 $u_{n+1}=q u_n$ ...
2 votes
2 answers
285 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 ...
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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) ...
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1 vote
2 answers
86 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?
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0 votes
2 answers
102 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, ...
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2 votes
1 answer
3k 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 ...
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0 votes
2 answers
154 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 $3$...
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0 votes
0 answers
138 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 ...
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0 votes
1 answer
75 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?
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0 votes
2 answers
63 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(...
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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 $\Bbb{R}$, ...
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1 vote
1 answer
385 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 ...
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0 votes
3 answers
253 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 ...
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3 votes
1 answer
181 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 $...
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-1 votes
2 answers
199 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?
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0 votes
2 answers
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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 ...
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0 votes
4 answers
110 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 ...
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2 votes
2 answers
126 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,...
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-1 votes
3 answers
315 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?
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-1 votes
1 answer
331 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 ?
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-2 votes
3 answers
335 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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2 votes
3 answers
5k 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 ...
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2 votes
2 answers
221 views

Using the rational root test (subject Math GRE exam 9768 Q.31)

I used the rational root test and my answer was B as -5 does not divide 9, but the correct answer is C. Could anyone clarify this for me please?
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1 vote
3 answers
130 views

Math subject GRE exam 9768 Q.30 (condition that a basis of a real vector space must satisfy)

I am sure that A,B and E are wrong, but I do not know which is right C or D, and why, could anyone help me please?
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0 votes
1 answer
397 views

Sets Whose Elements Sum to an Even Integer

From the set of integers $\{1,...,9\}$, how many nonempty subsets sum to an even integer. This is probably trivial for most, but I am notoriously bad at counting, so I just want to make sure I am ...
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1 vote
1 answer
111 views

Calculating the value of a definite integral knowing the value of the integrand and its derivative on the boundaries.

I do not know how the givens are useful in solving this question: Could anyone help me please?
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0 votes
3 answers
2k views

What is the smallest possible dimension $V_1$ intersection $V_2$ must have.

My answer was $A$ because the two vector spaces may be disjoint and hence intersection is $\{0\}$ whose dimension is zero by convention, but the correct answer is $C$. Could anyone clarify this for ...
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0 votes
1 answer
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Let $f$ be a function such that $f(x) = f(1-x)$ for all real numbers $x$. If $f$ is differentiable everywhere, then $f'(0)$

I do not know how to solve this question: Could anyone help me please?
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0 votes
3 answers
275 views

Math subject GRE test 9768 Q.26

What is the fastest way to solve this question? I checked and I found that the derivative exists at $x = 1$.
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2 votes
2 answers
158 views

Weird GRE mistake [duplicate]

According to the answer key, the correct answer is (a).... This is obviously a mistake, right? If a square matrix is invertible, then it has full rank.
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1 vote
2 answers
259 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?
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0 votes
2 answers
384 views

A basis for a subspace of Euclidean 4-space consisting of all vectors orthogonal to 2 vectors.(Math subject GRE 9768 Q.24)

The question is in the following picture: The answer is C. I know the method of finding all vectors orthogonal to a vector,but it will take a long time if I applied for 2 vectors, as I must answer ...
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0 votes
1 answer
56 views

Determining the measure of a central angle in a circle ( subject math GRE exam 9768 Q.23).

The question is given in the following picture: I know that the triangle ABC will be an isosceles triangle but I do not know how to use this knowledge in the solution, could anyone help me please ?
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