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Questions tagged [gre-exam]

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

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2answers
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Determining whether one area is greater or equal to another

This problem was in my GRE practice textbook Their answer was that the two quantities are equal, but I keep on getting a different answer. Let $\overline{BC} = y $ and $\overline{AE}=x$. Then it ...
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2answers
15 views

How many consecutive zeros to the left of the decimal does $125^{14} \times48^{8}$ have?

If $125^{14}\times48^{8}$ were expressed as an integer, how many consecutive zeros would that integer have immediately to the left of the decimal point? I tried: $$125^{14} \times 48^{8} = (1.25\...
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0answers
52 views

How to interpret GRE quantitive word questions efficiently?

I am currently studying for the GRE quantitive section and have typically done well in math courses, but unfortunately during my studies have been struggling with interpreting the questions.I'd like ...
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0answers
66 views

Gre question related to finding unknown number

If $\displaystyle\frac{x^2}{4}$ is an integer greater than 50, then what is the smallest possible value of $x^2$ ? IMO the answer should be $204$, the next small integer after $50$ is $51$, therefore,...
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1answer
55 views

How to understand this GRE question on differentiability?

Question 53 from practice test: Let f and g be continuous real functions such that $g(x) = \int_{0}^{x}f(y)(y-x)dy$. If g is 3 times continuously differentiable, what is the greatest integer n for ...
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2answers
95 views

Gre question : finding length of sides of a triangle given 1 side

Need help in understanding the solution given for the problem in textbook. Below is the question Below is the solution Option F=10 is not an answer as its given that all 3 angles are different and ...
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2answers
91 views

GRE 9367 #62: Prove $X=[0,1]$ in lower limit topology ($[a,b)$) is not compact, is Hausdorff and is disconnected.

GRE9367 #62 Ian Coley's solution: Sean Sovine's solution: Prove $X$ is not compact. My first proof was similar to Ian Coley's, but I came up with another proof: If $X$ is compact, ...
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3answers
79 views

GRE 0568 #65: Disprove 'There is a continuous one-to-one function from $(0,1)$ onto $[0,1].$'

GRE 0568 #65 This has been asked about here: Why are there no continuous one-to-one functions from (0, 1) onto [0, 1]? There are proofs by: Charles Rambo Ian Coley DM Ashura aka Bill Shillito ...
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2answers
81 views

What is the Fastest Way to Solve Systems of Equations?

What is the quickest yet systematic way to solve this question? Consider the system of linear equations: $$w + 3x + 2y +2z = 0$$ $$w + 4x + y = 0$$ $$3w + 5x + 10y + 4z = 0$$ $$2w+ 5x + 5y + 6z =...
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1answer
58 views

GRE 9768 #60 Boolean non-commutative rings: Prove $(-s)^2=s^2$ without commutativity.

GRE 9768 #60 Ian Coley's approach is to prove $(I)$ and $(I) \implies (II) \implies (III)$ In proving $(I)$, how do we prove $$(-s)^2=s^2$$ without commutativity (but with $s=s^2$, if need ...
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1answer
273 views

How do I know the definition of rings or of anything on the GRE given that definitions can vary?

How do I know the definition of rings or of anything on the GRE given that definitions can vary? :| Context is rings: GRE 0568 #66: On whether or not exactly 2 right ideals give a non-commutative ...
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1answer
87 views

GRE 9768 #60 1. Does $(s+t)^2=s^2+t^2$ imply $s+s=0$? 2. Idempotent matrices do not form a ring?

GRE 9768 #60 on what appears to be Boolean rings: Ian Coley's approach is to prove $(I)$ and $(I) \implies (II) \implies (III)$ I think $(II) \implies (I)$. My attempt: $$(s+t)^2=s^2+t^2 \...
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1answer
89 views

GRE 0568 #66: On whether or not exactly 2 right ideals give a non-commutative field (field except multiplication is not commutative)

Algebra by Michael Ch11.3 Artin has different definitions of rings particularly that his rings are unital and commutative in both addition and multiplication. Therefore, ideals are neither right nor ...
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2answers
51 views

GRE question: maximize $\int_{0}^{3}f(x)dx$

Let $f$ be a differentiable real valued function such that $f(3)=7$ and $f'(x) \geq x$ for all positive $x$. What is the maximum possible value of $$\int_{0}^{3}f(x)dx$$ The answer is 12.. so far ...
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1answer
91 views

Quadratic equation approach used in one of the gre questions

Below is one of the gre practice question which i was able to solve but could not understand why my first approach dint worked. In order to find the value of x, I used the below quadratic equation ...
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0answers
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What is the value of $F_{XY}(x,y)$?

If $X$ represents the sides of a 6-sided die, and $Y$ represents the sides of a fair coin, what would be the value of, say, $F_{XY}(3, H)$? Is it $\frac{1}{2}$? Why or why not? Note: To my ...
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1answer
50 views

Calculating time break in rate & work question [duplicate]

Working alone at their respective constant rates, Audrey can complete a certain job in 4 hours, while Ferris can do the same job in 3 hours. Audrey and Ferris worked together on the job and ...
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1answer
54 views

How does the notation of limits read in plain English? (2)

Related: How does the notation of limits read in plain English? How does the following notation read in plain English: I can't interpret it myself. $$\lim\limits_{x \to a^+} F(x, y) = F(a^+, y) = F(...
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2answers
83 views

How does the notation of limits read in plain English?

How does the following notation read in plain English: $$\lim\limits_{x \to \infty \\ y \to \infty} F(x, y) = 1$$ As far as I can read: If $x$ and $y$ approaches $\infty$, the value of ...
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0answers
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GRE probability - number of ways to select numbers in a range

Note: I am aware a solution already exists to this question on SE, but I am questioning why the approach I am using here is incorrect / incomplete. The only contents of a container are 10 disks ...
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1answer
52 views

Parabola-GRE doubt

How can one interpret just by seeing the equation of parabola that it opens UP/DOWN and or centered around $x$- or $y$-axis. I know parabola equation as $ax^2+bx+c$, I know that it opens up when $a&...
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1answer
37 views

Simple yet apparently not GRE quant problem

I am struggling with reconciling the fact that all the middle lines are the same length with the fact that the angles aren't the same.
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1answer
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$u$-substitution failure

I'm practicing for the GRE exam, and came across the following question: If $$ f(x) = \int_x^0 \frac{\cos(xt)}{t}\, dt, $$ find $f'(x)$. The answer given is $\frac{1}{x}(1 - 2\cos(x^2))$, and I see ...
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4answers
321 views

Find the sum of the First $50$ Natural Numbers starting from $11$. Is it from $11-50$ or $11-60$?

This a simple question yet confusing for me, I found the answer as 1220 by taking sum from $11$ to $50$, by inferring the question as first 50 natural numbers {$1,2,3,4,5,6,7,8,9,10,11,...49,50$} ...
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4answers
144 views

A student is given an exam consisting of 8 essay questions divided into 4 groups of 2 questions each.

From ETS Major Field Test in Mathematics A student is given an exam consisting of 8 essay questions divided into 4 groups of 2 questions each. The student is required to select a set of 6 ...
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2answers
123 views

Sum of $\frac{1}{1 \cdot 2} + \frac{1}{3\cdot 4} + \cdots$

I am practicing for the GRE, and came across the following question: Find the sum $$ \frac{1}{1 \cdot 2} + \frac{1}{3\cdot 4} + \frac{1}{5\cdot 6}\cdots. $$ The answer is given to be $\log(2)$, with ...
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2answers
196 views

If a = 3 + b, which of the following is true? [closed]

See: Nova GRE Math Bible. Page-$234$. Problem #06 If a = 3 + b, which of the following is true? (I) a > b + 2.5 (II) a < b + 2.5 (III) a > 2 + b (A) I only (B) II ...
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2answers
67 views

What are the main points to remember to solve these kinds of problems? [closed]

Problem #$1$ If $ab>0$, then which one of the following must be true? $(A)$ $a/b>0 $ $(B)$ $a-b>0 $ $(C)$ $a+b>0 $ $(D)$ $b-a>0 $ $(E)$ $a+b<0 $ Problem #$2$ ...
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0answers
267 views

Mathematics GRE subject test Prerequisites

I looked at the Mathematics GRE subject test's website and it says the material covered is 50 % Calculus, 25 % Algebra, 25 % Additional Topics. I have taken two semesters of real analysis, abstract ...
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3answers
91 views

If (x+1)^2 - 2x>2(x+1) +2, then x cannot equal which of the following?

See: Nova GRE Math Bible. Page-$235$. Problem #$10$. If $(x+1)^2 - 2x>2(x+1) +2$, then $x$ cannot equal which of the following? (A) $-5$ (B) $-3$ (C) $0$ (D) $3$ (E) $5$ $(x+1)^2 - ...
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2answers
56 views

If $x+3$ is positive, then which one of the following must be positive?

See: Nova GRE Math Bible. Page-$235$. Problem#$09$ If $x+3$ is positive, then which one of the following must be positive? (A) $x-3$ (B) $(x-3)(x-4)$ (C) $(x-3)(x+3)$ (D) $(x-3)(x+4)$ ...
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1answer
31 views

Alternative resolution to find a ratio from averages.

Problem: A club sold an average(arithmetic mean) of 92 raffle tickets per number. Among the female members, average number sold was 84, and among the male members, the average number sold was 96. What ...
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3answers
60 views

How many cases on a GRE question

This is more or less a question about how many cases I should be trying in general on the quantitative section of the GRE. I got this question wrong and it is because I did not try enough cases, so ...
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4answers
84 views

Counting: A committee made of men and women (GRE question)

In how many ways can a committee of $5$ members be formed from $4$ women and $6$ men such that at least $1$ woman is a member of the committee. I know that the correct answer is: $\binom{10}{5} - \...
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2answers
250 views

How many $5$-digit positive even numbers can be formed by using all of the digits $1$, $2$, $3$ and $6$?

The $5$-digit numbers must be even and positive. All the digits $1$, $2$, $3$ and $6$ must be used in each number formed. In how many ways can a $5$-digit positive even number be formed by using all ...
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3answers
91 views

Is this a valid random variable?

As I know it, A Random Variable is a variable which represents the outcome of a random experiment. Is this correct? . According to the above definition, the following is not a Random ...
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1answer
34 views

Why doesn't this problem fall under the category of Total Probability?

A box contains $6$ white balls and $4$ red balls. We randomly (and without replacement) draw $2$ balls from the box. What is the probability that the second ball selected is red? I know this is a ...
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1answer
248 views

Can I solve the following problem with the Law of Total Probability?

According to this link, (...) Usually, in the elementary exercises in probability texts, there would be 2 such sub-experiments, one followed by the other. You would have to compute the ...
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2answers
70 views

Find the probability that the maximum of the two numbers is greater than $4$.

My attempted solution: $E=\{(1,5), (2,5), (3,5), (4,5), (5,5), (6,5),$ $(1,6), (2,6), (3,6), (4,6), (5,6), (6,6),$ $(5,1), (5,2), (5,3), (5,4), (5,6),$ $(6,1), (6,2), (6,3), (6,4), (6,5)\}$ ...
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2answers
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What is the probability that a specific element is always present?

My attempted solution: Since $A$ can be chosen in only $1$ way from $10$, and rest of the two in $9$ and $8$ respectively, $P(A$ belongs to the committee$) = \frac{1 \cdot 9 \cdot 8}{^{10}C_3} = \...
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2answers
58 views

What does it mean by “odds that an event will occur is $2$ to $3$”?

What does it mean by odds that an event will occur is $2$ to $3$?
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1answer
666 views

A die is weighted so that each even number is twice as likely to appear as any odd number.

My attempted solution of $(ii)$ $P($an odd number$) = \frac{1}{9}$ $P($an even number$) = \frac{2}{9}$ $P($all prime numbers$)=P(1, 2, 3, 5) = (\frac{1}{9}+\frac{2}{9}+\frac{1}{9}+\frac{1}{9}) = \...
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2answers
53 views

equivalent integral results for subj GRE

I am currently revising for the math subject GRE and when I check my work against Wolfram Alpha and https://www.integral-calculator.com, my solution is (almost) always of the latter form rather than ...
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1answer
35 views

How can I solve the problems of Combination + indistinguishable objects + repetition allowed? [duplicate]

Can I solve the problems of Combination with indistinguishable objects plus repetition allowed using a formula? For instance, How many $3$-letter combinations could be formed from the word $BBA$ ...
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3answers
150 views

What is the formula for Combination with indistinguishable objects?

Take a look at the following question, There is a group of $10$ objects, $2$ red, $3$ blue, and $5$ green. The objects are indistinguishable. In how many ways they can be arranged on a line? ...
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2answers
471 views

What is the formula for Combination with repetition?

What is the number of ways we can choose three letters from $\{A,B,...,Z\}$ if repetition is allowed? This is not a permutation. Is there any formula to solve this kind of problems?
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3answers
31 views

Why is the average rate isn't the average of the two rates given for the two legs of the journey?

If an object moves the same distance twice, but at different rates, then the average rate will never be an average of the two rates given for the two legs of the journey. Why is that so?
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2answers
123 views

Catch-up problems in Rate, Time, Distance (RTD) category.

Car-X is $40$-miles West of Car-Y. Both cars are traveling East, and Car-$X$ is going $50$% faster than Car-$Y$. If both cars travel at a constant rate, and it takes Car-$X$ $2$ hours and $40$ minutes ...
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1answer
113 views

(GRE) How to best determine standard deviation from frequency distribution

The full question asks whether $s_A > s_B$, $s_A < s_B$, $s_A = s_B$, or it is impossible to determine. By doing hand calculations, I found that $s_A\approx 13.8$ and $s_B\approx 16.45$. Is ...
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5answers
74 views

If $x>y$, is $|x+y|$ or $|x-y|$ bigger, or neither? [closed]

Question: If $x>y$, is $|x+y|$ or $|x-y|$ bigger, or neither? I got this question wrong on a GRE practice test, and now I know the correct answer, but I am curious what your thought process is for ...