Questions tagged [gre-exam]
For questions relevant to the general or subject-specific Graduate Record Examination, abbreviated GRE.
0
votes
2answers
20 views
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 ...
0
votes
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\...
0
votes
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 ...
3
votes
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,...
1
vote
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 ...
0
votes
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 ...
1
vote
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, ...
0
votes
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
...
0
votes
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 =...
2
votes
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 ...
0
votes
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 ...
2
votes
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:
$$(s+t)^2=s^2+t^2 \...
1
vote
1answer
89 views
GRE 0568 #66: On whether or not exactly 2 right ideals give a non-commutative field (field except multiplication is not commutative)
Algebra by Michael Ch11.3
Artin has different definitions of rings particularly that his rings are unital and commutative in both addition and multiplication. Therefore, ideals are neither right nor ...
1
vote
2answers
51 views
GRE question: maximize $\int_{0}^{3}f(x)dx$
Let $f$ be a differentiable real valued function such that $f(3)=7$ and $f'(x) \geq x$ for all positive $x$. What is the maximum possible value of $$\int_{0}^{3}f(x)dx$$
The answer is 12.. so far ...
1
vote
1answer
91 views
Quadratic equation approach used in one of the gre questions
Below is one of the gre practice question which i was able to solve but could not understand why my first approach dint worked.
In order to find the value of x, I used the below quadratic equation ...
1
vote
0answers
32 views
What is the value of $F_{XY}(x,y)$?
If $X$ represents the sides of a 6-sided die, and $Y$ represents the sides of a fair coin, what would be the value of, say, $F_{XY}(3, H)$?
Is it $\frac{1}{2}$? Why or why not?
Note: To my ...
-1
votes
1answer
50 views
Calculating time break in rate & work question [duplicate]
Working alone at their respective constant rates, Audrey can complete
a certain job in 4 hours, while Ferris can do the same job in 3 hours.
Audrey and Ferris worked together on the job and ...
0
votes
1answer
54 views
How does the notation of limits read in plain English? (2)
Related: How does the notation of limits read in plain English?
How does the following notation read in plain English:
I can't interpret it myself.
$$\lim\limits_{x \to a^+} F(x, y) = F(a^+, y) = F(...
0
votes
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 ...
1
vote
0answers
71 views
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 ...
-1
votes
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&...
0
votes
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.
6
votes
1answer
75 views
$u$-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 ...
2
votes
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 {$1,2,3,4,5,6,7,8,9,10,11,...49,50$}
...
4
votes
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 ...
1
vote
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 ...
0
votes
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 ...
-2
votes
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 #$2$
...
2
votes
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 ...
-1
votes
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 - ...
0
votes
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) $(x-3)(x+4)$
...
1
vote
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 ...
0
votes
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 ...
2
votes
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} - \...
0
votes
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 ...
-1
votes
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 ...
0
votes
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 ...
1
vote
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 ...
0
votes
2answers
70 views
Find the probability that the maximum of the two numbers is greater than $4$.
My attempted solution:
$E=\{(1,5), (2,5), (3,5), (4,5), (5,5), (6,5),$
$(1,6), (2,6), (3,6), (4,6), (5,6), (6,6),$
$(5,1), (5,2), (5,3), (5,4), (5,6),$
$(6,1), (6,2), (6,3), (6,4), (6,5)\}$
...
0
votes
2answers
21 views
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} = \...
3
votes
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 $3$?
1
vote
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}) = \...
0
votes
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 ...
-1
votes
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 $BBA$ ...
-1
votes
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?
...
1
vote
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?
0
votes
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?
0
votes
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 ...
0
votes
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 ...
-1
votes
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 ...
