## A couple questions from today's test

Forum for the GRE subject test in mathematics.
26186514
Posts: 24
Joined: Sat Sep 22, 2012 4:34 pm

### A couple questions from today's test

Questions removed...
Thought I was doing a nice thing, but it's not allowed...
Last edited by 26186514 on Sun Oct 14, 2012 12:25 am, edited 1 time in total.

Posts: 90
Joined: Sat Oct 13, 2012 11:12 am

### Re: A couple questions from today's test

dumplinghao123 wrote:1. (This is actually the last question of the test.)
Q: Z17 is the modular 17 ring. Consider the group of all the invertible elements under multiplication. Which of the following is the generator of such group?
I.5
II.8
III.16
A: I thought they all are (at the test). But the correct answer is 5 only. Could refer to this wiki link for generators:
http://en.wikipedia.org/wiki/Multiplica ... s_modulo_n

2. There is a tank with salty water. The total volume is 100 liter, and 3 grams of salt was initially there. Now pour in the water with 0.02 per liter salty water with speed of 4 liters per minute. Assuming the salt and water mix instantly, and also pouring out the water at 4 liters per minute. In 100 minutes, how many grams of salt are there in this tank?
A: Set the function for salt is f(t). df/dt = 0.08-4*f(t)/100.
Solving this ODE by multiplying e^0.04t.
d(e^0.04t*f)=d(2*e^0.04t)
e^0.04t*f=2*e^0.04t+c
f=2+c/e^0.04t
at t=0, f=3, solve for c, get c=1
thus at t=100, f=2+e^0.04t

3.
Q: There is a line in 3-D space with the following expression:
x=5*cos(t)
y=5*sin(t)
z=t
If there is a point from which to (5,0,0) the length is 26. What’s the distance from this point to the origin?
A: dr = sqrt(26)*dt, so solve it, and get t = -sqrt(26), so the point is sqrt(25+26)=sqrt(51).

4.
Asking for a plane that’s orthogonal to both of the planes.

5.
Giving a matrix, asking the orthonormal basis of the column space.

6.
Q: How many spanning trees are there for 5 vertices under to isormorphism?

I will post more if I could remember...
Wow, it seems that we did not take the same exam! Are you based in China?

etcetera
Posts: 1
Joined: Sat Oct 13, 2012 9:25 pm

### Re: A couple questions from today's test

Yeah, I instinctively assumed Z17 was of prime order as well.

And I had the same test and am the US.

26186514
Posts: 24
Joined: Sat Sep 22, 2012 4:34 pm

### Re: A couple questions from today's test

dumplinghao123 wrote:1. (This is actually the last question of the test.)
Q: Z17 is the modular 17 ring. Consider the group of all the invertible elements under multiplication. Which of the following is the generator of such group?
I.5
II.8
III.16
A: I thought they all are (at the test). But the correct answer is 5 only. Could refer to this wiki link for generators:
http://en.wikipedia.org/wiki/Multiplica ... s_modulo_n

2. There is a tank with salty water. The total volume is 100 liter, and 3 grams of salt was initially there. Now pour in the water with 0.02 per liter salty water with speed of 4 liters per minute. Assuming the salt and water mix instantly, and also pouring out the water at 4 liters per minute. In 100 minutes, how many grams of salt are there in this tank?
A: Set the function for salt is f(t). df/dt = 0.08-4*f(t)/100.
Solving this ODE by multiplying e^0.04t.
d(e^0.04t*f)=d(2*e^0.04t)
e^0.04t*f=2*e^0.04t+c
f=2+c/e^0.04t
at t=0, f=3, solve for c, get c=1
thus at t=100, f=2+e^0.04t

3.
Q: There is a line in 3-D space with the following expression:
x=5*cos(t)
y=5*sin(t)
z=t
If there is a point from which to (5,0,0) the length is 26. What’s the distance from this point to the origin?
A: dr = sqrt(26)*dt, so solve it, and get t = -sqrt(26), so the point is sqrt(25+26)=sqrt(51).

4.
Asking for a plane that’s orthogonal to both of the planes.

5.
Giving a matrix, asking the orthonormal basis of the column space.

6.
Q: How many spanning trees are there for 5 vertices under to isormorphism?

I will post more if I could remember...
Wow, it seems that we did not take the same exam! Are you based in China?

No, I am in US. What you got? How was your questions, are they difficult?

26186514
Posts: 24
Joined: Sat Sep 22, 2012 4:34 pm

### Re: A couple questions from today's test

etcetera wrote:Yeah, I instinctively assumed Z17 was of prime order as well.

And I had the same test and am the US.
How did you do?
Ah, I keep thinking about the test, lol.
I can't wait to know how I did... Hope that wasn't as bad as I thought.

Posts: 90
Joined: Sat Oct 13, 2012 11:12 am

### Re: A couple questions from today's test

dumplinghao123 wrote:
dumplinghao123 wrote:1. (This is actually the last question of the test.)
Q: Z17 is the modular 17 ring. Consider the group of all the invertible elements under multiplication. Which of the following is the generator of such group?
I.5
II.8
III.16
A: I thought they all are (at the test). But the correct answer is 5 only. Could refer to this wiki link for generators:
http://en.wikipedia.org/wiki/Multiplica ... s_modulo_n

2. There is a tank with salty water. The total volume is 100 liter, and 3 grams of salt was initially there. Now pour in the water with 0.02 per liter salty water with speed of 4 liters per minute. Assuming the salt and water mix instantly, and also pouring out the water at 4 liters per minute. In 100 minutes, how many grams of salt are there in this tank?
A: Set the function for salt is f(t). df/dt = 0.08-4*f(t)/100.
Solving this ODE by multiplying e^0.04t.
d(e^0.04t*f)=d(2*e^0.04t)
e^0.04t*f=2*e^0.04t+c
f=2+c/e^0.04t
at t=0, f=3, solve for c, get c=1
thus at t=100, f=2+e^0.04t

3.
Q: There is a line in 3-D space with the following expression:
x=5*cos(t)
y=5*sin(t)
z=t
If there is a point from which to (5,0,0) the length is 26. What’s the distance from this point to the origin?
A: dr = sqrt(26)*dt, so solve it, and get t = -sqrt(26), so the point is sqrt(25+26)=sqrt(51).

4.
Asking for a plane that’s orthogonal to both of the planes.

5.
Giving a matrix, asking the orthonormal basis of the column space.

6.
Q: How many spanning trees are there for 5 vertices under to isormorphism?

I will post more if I could remember...
Wow, it seems that we did not take the same exam! Are you based in China?

No, I am in US. What you got? How was your questions, are they difficult?
I believe that I can't post the questions online but yeah, it's different. I'm based in Asia so I guess I took the exam a little bit earlier than you. But it is indeed different from what I had. Well, the differential equation problem I got is much more difficult than the one you posted...

Legendre
Posts: 217
Joined: Wed Jun 03, 2009 1:05 am

### Re: A couple questions from today's test

We aren't supposed to reveal test questions. I am in south east asia and none of your questions appeared in my test. Mine had questions asking about things which I didn't know was part of the syllabus!

Gelor
Posts: 5
Joined: Tue Sep 18, 2012 7:35 am

### Re: A couple questions from today's test

Yes, it seems it's not the twst i've taken yesterday.
I wonder if they diversify tasks because of time zones. I mean when the test begins in one part of the world it has already ended in another so there would be a slight possibility of cheating.