GRE 8768 Questions: 58 and 60
Posted: Thu Nov 06, 2008 6:31 pm
I just finished taking the GRE 8767 under a time limit and did rather well but would like to go over some of the problems I got wrong.
Question 58
If f(z) is an analytic function that maps the entire finite complex plane to the real line, then the imaginary axis must be mapped onto?
A) Entire Real Axis
B) A point
C) A ray
D) An open interval
E) The empty set
Answer is B, I guessed A
So my incorrect logic was considering e^x which does not satisfy all the conditions. Whats an easy way to see that it must be mapped to a point? Is the function a+bi -> a , an analytic function?
Question 60
A fair die is rolled 360 times. The probability that 6 comes up on 70 or more rolls is?
A) Greater then .5
B) Between .16 and .5
C) Between .02 and .16
D) Between .01 and .02
E) Lower then .01
Answer C, Guessed B
Firstly I ignored the 0 and was trying to find the probability of 7+ six's on 36 rolls. The best way I found out how to find the probability was to:
(36C7 + 36C8 + 36C9 + 36C10 + 36C11 + 36C12 + 36C13...) / 6^36
But I didnt want to spend my time trying to figure this out by brute force. What is a better way to find this? I just realized I could find the probability of rolling 6 or lower six's, though that still seems like alot of calculation.
After reading a bit about it apparently there is an approximation method though it looks a little time consuming.
Question 58
If f(z) is an analytic function that maps the entire finite complex plane to the real line, then the imaginary axis must be mapped onto?
A) Entire Real Axis
B) A point
C) A ray
D) An open interval
E) The empty set
Answer is B, I guessed A
So my incorrect logic was considering e^x which does not satisfy all the conditions. Whats an easy way to see that it must be mapped to a point? Is the function a+bi -> a , an analytic function?
Question 60
A fair die is rolled 360 times. The probability that 6 comes up on 70 or more rolls is?
A) Greater then .5
B) Between .16 and .5
C) Between .02 and .16
D) Between .01 and .02
E) Lower then .01
Answer C, Guessed B
Firstly I ignored the 0 and was trying to find the probability of 7+ six's on 36 rolls. The best way I found out how to find the probability was to:
(36C7 + 36C8 + 36C9 + 36C10 + 36C11 + 36C12 + 36C13...) / 6^36
But I didnt want to spend my time trying to figure this out by brute force. What is a better way to find this? I just realized I could find the probability of rolling 6 or lower six's, though that still seems like alot of calculation.
After reading a bit about it apparently there is an approximation method though it looks a little time consuming.