I was trying to help my sister study for the SATs and I came across two problems that i didn't know how to do. Here they are:
Consider a positive odd integer n. Let X = twice the number of factors of n, and let Y = the number of factors of 2n. Which of the following must be true?
A)X = 4
B)X > Y
C)Y > X
D)X = Y
E)There is not enough information to solve the problem
Let the expectal(x) be defined for all x as the smallest prime number that is greater than x/2. What is the value of:
expectal(8.1)expectal(5.2)
Thanks in advance!!
Well let n have r factors these are all odd, so each of these is a factor of 2n, and so is 2 times any of them and these are different from any of the factors of n, so Y>=X.
Now all the factors of 2n are or the form f, where f is a factor of n, or 2f, where again f is a factor of n (since n is odd) So X>=Y
Together these twi inequalities imply that X=Y.
RonL
The first skill is dividing by 2.Let the expectal(x) be defined for all x as the smallest prime number that is greater than x/2. What is the value of:
expectal(8.1)expectal(5.2)
8.1/2 = 4.05
5.2/2 = 2.6
The next skill is identifying prime numbers.
8.1/2 = 4.05 ==> 5
5.2/2 = 2.6 ==> 3
Now what?