2 problems

• Jul 30th 2008, 09:39 AM
PensFan10
2 problems
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)

• Jul 30th 2008, 10:05 AM
Quick
Quote:

Originally Posted by PensFan10
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

The answer is D)X = Y

When you multiply an odd number by two, the number of it's factors doubles (Surprised)

Try a few examples and you should see why.
• Jul 30th 2008, 10:06 AM
CaptainBlack
Quote:

Originally Posted by PensFan10
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!!

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
• Jul 30th 2008, 10:08 AM
TKHunny
Quote:

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)
The first skill is dividing by 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?
• Jul 30th 2008, 10:09 AM
CaptainBlack
Quote:

Originally Posted by PensFan10
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)

What is the smallest prime graeter than 4.05?

And the smallest prime greater than 2.6?

RonL
• Jul 30th 2008, 11:44 AM
PensFan10
Okay
Thanks for all the help. It all makes sense now :D