PSAT Math - How to add odd numbers

1

Solve:

2

You are given that are all positive integers. Also, you are given that:

You are given that is odd, but you are not told whether is even or odd. What can you tell about whether the values of the other four variables are even or odd?

3

, , , and are positive integers.

is odd.

Which of the following is possible?

I) Exactly two of $\left { A, B,C, D\right }$ are odd.

II) Exactly three of $\left { A, B,C, D\right }$ are odd.

III) All four of $\left { A, B,C, D\right }$ are odd.

4

$\dpi{100} p+r=20$ , where $\dpi{100} p$ and $\dpi{100} r$ are distinct positive integers. Which of the following could be values of $\dpi{100} p$ and $\dpi{100} r$ ?

5

You are given that are all positive integers. Also, you are given that:

is an odd number. can be even or odd. What is known about the odd/even status of the other four numbers?

6

You are given that are all positive integers. Also, you are given that:

$A+ B^{2}= C$

$A+ C^{3}= D$

$A+ D^{4}= E$

$A+E^{5}= F$

is an odd number. can be even or odd. What is known about the odd/even status of the other four numbers?

7

At a certain high school, everyone must take either Latin or Greek. There are more students taking Latin than there are students taking Greek. If there are students taking Greek, how many total students are there?