ACT Math : How to multiply even numbers

Example Questions

Example Question #1 : How To Multiply Even Numbers

is even

is even

Therefore, which of the following must be true about ?

It must be even.

It must be odd.

It could be either even or odd.

It could be either even or odd.

Explanation:

Recall that when you multiply by an even number, you get an even product.

Therefore, we know the following from the first statement:

is even or  is even or both  and  are even.

For the second, we know this:

Since  is even, therefore,  can be either even or odd. (Regardless of what it is, we can get an even value for .)

Based on all this data, we can tell nothing necessarily about . If  is even, then  is even, even if  is odd. However, if  is odd while  is even, then  will be even.

Example Question #2 : How To Multiply Even Numbers

In a group of philosophers,  are followers of Durandus. Twice that number are followers of Ockham. Four times the number of followers of Ockham are followers of Aquinas. One sixth of the number of followers of Aquinas are followers of Scotus. How many total philosophers are in the group?

Explanation:

In a group of philosophers,  are followers of Durandus. Twice that number are followers of Ockham. Four times the number of followers of Ockham are followers of Aquinas. One sixth of the number of followers of Aquinas are followers of Scotus. How many total philosophers are in the group?

To start, let's calculate the total philosophers:

Ockham:  * <Number following Durandus>, or

Aquinas:  * <Number following Ockham>, or

Scotus:  divided by , or

Therefore, the total number is:

Example Question #3 : How To Multiply Even Numbers

Explanation:

We know that when you multiply any integer by an even number, the result is even. Thus, if  is odd but when you multiply this by  the number  is even, we know that  must be even. You cannot say anything about the sign value of any of the numbers. Likewise, it is impossible for either  or  to be even.

Example Question #4 : How To Multiply Even Numbers

The product of three consecutive nonzero integers is taken. Which statement must be true?

Explanation:

Three consecutive integers will include at least one, and possibly two, even integers. Since the addition of even a single even integer to a chain of integer products will make the final product even, we know the product must be even.

Example Question #1 : How To Multiply Even Numbers

Which of the following integers has an even integer value for all positive integers  and ?