How to multiply even numbers - ACT Math
Card 0 of 45
Which of the following integers has an even integer value for all positive integers 
and 
?
Which of the following integers has an even integer value for all positive integers
There are certain patterns that can be used to predict whether the product or sum of numbers will be odd or even. The sum of two odd numbers is always even, as is the sum of two even numbers. The sum of an odd number and an even number is always odd. In multiplication the product of two odd numbers is always odd. While the product of even numbers, as well as the product of odd numbers multiplied by even numbers is always even. So for this problem we need to find scenarios where the only possibile answers are even. 
can only result in even numbers no matter what positive integers are used for 
and 
, because 
must can only result in even products; the same can be said for 
. The rules provide that the sum of two even numbers is even, so 
is the answer.
There are certain patterns that can be used to predict whether the product or sum of numbers will be odd or even. The sum of two odd numbers is always even, as is the sum of two even numbers. The sum of an odd number and an even number is always odd. In multiplication the product of two odd numbers is always odd. While the product of even numbers, as well as the product of odd numbers multiplied by even numbers is always even. So for this problem we need to find scenarios where the only possibile answers are even.
Compare your answer with the correct one above
is even
is even
Therefore, which of the following must be true about 
?
Therefore, which of the following must be true about
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.
Recall that when you multiply by an even number, you get an even product.
Therefore, we know the following from the first statement:
For the second, we know this:
Since
Based on all this data, we can tell nothing necessarily about
Compare your answer with the correct one above
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?
In a group of philosophers,
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: 
* , or 
Aquinas: 
* , or 
Scotus: 
divided by 
, or 
Therefore, the total number is:
In a group of philosophers,
To start, let's calculate the total philosophers:
Ockham:
Aquinas:
Scotus:
Therefore, the total number is:
Compare your answer with the correct one above
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.
We know that when you multiply any integer by an even number, the result is even. Thus, if
Compare your answer with the correct one above
The product of three consecutive nonzero integers is taken. Which statement must be true?
The product of three consecutive nonzero integers is taken. Which statement must be true?
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.
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.
Compare your answer with the correct one above
is even
is even
Therefore, which of the following must be true about ?
Therefore, which of the following must be true about
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.
Recall that when you multiply by an even number, you get an even product.
Therefore, we know the following from the first statement:
For the second, we know this:
Since
Based on all this data, we can tell nothing necessarily about
Compare your answer with the correct one above
Which of the following integers has an even integer value for all positive integers and ?
Which of the following integers has an even integer value for all positive integers
There are certain patterns that can be used to predict whether the product or sum of numbers will be odd or even. The sum of two odd numbers is always even, as is the sum of two even numbers. The sum of an odd number and an even number is always odd. In multiplication the product of two odd numbers is always odd. While the product of even numbers, as well as the product of odd numbers multiplied by even numbers is always even. So for this problem we need to find scenarios where the only possibile answers are even. can only result in even numbers no matter what positive integers are used for and , because must can only result in even products; the same can be said for . The rules provide that the sum of two even numbers is even, so is the answer.
There are certain patterns that can be used to predict whether the product or sum of numbers will be odd or even. The sum of two odd numbers is always even, as is the sum of two even numbers. The sum of an odd number and an even number is always odd. In multiplication the product of two odd numbers is always odd. While the product of even numbers, as well as the product of odd numbers multiplied by even numbers is always even. So for this problem we need to find scenarios where the only possibile answers are even.
Compare your answer with the correct one above
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?
In a group of philosophers,
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: * , or
Aquinas: * , or
Scotus: divided by , or
Therefore, the total number is:
In a group of philosophers,
To start, let's calculate the total philosophers:
Ockham:
Aquinas:
Scotus:
Therefore, the total number is:
Compare your answer with the correct one above
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.
We know that when you multiply any integer by an even number, the result is even. Thus, if
Compare your answer with the correct one above
The product of three consecutive nonzero integers is taken. Which statement must be true?
The product of three consecutive nonzero integers is taken. Which statement must be true?
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.
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.
Compare your answer with the correct one above
is even
is even
Therefore, which of the following must be true about ?
Therefore, which of the following must be true about
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.
Recall that when you multiply by an even number, you get an even product.
Therefore, we know the following from the first statement:
For the second, we know this:
Since
Based on all this data, we can tell nothing necessarily about
Compare your answer with the correct one above
Which of the following integers has an even integer value for all positive integers and ?
Which of the following integers has an even integer value for all positive integers
There are certain patterns that can be used to predict whether the product or sum of numbers will be odd or even. The sum of two odd numbers is always even, as is the sum of two even numbers. The sum of an odd number and an even number is always odd. In multiplication the product of two odd numbers is always odd. While the product of even numbers, as well as the product of odd numbers multiplied by even numbers is always even. So for this problem we need to find scenarios where the only possibile answers are even. can only result in even numbers no matter what positive integers are used for and , because must can only result in even products; the same can be said for . The rules provide that the sum of two even numbers is even, so is the answer.
There are certain patterns that can be used to predict whether the product or sum of numbers will be odd or even. The sum of two odd numbers is always even, as is the sum of two even numbers. The sum of an odd number and an even number is always odd. In multiplication the product of two odd numbers is always odd. While the product of even numbers, as well as the product of odd numbers multiplied by even numbers is always even. So for this problem we need to find scenarios where the only possibile answers are even.
Compare your answer with the correct one above
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?
In a group of philosophers,
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: * , or
Aquinas: * , or
Scotus: divided by , or
Therefore, the total number is:
In a group of philosophers,
To start, let's calculate the total philosophers:
Ockham:
Aquinas:
Scotus:
Therefore, the total number is:
Compare your answer with the correct one above
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.
We know that when you multiply any integer by an even number, the result is even. Thus, if
Compare your answer with the correct one above
The product of three consecutive nonzero integers is taken. Which statement must be true?
The product of three consecutive nonzero integers is taken. Which statement must be true?
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.
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.
Compare your answer with the correct one above
is even
is even
Therefore, which of the following must be true about ?
Therefore, which of the following must be true about
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.
Recall that when you multiply by an even number, you get an even product.
Therefore, we know the following from the first statement:
For the second, we know this:
Since
Based on all this data, we can tell nothing necessarily about
Compare your answer with the correct one above
Which of the following integers has an even integer value for all positive integers and ?
Which of the following integers has an even integer value for all positive integers
There are certain patterns that can be used to predict whether the product or sum of numbers will be odd or even. The sum of two odd numbers is always even, as is the sum of two even numbers. The sum of an odd number and an even number is always odd. In multiplication the product of two odd numbers is always odd. While the product of even numbers, as well as the product of odd numbers multiplied by even numbers is always even. So for this problem we need to find scenarios where the only possibile answers are even. can only result in even numbers no matter what positive integers are used for and , because must can only result in even products; the same can be said for . The rules provide that the sum of two even numbers is even, so is the answer.
There are certain patterns that can be used to predict whether the product or sum of numbers will be odd or even. The sum of two odd numbers is always even, as is the sum of two even numbers. The sum of an odd number and an even number is always odd. In multiplication the product of two odd numbers is always odd. While the product of even numbers, as well as the product of odd numbers multiplied by even numbers is always even. So for this problem we need to find scenarios where the only possibile answers are even.
Compare your answer with the correct one above
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?
In a group of philosophers,
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: * , or
Aquinas: * , or
Scotus: divided by , or
Therefore, the total number is:
In a group of philosophers,
To start, let's calculate the total philosophers:
Ockham:
Aquinas:
Scotus:
Therefore, the total number is:
Compare your answer with the correct one above
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.
We know that when you multiply any integer by an even number, the result is even. Thus, if
Compare your answer with the correct one above
The product of three consecutive nonzero integers is taken. Which statement must be true?
The product of three consecutive nonzero integers is taken. Which statement must be true?
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.
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.
Compare your answer with the correct one above