All SAT Math Resources
Example Questions
Example Question #21 : Even / Odd Numbers
is even
is even
Therefore, which of the following must be true about ?
It must be even.
It could be either even or odd.
It must be odd.
It could be either even or odd.
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 #3 : 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?
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 #2 : How To Multiply Even Numbers
If n is an integer that is not equal to 0, which of the following must be greater than or equal to n?
I. 7n
II. n + 5
III. n2
I, II, and III
II only
II and III only
I and III only
I and II only
II and III only
I is not always true because a negative number multiplied by 7 will give a number that is more negative than the original. II is true because adding 5 to any number will increase the value. III is true because squaring any number will increase the magnitude of the value, and squaring a negative number will make it positive.
Example Question #1 : How To Multiply Even Numbers
Which of the following integers has an even integer value for all positive integers and ?
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.
Example Question #2 : How To Add / Subtract / Multiply / Divide Negative Numbers
If x is a negative integer, what else must be a negative integer?
x – (–x)
x – x
x² – x
x²
x – (–x)
By choosing a random negative number, for example: –4, we can input the number into each choice and see if we come out with another negative number. When we put –4 in for x, we would have –4 – (–(–4)) or –4 – 4, which is –8. Plugging in the other options gives a positive answer. You can try other negative numbers, if needed, to confirm this still works.
Example Question #31 : Integers
–7 – 7= x
–7 – (–7) = y
what are x and y, respectively
x = –14, y = 14
x = 0, y = 0
x = –14, y = 0
y = 0, x = 14
x = 14, y = –14
x = –14, y = 0
x: –7 – 7= –7 + –7 = –14
y: –7 – (–7) = –7 + 7 = 0
when subtracting a negative number, turn it into an addition problem
Example Question #1 : How To Subtract Negative Numbers
Evaluate:
Reconvert into single signs. Remember that double negatives will turn into a positive.
Example Question #2 : How To Subtract Negative Numbers
Subtract:
Subtracting a negative number moves the number farther left of the zero digit on the number line.
The answer is:
Example Question #3 : Negative Numbers
Subtract:
Simplify the expression by eliminating the double negative signs. Two negatives multiplied by one another will result in a positive number.
Convert the signs.
Add the right side of the equation.
The answer is .
Example Question #3 : How To Subtract Negative Numbers
Simplify the following expression:
Simplify the following expression:
To subtract negative numbers, we must recall that subtracting negative numbers is the same as adding a positive. The two negatives cancel each other out to become positive.
So our answer is negative 220