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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.
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