Algebra 1 : Counting / Sets
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Example Questions
Example Question #1 : How To Find The Missing Number In A Set
If the mean of the following set is 12, what is 
(1,14,3,15,16,
Since we are given the mean, we need to find the sum of the numbers. From there we can figure out 
We can use this to find the sum by plugging in
So our sum is 96.
So we know that our total sum minus the sum of the given numbers is equal to 
So, 
Example Question #1 : How To Find The Missing Number In A Set
There are 5 men and 4 women competing for an executive body consisting of :
- President
- Vice President
- Secretary
- Treasurer
It is required that 2 women and 2 men must be selected
How many ways the executive body can be formed?
2 men can be selected:
2 women can be selected out of 4 women:
Finally, after the selection process, these men and women can fill the executive body in 
This gives us a total of
Example Question #11 : Counting / Sets
Which number is needed to complete the following sequence:
1,5,_,13,17
This is a sequence that features every other positive, odd integers. The missing number in this case is 9.
Example Question #6 : How To Find The Missing Number In A Set
Find the missing number:
Find the missing number:
To find the missing number, we need to find the pattern.
If we look closely, our numbers are going up by the same number each time: 13
To check this, find the difference between neighboring numbers
You get the idea.
So, to find the missing number, simply do the following:
Example Question #5 : How To Find The Missing Number In A Set
Find n in the following sequence:
You need to evaluate the terms in the sequence to determine the pattern that is shown. In this case, the first term is multiplied by 2 and the second term is found by adding 3.
Example Question #4 : How To Find The Missing Number In A Set
The first four numbers in the following set are parabolic: 
Notice that the world parabolic is given. This means that our parent function will be in the form:
The terms resemble a pattern where the parent function 
We can find the two missing terms by substituting 
The first number is:
The second number is:
The respective numbers are:
Example Question #1 : How To Find The Missing Number In A Set
Find the missing numbers in the set of numbers:
Notice that the second and third terms in the set of numbers can be subtracted to determine the displacement of each number in the set.
Subtract negative three from one. Enclose the negative number with parentheses.
Each number is spaced four units.
Subtract four from negative three to find the first number.
Add four to one to find the number for the second question mark.
This number is also four units from nine.
The answer is:
Example Question #7 : How To Find The Missing Number In A Set
Find the missing numbers, respectively:
Determine the distance between each number.
The second and the third number are spaced 
Check the third and fourth number if this is also has the same displacement.
Since this is true, this means that the numbers are also spaced at 
Notice the fractions are in decreasing order.
Add 
Reduce this fraction.
The first term is:
Subtract 
Reduce this fraction.
The fifth term is:
The correct answer is:
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