SAT Math : SAT Mathematics
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Example Questions
Example Question #3001 : Sat Mathematics
A certain group of 12 students has an average age of 17. Two new students enter the group. The average age of the group goes up to 18. What is the average age of the two new students that came in?
12
28
24
16
20
24
If 12 students have an average age of 17, we can say 
Therefore the sum of the students' ages is 12 x 17 = 204.
Two students enter the group, so the total number of students goes up to 14.
We are told that the new average age is 18.
Thus, the sum of the ages of the 14 students is 14 x 18 = 252.
The difference of the two sums gives us the sum of the ages of the two new students:
252 - 204 = 48
The average age of the two new students is then 48/2 = 24.
Example Question #3002 : Sat Mathematics
On her first four math tests, Kelly earned scores of 75, 85, 92, and 80. What must she score on the fifth test to make her class average 84?
83
85
84
88
90
88
The average of five tests scores must be 84. In other words, (sum of five scores)/5 = 84.
Let's multiply both sides by 5:
sum of five scores = 420
The sum of the first four scores plus the fifth score must be 420. The sum of the first four scores is 75 + 85 + 92 + 80 = 332.
Therefore, 332 + fifth score = 420.
Subtract 332 from both sides:
fifth score = 88.
The answer is 88.
Example Question #51 : Arithmetic Mean
A teacher tells the class that that mean on the test of six students was an 82. However the teacher only knows five of the students scores as follows:
What did the other student score on the test?
Let 
Cross multiplying and combining the known test scores gives:
Subtracting 410 from both sides gives:
Example Question #3003 : Sat Mathematics
Determine the mean of the following data set.
Divide this number by three to find the mean.
The mean is:
Example Question #51 : Arithmetic Mean
Express the mean of 
The mean of two numbers is half their sum, so the mean of 
Example Question #81 : Data Analysis
Bill needs a test average of at least 82% percent in order to pass his class. He received 71% and 78% on his first two tests, respectively. What is the lowest score Bill can recieve on his third test to pass the class? Assume all tests are weighted equally.
The purpose of this question is to understand averaging percentages. Assuming all tests are weighted equally, all tests are 100 points and therefore the percentages will directly translate into their point values.
Adding the 71 points and the 78 points together of the first two tests, it is 149 points scored out of the possible 200.
With all three tests, there are a possible 300 points; and the necessary 82% of those 300 points is 246.
This means that a total of at least 246 points must be scored for Bill to pass the class. Since 149 have already been scored, it leaves 
Example Question #51 : Arithmetic Mean
The average of 
If you average consecutive integers, the average will be the middle number. That means that 
Example Question #51 : Arithmetic Mean
Find the mean of the following numbers:
The mean is the sum of all the numbers in the set over the total numbers in the set.
Add the numbers in the set.
Divide this number by three, since there are three numbers in this set.
The mean is 
Example Question #52 : Arithmetic Mean
Five boys took a biology test. Their scores were as follows:
75, 85, 95, x, 80
If the average of the boys' scores was 80, then what is the value of x?
The average of the test scores can be written as follows:
Simplifying this equation, we get
Therefore, the fourth boy's score was 65.
Example Question #53 : Arithmetic Mean
Five students take a test. Their scores are listed below:
If the average score for the students is 
We can express the average score in the class as
Then, we can solve for x.
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