SAT Math : SAT Mathematics
Study concepts, example questions & explanations for SAT Math
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Example Questions
Example Question #21 : Expressions
x * y = –a, a – x = 2a. What is y?
1
a
-a
Insufficient Information.
-2
1
Use the second equation to find x in terms of a. Plug it back in the second equation, that will give you 1 = y.
Example Question #2501 : Sat Mathematics
The projected sales of a movie are given by the function s(p) = 3000/(2p + a) where s is the number of movies sold, in thousands; p is the price per movie, in dollars; and a is a constant. If according to projections, 75,000 cartidges will be sold at $15 each, how many movies are sold at $20 each?
60,000
200,000
20,000
150,000
50,000
60,000
You set up the equation to solve for a.
75 = 3000/(2(15) + a)
a = 10
You then set up the formula again for each movie costing $20, s(20) = 3000/(2(20) + 10), and solve for x, the number sold, giving you 60.
Example Question #23 : Expressions
Half of one hundred divided by five and multiplied by one-tenth is __________.
1/2
10
1
5
2
1
Let's take this step by step. "Half of one hundred" is 100/2 = 50. Then "half of one hundred divided by five" is 50/5 = 10. "Multiplied by one-tenth" really is the same as dividing by ten, so the last step gives us 10/10 = 1.
Example Question #24 : Expressions
Let x&y be defined as (x – y)xy . What is the value of –1&2?
–1/3
3
1/9
–3
–1/9
1/9
We are told that x&y = (x – y)xy .
–1&2 = (–1 – 2)(–1)(2) = (–3)–2
To simplify this, we can make use of the property of exponents which states that a–b = 1/(ab ).
(–3)–2 = 1/(–3)2 = 1/9
The answer is 1/9.
Example Question #21 : Expressions
If 18 – w is 8 less than 32, what is the value of 
2
–3
3
–2
–6
2
We need to rewrite this problem in mathematic terms.
8 less than 32 can be written as 32 – 8
so we will get the equation
18 – w = 32 – 8.
Now, we need to solve for w.
–w = 32 – 8 – 18
–w = 6
w = –6
Find the value of the given expression, 
Example Question #26 : Expressions
If x and y are integers such that x > y > 0 and x2 + y2 = 100
Which of the following can be the value of x + y?
I. 10
II. 12
III. 14
IV. 16
V. 18
18
12
16
10
14
14
Note that x must be greater than y and that y must be greater than 0. This means that x and y are different, positive integers. In addition, the sum, x2 + y2 must equal to 100. If we list squares beginning from the square of the first integer greater than 0 (12) up to the square of the greatest integer less than 100 (92) we will get:
1, 4, 9, 16, 25, 36, 49, 64, 81
We must observe that the only two numbers that will add up to 100 are 36 and 64.
Remember that x > y > 0 and that x2 + y2 =100.
This means that x must be 
When we solve for x and y we get:
x = 8
and y = 6.
Therefore, x + y can only be 14.
Example Question #27 : Expressions
If 
Plug in numbers for each alternative. If both sides of the inequality 
Example Question #41 : Expressions
Billy began lifting weights in February. After 6 months, he can lift 312 lbs, a 20% increase in the amount he could lift in February. How much weight could Billy lift in February?
Example Question #42 : Expressions
A metal rod is 36 inches long and divided into 3 sections. The middle section is twice as long as the first section. The third section is 4 inches shorter than the first section. How long are the sections?
The first piece is 15 inches, the second piece is 15 inches and the third piece is 6 inches
The first piece is 6 inches, the second piece is 10 inches and the third piece is 20 inches
None of the above answers
First piece is 20 inches, the second piece is 10 inches and the third piece is 6 inches
First piece is 10 inches, the middle piece is 20 inches, and third piece is 6 inches long.
First piece is 10 inches, the middle piece is 20 inches, and third piece is 6 inches long.
Assume the first section equals 
Example Question #43 : Expressions
A B
1 2
2 4
3 10
5 34
Using the table above, please select the answer below that expresses the relationship between A and B.
By testing the answers, it can be seen that the only equation to satisfy all cases in the table above is
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