SAT Math : Algebra
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Example Question #721 : Algebra
The operation x || y is evaluated as: 3x – 14y
What is the value of 5 || (6 || 2)?
–10
–235
None of the other answers
155
140
155
The operation x || y is evaluated as: 3x – 14y
What is the value of 5 || (6 || 2)?
Do this in parts. Start with 6 || 2:
6 || 2 = 3 * 6 – 14 * 2 = 18 – 28 = –10
This leaves us with:
5 || –10 = 3 * 5 – (14 * –10) = 15 – (–140) = 15 + 140 = 155
Example Question #722 : Algebra
If the first term of a sequence is 15 and each term is 8 more than the previous term, what is the 24th term of the sequence?
207
191
199
184
199
Taking 23 terms * 8 = 184; adding the original term of 15 yields 199.
Example Question #31 : Expressions
If f(x) = 5x/a, and g(x) = ax/10, what is f(2) + g(5)?
a/10
(20+a2)/2a
5a
a
10
(20+a2)/2a
(20+a2) / 2a is the answer. Find a common denominator to add the 2 fractions after plugging in the values. So we get 10/a + a/2 after plugging in the values. The lowest common denominator would be 2a. Mutiply 10/a by 2/2, and multiply a/2 by a/a. The new equation appears as 20/2a + a2/2a. Add them together to get (20 + a2)/2a.
Example Question #14 : How To Evaluate Algebraic Expressions
(√(4) + √(16))2 = ?
36
20
√20
√30
6
36
If we use order of operations (PEMDAS), the answer is 36.
Example Question #15 : Evaluating Expressions
x * y = –a, a – x = 2a. What is y?
1
-2
a
-a
Insufficient Information.
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 #723 : Algebra
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?
20,000
200,000
60,000
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 #22 : Evaluating Expressions
Half of one hundred divided by five and multiplied by one-tenth is __________.
10
1
1/2
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 #23 : Evaluating Expressions
Let x&y be defined as (x – y)xy . What is the value of –1&2?
3
–1/3
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 #724 : Algebra
If 18 – w is 8 less than 32, what is the value of 
–6
–3
–2
2
3
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 #23 : Evaluating 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
12
16
18
14
10
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.
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