SAT Math : Evaluating Expressions
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Example Questions
Example Question #11 : How To Evaluate Algebraic Expressions
Let x&y = xy – x + y. Which of the following is equal to 5&3 ?
3&(5&2)
4&(3&4)
2&(8&1)
11&(0&2)
8&(2&0)
11&(0&2)
First, we need to evaluate 5&3.
Since x&y = xy – x + y, we can find 5&3 as follows:
5&3 = 5(3) – 5 + 3
= 15 – 5 + 3
= 13
Now, we need to go through each of the choices and determine which one equals 13.
Let's start with 2&(8&1). Remember that we must first evaluate inside the parantheses.
2&(8&1) = 2&(8(1) – 8 + 1)
= 2&(8 – 8 + 1)
= 2&(1)
= 2(1) – 2 + 1 = 1, which doesn't equal 13.
Next, let's evaluate 4&(3&4).
4&(3&4) = 4&(3(4) – 3 + 4)
= 4&(13) = 4(13) – 4 + 13 = 61.
Next, we can evaulate 8&(2&0).
8&(2&0) = 8&(2(0) – 2 + 0)
= 8&(–2) = 8(–2) – 8 + 2 = –22.
Next, let's find 3&(5&2).
3&(5&2) = 3&(5(2) – 5 + 2)
= 3&(7) = 3(7) – 3 + 7 = 25.
Finally, lets evaluate 11&(0&2).
11&(0&2) = 11&(0(2) – 0 + 2)
= 11&(2) = 11(2) – 11 + 2 = 13.
The answer is 11&(0&2).
Example Question #391 : Algebra
x is 75% of y, which is 8 times the amount of 150% of z. What is x in terms of z?
9z
6z
7.5z
12z
None of the other answers
9z
Just take this step by step. First write out each equation:
x = 0.75y
y = 8(1.5z)
First, simplify the second equation:
y = 12z
Then, substitute y from this equation into the first:
x = 0.75(12z) = 9z
Example Question #11 : Expressions
2x + 6y = 44
What is x + 3y + 33?
The answer cannot be determined
55
77
81
23
55
The key to solving this question is noticing that we can factor out a two:
2x + 6y = 44 is the same as 2(x + 3y) = 44
Therefore, x + 3y = 22
In this case, x + 3y + 33 is the same as 22 + 33 or 55
Example Question #11 : Evaluating And Simplifying Expressions
John has four more dollars than four times the amount of dollars that Sandy has.
Peter has three times that of John.
Sandy has $20.
How much money does Peter have?
60
252
84
288
64
252
Let's make 3 equations based on our data:
J = 4S + 4
P = 3J
S = 20
All we have to do is sequentially replace values.
Substitute 20 for S in the J equation:
J = 4 * 20 + 4 = 84
Now, we can calculate P: P = 3 * 84 = 252
Example Question #21 : Expressions
There are 42 marbles in a bag. Half are red. The remaining ones are green and blue. There are five more blue marbles than green ones. How many marbles are there of each type?
4 Red, 15 Blue, 21 Green
None of the other answers
21 Red, 13 Blue, 8 Green
21 Red, 8 Blue, 13 Green
21 Red, 16 Blue, 5 Green
21 Red, 13 Blue, 8 Green
Rewrite our question as a set of equations:
R + G + B = 42
R = 42/2 = 21
Therefore, we already know:
G + B = 21
Also, we know that B = 5 + G
Replace that value into the B + G equation:
G + 5 + G = 21 → 2G + 5 = 21 → 2G = 16; G = 8
Therefore, we know that there are 5 + 8 or 13 blue marbles.
The total is therefore 21 Red, 13 Blue, 8 Green
Example Question #22 : Expressions
The operation x || y is evaluated as: 3x – 14y
What is the value of 5 || (6 || 2)?
155
–235
140
None of the other answers
–10
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 #12 : Expressions
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
184
199
199
Taking 23 terms * 8 = 184; adding the original term of 15 yields 199.
Example Question #11 : Evaluating Expressions
If f(x) = 5x/a, and g(x) = ax/10, what is f(2) + g(5)?
a
a/10
5a
10
(20+a2)/2a
(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 #13 : Expressions
(√(4) + √(16))2 = ?
√20
√30
6
36
20
36
If we use order of operations (PEMDAS), the answer is 36.
Example Question #31 : Expressions
x * y = –a, a – x = 2a. What is y?
1
-2
a
Insufficient Information.
-a
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.
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