Evaluating and Simplifying Expressions - PSAT Math
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Which of the following phrases can be written as the algebraic expression 
?
Which of the following phrases can be written as the algebraic expression
is the cube of 
, which is the difference of a number and nineteen; therefore, 
is "the cube of the difference of a number and nineteen."
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Which of the following phrases can be written as the algebraic expression 
?
Which of the following phrases can be written as the algebraic expression
is seventeen decreased by 
, which is the cube of a number; therefore, 
is "seventeen decreased by the cube of a number."
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Increase 
by 70%. Which of the following will this be equal to?
Increase
A number increased by 70% is equivalent to 100% of the number plus 70% of the number. This is taking 170% of the number, or, equivalently, multiplying it by 1.7.
Therefore, 
increased by 70% is 1.7 times this, or
A number increased by 70% is equivalent to 100% of the number plus 70% of the number. This is taking 170% of the number, or, equivalently, multiplying it by 1.7.
Therefore,
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Which of the following operations could represent the expression 
?
Which of the following operations could represent the expression
Begin by putting the equation given into your own words. It might sound something similar to:
2 times x squared plus 7
Now, go through each answer choice and see if any of them are similar to this. We immediately see that the answer "7 more than 2 times the square of x" is similar to what we came up with. Let's do a quick run through of the other choices to be sure of our choice:
"2 times 7 more than the square of x" is equal to 
, which is equivalent to 
.
"2 times 7 less than the square of x" is equal to 
, which is equivalent to 
.
"7 more than the square of 2x" is equal to 
, which is equivalent to 
.
"7 less than the square of 2x" is equal to 
, which is equivalent to 
.
The only answer that works is "7 more than 2 times the square of x". This is the correct answer.
Begin by putting the equation given into your own words. It might sound something similar to:
2 times x squared plus 7
Now, go through each answer choice and see if any of them are similar to this. We immediately see that the answer "7 more than 2 times the square of x" is similar to what we came up with. Let's do a quick run through of the other choices to be sure of our choice:
"2 times 7 more than the square of x" is equal to
"2 times 7 less than the square of x" is equal to
"7 more than the square of 2x" is equal to
"7 less than the square of 2x" is equal to
The only answer that works is "7 more than 2 times the square of x". This is the correct answer.
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What does 
equal?
What does
When solving a complex expression, remember the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). Reading left to right, begin by doing all operations within the innermost Parentheses first:
Continue simplifying using the acronym PEMDAS:
The expression is equal to -63.
When solving a complex expression, remember the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). Reading left to right, begin by doing all operations within the innermost Parentheses first:
Continue simplifying using the acronym PEMDAS:
The expression is equal to -63.
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Which of the following phrases can be written as the algebraic expression ?
Which of the following phrases can be written as the algebraic expression
is seventeen decreased by , which is the cube of a number; therefore, is "seventeen decreased by the cube of a number."
Compare your answer with the correct one above
Increase by 70%. Which of the following will this be equal to?
Increase
A number increased by 70% is equivalent to 100% of the number plus 70% of the number. This is taking 170% of the number, or, equivalently, multiplying it by 1.7.
Therefore, increased by 70% is 1.7 times this, or
A number increased by 70% is equivalent to 100% of the number plus 70% of the number. This is taking 170% of the number, or, equivalently, multiplying it by 1.7.
Therefore,
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Which of the following phrases can be written as the algebraic expression ?
Which of the following phrases can be written as the algebraic expression
is the cube of , which is the difference of a number and nineteen; therefore, is "the cube of the difference of a number and nineteen."
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Which of the following operations could represent the expression ?
Which of the following operations could represent the expression
Begin by putting the equation given into your own words. It might sound something similar to:
2 times x squared plus 7
Now, go through each answer choice and see if any of them are similar to this. We immediately see that the answer "7 more than 2 times the square of x" is similar to what we came up with. Let's do a quick run through of the other choices to be sure of our choice:
"2 times 7 more than the square of x" is equal to , which is equivalent to .
"2 times 7 less than the square of x" is equal to , which is equivalent to .
"7 more than the square of 2x" is equal to , which is equivalent to .
"7 less than the square of 2x" is equal to , which is equivalent to .
The only answer that works is "7 more than 2 times the square of x". This is the correct answer.
Begin by putting the equation given into your own words. It might sound something similar to:
2 times x squared plus 7
Now, go through each answer choice and see if any of them are similar to this. We immediately see that the answer "7 more than 2 times the square of x" is similar to what we came up with. Let's do a quick run through of the other choices to be sure of our choice:
"2 times 7 more than the square of x" is equal to
"2 times 7 less than the square of x" is equal to
"7 more than the square of 2x" is equal to
"7 less than the square of 2x" is equal to
The only answer that works is "7 more than 2 times the square of x". This is the correct answer.
Compare your answer with the correct one above
What does equal?
What does
When solving a complex expression, remember the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). Reading left to right, begin by doing all operations within the innermost Parentheses first:
Continue simplifying using the acronym PEMDAS:
The expression is equal to -63.
When solving a complex expression, remember the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). Reading left to right, begin by doing all operations within the innermost Parentheses first:
Continue simplifying using the acronym PEMDAS:
The expression is equal to -63.
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A rowing team paddles upstream at a rate of 10 miles every 2 hours and downstream at a rate of 27 miles every 3 hours. Assuming they are paddling at the same rate up and downstream, what is the speed of the water?
A rowing team paddles upstream at a rate of 10 miles every 2 hours and downstream at a rate of 27 miles every 3 hours. Assuming they are paddling at the same rate up and downstream, what is the speed of the water?
Upstream: p – w = (10/2) or p – w = 5 miles/hour
Downstream: p + w = (27/3) or p + w = 9 miles/hour
Then we add the two equations together to cancel out the w's. After adding we see
2p = 14
p = 7 miles/hour where p is the rate of the paddling. We plug p into the equation to find
w = 2 miles/hour where w is the rate of the stream's water.
Upstream: p – w = (10/2) or p – w = 5 miles/hour
Downstream: p + w = (27/3) or p + w = 9 miles/hour
Then we add the two equations together to cancel out the w's. After adding we see
2p = 14
p = 7 miles/hour where p is the rate of the paddling. We plug p into the equation to find
w = 2 miles/hour where w is the rate of the stream's water.
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If ab - bc + d = d2 - c2, then what is the value of a when b is two, c is negative one, and d is zero?
If ab - bc + d = d2 - c2, then what is the value of a when b is two, c is negative one, and d is zero?
ab - bc + d = d2 - c2
We need to substitute values in for b, c, and d, and then solve the equation for a.
a(2) - 2(-1) + 0 = 02 - (-1)2
2a +2 + 0 = 0 - (1)
2a + 2 = -1
2a = -3
a = -3/2
The answer is -3/2.
ab - bc + d = d2 - c2
We need to substitute values in for b, c, and d, and then solve the equation for a.
a(2) - 2(-1) + 0 = 02 - (-1)2
2a +2 + 0 = 0 - (1)
2a + 2 = -1
2a = -3
a = -3/2
The answer is -3/2.
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If 11x + 4 = 19x – 12, then what is 2x – 4?
If 11x + 4 = 19x – 12, then what is 2x – 4?
First solve for x. The first equation would simplify as:
16 = 8x
x = 2
If we plug x = 2 into the second expression:
2(2) – 4 = 0
0 is the correct answer.
First solve for x. The first equation would simplify as:
16 = 8x
x = 2
If we plug x = 2 into the second expression:
2(2) – 4 = 0
0 is the correct answer.
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If x = 2 and y = 3, then evaluate 2(x – 3) + 5y2
If x = 2 and y = 3, then evaluate 2(x – 3) + 5y2
To evaluate an expression we make substitutions into the expression
2(x – 3) + 5y2 becomes 2(2 – 3) + 5 * 32 = –2 + 45 = 43
To evaluate an expression we make substitutions into the expression
2(x – 3) + 5y2 becomes 2(2 – 3) + 5 * 32 = –2 + 45 = 43
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IF 5x3 = 40, then what is the value of 12x – (x/2)?
IF 5x3 = 40, then what is the value of 12x – (x/2)?
Use the first equation to solve for x, then plug into the 2nd equation to find a value.
5x3 = 40
x3 = 8
x = 2
12(2) – (2/2) = 24 – 1 = 23
Use the first equation to solve for x, then plug into the 2nd equation to find a value.
5x3 = 40
x3 = 8
x = 2
12(2) – (2/2) = 24 – 1 = 23
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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?
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?
Taking 23 terms * 8 = 184; adding the original term of 15 yields 199.
Taking 23 terms * 8 = 184; adding the original term of 15 yields 199.
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Twenty percent of a number, 
, is four greater than the product of that number and six. Which of the following algebraic equations could be used to find 
?
Twenty percent of a number,
The "is" in the question means "equal," so whatever comes before "is" must be equal to whatever comes after. We will find an expression for the information before "is" and an expression for the information after "is," and then we will set these two expressions equal.
Twenty percent of a number can be represented as 0.2n, because 20% expressed as a decimal is 0.2, and because twenty percent "of" a number means the product of that number and twenty percent.
Four greater than the product of a number and six means that we must first find the product of that number and six, and then increase this value by 4.
The product of a number and six means that we must multiply this number by six, which can be represented by 6n. Increasing 6n by 4 can be modeled by the expression 6n + 4, or 4 + 6n (because of the commutative property of addition).
Setting the two expressions equal gives us 0.2n = 4 + 6n .
The "is" in the question means "equal," so whatever comes before "is" must be equal to whatever comes after. We will find an expression for the information before "is" and an expression for the information after "is," and then we will set these two expressions equal.
Twenty percent of a number can be represented as 0.2n, because 20% expressed as a decimal is 0.2, and because twenty percent "of" a number means the product of that number and twenty percent.
Four greater than the product of a number and six means that we must first find the product of that number and six, and then increase this value by 4.
The product of a number and six means that we must multiply this number by six, which can be represented by 6n. Increasing 6n by 4 can be modeled by the expression 6n + 4, or 4 + 6n (because of the commutative property of addition).
Setting the two expressions equal gives us 0.2n = 4 + 6n .
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An elementary school class consists of 
boys and 
girls. What fraction of the class is female?
An elementary school class consists of
There are B+G total students in the elementary school class, so G out of B+G are girls.
There are B+G total students in the elementary school class, so G out of B+G are girls.
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A total of 150 million votes were tallied in a presidential election. Votes were cast for either Hillary Clinton, Rand Paul, Al Gore, or Gary Johnson. If Clinton received 3 times the number of votes as Johnson, Paul received 30% of the vote, and Gore receieved 30 million total votes, who received the most votes in the election?
A total of 150 million votes were tallied in a presidential election. Votes were cast for either Hillary Clinton, Rand Paul, Al Gore, or Gary Johnson. If Clinton received 3 times the number of votes as Johnson, Paul received 30% of the vote, and Gore receieved 30 million total votes, who received the most votes in the election?
There are a few ways to do this problem, but we will focus on the total number of votes method as follows. First, let Clinton = C, Gore = G, Paul = P, and Johnson = J. We know C + G + P + J = 150 million. We also know that C = 3J. Paul received 30% of the vote which is 150,000,000 * .3 = 45 million votes. Gore received 30 million votes. We can now create an equation with individual totals and substitute 3J for Clinton's vote total:
3J + 30 million + 45 million + J = 150 million
4J = 75 million
J = 18.75 million
Then C = 3J = 56.25 million. So Clinton received 56.25 million votes, Paul received 45 million votes, Gore received 30 million votes, and Johnson received 18.75 million votes. The correct answer is Hillary Clinton.
There are a few ways to do this problem, but we will focus on the total number of votes method as follows. First, let Clinton = C, Gore = G, Paul = P, and Johnson = J. We know C + G + P + J = 150 million. We also know that C = 3J. Paul received 30% of the vote which is 150,000,000 * .3 = 45 million votes. Gore received 30 million votes. We can now create an equation with individual totals and substitute 3J for Clinton's vote total:
3J + 30 million + 45 million + J = 150 million
4J = 75 million
J = 18.75 million
Then C = 3J = 56.25 million. So Clinton received 56.25 million votes, Paul received 45 million votes, Gore received 30 million votes, and Johnson received 18.75 million votes. The correct answer is Hillary Clinton.
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Based on the chart, which equation represents the table data?
Based on the chart, which equation represents the table data?
| | | | |
|---|---|---|---|---|
| | | | |
The easiest way to solve this problem is to guess-and-check the answer choices. The equation that can be used to match the table will be correct.
We can see that the values in the table match the equation 
for each given value. Thus, this must be our answer.
We can also determine certain characteristics from the table itself. For example, as x increases, y(x) decreases. This tells us that there is likely a negative coefficient, which can help narrow down the answer options.
The easiest way to solve this problem is to guess-and-check the answer choices. The equation that can be used to match the table will be correct.
We can see that the values in the table match the equation
We can also determine certain characteristics from the table itself. For example, as x increases, y(x) decreases. This tells us that there is likely a negative coefficient, which can help narrow down the answer options.
Compare your answer with the correct one above