GRE Test Preparation

GRE Math Practice Test II
Answer Key with Explanations
P. 1 (Problems 1 - 9)

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WTAMU > Virtual Math Lab > GRE Math

Because of the enormity of this part, I split the answer/discussion into three pages.  This page, P. 1, has the answer/explanations to all levels of the first 9 problems. P. 2 has the answer/explanations to all levels of problems 10 - 19. P. 3 has the answer/explanations to all levels of problems 20 - 28.

This page also has links to the mathematical area(s) that each question comes from in case you need to go back and review.

Printing warning: Note that because of all of the levels per problem, there are a lot of questions on this page.  So if you wish to print this out, note that there will be a lot of pages to print.

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If x and y are integers, that means they can be negative, positive or zero.  Since Column A has an absolute value around x + y, that means its value will always be nonnegative.  Now, Column B does not have an absolute value around x + y.  Its value can be negative, positive or zero.  When Column B comes out nonnegative, then it will be equal to Column A.  However, if Column B’s value is negative then, Column A’s value is going to be greater. 

For example if x = 1 and y = 2, then both columns will have a value of 3.  But if x = 5 and y = -10, then Column A will be 5 and Column B will be -5. 

Since we don’t know which it will be, the relationship cannot be determined from the information given. 

Need more help on this topic?   Absolute Value

 

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Since 1/16 is greater than 1/27, Column B's value is greater than Column A's value. 

Need more help on this topic?   Fractions and Exponents

 

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Hey, they look a lot alike, but they are not exactly the same. Can you see the difference between the two?? Hopefully, you noticed that in Column A, there was a ( ) around the - and the 2. In Column B, there is no ( ). This means the - is NOT part of the base, so it will not get expanded like it did in Column A. It is interpreted as finding the negative or opposite of 2 squared. 

Hence, Column A's value is greater than Column B's value. 
 

Need more help on this topic?   Exponents

 

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We need to know the formula for the volume of a cylindrical building:

Filling in 20 for radius and 50 for height we get: 

The volume of the building is  cubic feet.
 

Need more help on this topic?   Formulas for Three-Dimensional Figures

 

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We need to know the formula for the volume of a cylindrical building:

Note how the problem gave us the DIAMETER.  To find the radius we need to divide the diameter of 17 by 2.  This will give us 8.5 for our radius. 

Filling in 8.5 for radius and 40 for height we get: 

The volume of the building is  cubic feet.
 

Need more help on this topic?   Formulas for Three-Dimensional Figures

 

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First, let’s find the volume of each cylindrical building.  The volume of a cylindrical building is 

Note how the problem gave us the DIAMETER.  To find the radius we need to divide the diameter of 21 by 2.  This will give us 10.5 for our radius.

Filling in 10.5 for radius and 30 for height we get:

Next we want to consider the fact that we have two buildings. Multiplying the volume by two we get:

Next we want to consider that there are about 7 pounds of wheat per cubic foot.  Multiplying the volume of the two cylinders by 7 we get: 

Next notice that none of the answers has the pi symbol in them. That means we will have to put in 3.14 for pi and see what we get:

About 145,398 pounds of wheat could be stored in these two buildings.
 

Need more help on this topic?   Formulas for Three-Dimensional Figures

 

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Need more help on these topics?   Decimals and Percents

 

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*Move decimal two places to the RIGHT

 

Need more help on these topics?   Decimals, Percents, and Scientific Notation

 

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*Move decimal on 7.5% two places to the left

*Move decimal two places to the RIGHT

 

Need more help on these topics?   Decimals, Percents, and Scientific Notation

 

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*Move decimal on .065% two places to the left

*Move decimal four places to the LEFT

 

Need more help on these topics?   Decimals, Percents, and Scientific Notation

 

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Solving the equation for x we get:

 

*Inverse of mult. by 3 is divide by 3

 

 

Need more help on these topics?   Solving Linear Equations

 

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Solving the equation for x we get:

 

*Inverse of add 12 is sub. 12 from BOTH sides
 

 

Need more help on these topics?   Solving Linear Equations

 

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Doing a cross multiplication we get:

 

*Cross multiplication

 

 


 

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The first step here is to find the value of x.  If we know that, then we can plug that in to the second expression and find out what x + 7 is. 

Solving the equation for x we get:  Solving Linear Equations and Operations with Algebraic Expressions

 

*Mult. BOTH sides by the LCD of -2
 

*Inverse of sub. 6 is add 6 to BOTH sides
 

 

We still need to plug in -4 for x in the given expression:

 


 

Need more help on these topics?   Solving Linear Equations and Operations with Algebraic Expressions

 

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The first step here is to find the value of x.  If we know that, then we can plug that in to the second expression and find out what  is. 

Solving the equation for x we get: 

 

*Inverse of add 20 is sub. 20 to BOTH sides

*Inverse of mult. by 2 is divide by 2
 

 

We still need to plug in -15 for x in the given expression:

 


 

Need more help on these topics?   Solving Linear Equations and Operations with Algebraic Expressions

 

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We can use the fundamental counting principle to answer this question.  Basically we need to take the product of the number of ways each event can occur. 

There are 2 stages or events: coin 1 and coin 2 

There are two possibilities for each coin, heads or tails. 

Putting that all together we get:

 

Coin 1   Coin 2   Total 2 x 2 = 4
 

Need more help on this topic?  Counting Principle

 

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We can use the fundamental counting principle to answer this question.  Basically we need to take the product of the number of ways each event can occur. 

There are 3 stages or events: choosing a sandwich, chips, and a drink. 

There are four types of sandwiches, three types of chips and three types of drinks. 

Putting that all together we get:

 

Sandwich   Chips
Drinks   Total 4 x 3 x 3 = 36
 

Need more help on this topic?  Counting Principle

 

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Since we are counting how many ways to ARRANGE the CD’s, this is a permutation problem.  The permutation of n things taken r at a time is 

Putting a 5 in for r and for n we get:

 

*Plugging 5 for n and r
 
 
 
 

*0! = 1
 
 
 

 

 

Need more help on this topic?  Permutations

 

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In Column A, each name has an equally likely chance of being picked. 

The probability of randomly selecting a given name out of a hat containing 15 different names can be found by taking the number of names being selected, which in this case is 1, and put that over the total number of names, which is 15: 

Since .07 is larger than .066666....,  .07 is a larger value than the probability of randomly selecting a given name out if a hat containing 15 different names.

Need more help on this topic?   Probability

 

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In Column A, each jelly bean has an equally likely chance of being picked. 

The probability of randomly selecting a jelly bean that is not red can be found by taking the number of jelly beans that are not red, which in this case is 26, and put that over the total  number of jelly beans, which is 30: 

Since 13/15 is larger than 2/15, the probability of randomly selecting a jelly bean that is not red is larger than 2/15.

Need more help on this topic?   Probability

 

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Solving the given equation for x we get:

 

*Set 1st factor = 0
 
 
 
 
 

*Set 2nd factor = 0

 

Need more help on these topics?   Solving Quadratic Equations

 

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Since x can be ANY value greater than 0, that means it could be a fractional number between 0 and 1, or a number greater than or equal to 1. 

If x is ½, then 

In this case Column B’s value is greater. 

But let’s look at an example where x is greater than 1. 

Let's try 2:

This time Column A’s value is greater. 

If x was 1, the two values would be the same. 

Hence, the relationship cannot be determined from the information given.

Need more help on these topics?   Exponents

 

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Since x can be ANY value greater than 0, that means it could be a fractional number between 0 and 1, or a number greater than or equal to 1. 

If x is ½, then

In this case Column B’s value is greater. 

But let’s look at an example where x is greater than 1. 

Lets try 2:

This time Column A’s value is greater. 
 

Hence, the relationship cannot be determined from the information given.

Need more help on these topics?   Exponents

 

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If we did a cross multiplication and solve for y we would get:

 

*Cross multiply
 

*Inv. of mult. by 2 is divide by 2
 
 

 

 

If x is 1, then y would equal 3/2.  If x is an integer greater than or equal to 2 then y would be greater than 3/2, which means y will always be greater than 1. 

y has a larger value than 1.
 

Need more help on these topics?   Solving Linear Equations

 

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The temptation here is to say that the two values are equal to each other.  However, if you put in any value such that 0 < y < x, you will find that Column A’s value is greater than Column B’s value. 

is a larger value than . 

Need more help on these topics?   Square Root

 

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In the figure above, if XY is a line segment, what is the number of degrees in the sum of a + b? 

a and b are measured in degrees.

Since XY is a line segment, that means its angle measurement is 180 degrees, which in turn means that 

Subtracting 50 from both sides will give us the sum of a and b: 

The sum of the angles a and b is 130 degrees.

Need more help on these topics?   Basic Geometry

 

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In the figure above, if AB is a straight line and , then how many degrees is y? 

x and y are measured in degrees.

Since AB is a straight line, its angle measurement is 180 degrees. This means that . 
 

We can use this to find our missing value.  Substituting in 2x for y we get:

 

*Inv. of mult. by 3 is divide by 3

 

 


 


 

Need more help on these topics?   Basic Geometry

 

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In the figure above, if XY is a line segment, how many degrees is 4a? 

a and b are measured in degrees.

Since 3 angles of measure a make up XY and  XY is a line segment, that means the 3 a angles would have to make up 180 degrees.

 

*Divide BOTH sides by 3

 

 


 

Need more help on these topics?    Basic Geometry

 

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a and b are measured in degrees.

Since 3 angles of measure a make up XY and  XY is a line segment, that means the 4 a angles would have to make up 180 degrees. 

Similarly, the 5 b angles would be 180 degrees. 

This would give us enough information to find out what aand b are equal to. 

Lets start with a:

 

*Divide BOTH sides by 3

 

 


 

*Divide BOTH sides by 5
 

 


 


 

Need more help on these topics?   Basic Geometry and Operations with Algebraic Expressions

 

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In the figure above, if XY is a line segment, what is the value of ? 

a and b are measured in degrees.

Since 3 angles of measure a make up XY and  XY is a line segment, that means the 4 a angles would have to make up 180 degrees. 

Similarly, the 5 b angles would be 180 degrees. 

This would give us enough information to find out what a and b are equal to. 

Let's start with a:

 

*Divide BOTH sides by 3

 

 


 

*Divide BOTH sides by 5
 

 


 

*Plug in 60 for a and 36 for b
 
 
 
 

 

 

Need more help on these topics?   Basic Geometry and Operations with Algebraic Expressions

 

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Using the distributive for Column A we get:

 

*commutative property

 

Need more help on these topics?   Multiplying Polynomials

 

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Factoring Column A we get:

 


 

Need more help on these topics?   Factoring

 

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Squaring Column A we get:

 


 

The relationship cannot be determined from the information given.

Need more help on these topics?   Multiplying Polynomials

 

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Cubing Column B we get:

 

 

 

The relationship cannot be determined from the information given.

Need more help on these topics?   Multiplying Polynomials

 

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*The sq. root of an expression squared is the abs. value of that expression
 

 

The relationship cannot be determined from the information given.

Need more help on these topics?   Factoring and Square Root

 
 

 

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WTAMU > Virtual Math Lab > GRE Math

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