Title

GRE Math Practice Test II
P. 1 (Problems 1 - 9)

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 1 - 3.

 Column A Column B

 Answer: D 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

 2 - 2.

 Column A Column B

 Answer: B 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

 2 - 4.

 Column A Column B

 Answer: A 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

 3 - 1.  A cylindrical building contains wheat.  The building has a radius of 20 feet and a depth of 50 feet.  What is the volume of this cylindrical building?

 Answer: D 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

 3 - 3.  A cylindrical building contains wheat.  The building has a diameter of 17 feet and a depth of 40 feet.  What is the volume of this cylindrical building?

 Answer: B 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

 3 - 5.  Two identical cylindrical buildings contain wheat.  Each building has a diameter of 21 feet and a depth of 30 feet.  If one cubic foot of wheat weighs 7 pounds, approximately how many pounds of wheat can be stored if both building are full.

 Answer: E 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

 4 - 1.

 Column A 30% of 50,000 Column B 1500

 Answer: A *Move decimal on 30% two places to the left

 Since 15000 > 1500, the answer is Column A’s quantity is greater. Need more help on these topics?   Decimals and Percents

 4 - 2.

 Column A 7% of 25,000 Column B

 Answer: A *Move decimal on 7% two places to the left *Move decimal two places to the RIGHT

 Since 1750 > 175, the answer is Column A’s quantity is greater. Need more help on these topics?   Decimals, Percents, and Scientific Notation

 4 - 4.

 Column A 7.5% of 8000 Column B

 Answer: C *Move decimal on 7.5% two places to the left *Move decimal two places to the RIGHT

 Since 600 = 600, the quantities are the same. Need more help on these topics?   Decimals, Percents, and Scientific Notation

 4 - 5.

 Column A .065% of .4 Column B

 Answer: C *Move decimal on .065% two places to the left *Move decimal four places to the LEFT

 Since .00026 = .00026, the quantities are the same. Need more help on these topics?   Decimals, Percents, and Scientific Notation

 5 - 1.  If , what is the value of x?

 Answer: C Solving the equation for x we get:

 *Inverse of sub. 5 is add 5 to BOTH sides   *Inverse of mult. by 3 is divide by 3

 So when , x =  4 2/3. Need more help on these topics?   Solving Linear Equations

 5 - 2.  If , what is the value of x?

 Answer: D Solving the equation for x we get:

 *Mult. BOTH sides by the LCD of 4 *Inverse of add 12 is sub. 12 from BOTH sides

 So when , x =  16. Need more help on these topics?   Solving Linear Equations

 5 - 3.  If , and a, b, c, and d are positive integers, then which of the following must be true?

 Answer: E Doing a cross multiplication we get:

 *Cross multiplication

 Need more help on these topics?   Solving Linear Equations

 5 - 4.  If , what is the value of ?

 Answer: B 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

 Now be careful, this is not our final answer.  We still need to plug in -4 for x in the given expression:

 *Plug in -4 for x

 So when , the expression x + 5 is equal to 3. Need more help on these topics?   Solving Linear Equations and Operations with Algebraic Expressions

 5 - 5.  If , what is the value of ?

 Answer: A 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:

 *Mult. BOTH sides by the LCD of -5   *Inverse of add 20 is sub. 20 to BOTH sides *Inverse of mult. by 2 is divide by 2

 Now be careful, this is not our final answer.  We still need to plug in -15 for x in the given expression:

 *Plug in -15 for x

 So when , the expression  is equal to -4.5. Need more help on these topics?   Solving Linear Equations and Operations with Algebraic Expressions

 6 - 1.

 Column A Two different coins are tossed.  The number of possible outcomes  of tossing the two coins. Column B 4

 Answer: C 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

 Since there are 4 different possible tosses of two coins, the two quantities are the same. Need more help on this topic?  Counting Principle

 6 - 2.

 Column A A combo special includes one sandwich,  one bag of chips and one drink.  There are four types of sandwiches,  three types of chips and three types of drinks.  The number of combos possible. Column B 24

 Answer: A 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

 Since 36 is larger than 24, the number of different possible combos is a larger value than 24. Need more help on this topic?  Counting Principle

 6 - 3.

 Column A The number of ways to arrange  five CD’s on a shelf. Column B 125

 Answer: B 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:

 *Permutation formula     *Plugging 5 for n and r         *0! = 1

 Since 125 is larger than 120, 125 is a larger value than the number of different possible arrangements of five CD's. Need more help on this topic?  Permutations

 6 - 4.

 Column A Probability of randomly selecting a  given name out of a hat containing  fifteen different names. Column B .07

 Answer: B 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

 6 - 5.

 Column A A bag contains four red, twelve green,  and 14 black jelly beans.  The probability that a red one is not picked. Column B

 Answer: A 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

 7 - 1.

 Column A x Column B 7

 Answer: D Solving the given equation for x we get:

 *Factor the Difference of Squares   *Set 1st factor = 0           *Set 2nd factor = 0

 Since x can be either 7 OR -7, the relationship cannot be determined from the information given. Need more help on these topics?   Solving Quadratic Equations

 7 - 2.

 Column A Column B

 Answer: D 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

 7 - 3.

 Column A Column B

 Answer: D 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

 7 - 4.  x is a positive integer:

 Column A y Column B 1

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

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

 It is given that x is a positive integer.  That could mean x is 1, 2, 3, ....  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

 7 - 5.

 Column A Column B

 Answer: A 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

 8 - 1.  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.

 Answer: D 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

 8 - 2. In the figure above, if AB is a straight line and , then how many degrees is y?  x and y are measured in degrees.

 Answer: C 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:

 *The sum of the angles is 180 *Substitute in 2x for y   *Inv. of mult. by 3 is divide by 3

 If x is 60 degrees and y = 2x, then

 *Plug in 60 for x

 y is 120 degrees. Need more help on these topics?   Basic Geometry

 8 - 3.  In the figure above, if XY is a line segment, how many degrees is 4a?  a and b are measured in degrees.

 Answer: D 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.

 *The 3 a angles = 180 degrees   *Divide BOTH sides by 3

 Now that we know what a is equal to, all we have to do is multiply that by 4 and get our answer:

 4a is equal to 240 degrees.   Need more help on these topics?    Basic Geometry

 8 - 4.  In the figure above, if XY is a line segment, what is the value of ?  a and b are measured in degrees.

 Answer: B 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:

 *The 3 a angles = 180 degrees   *Divide BOTH sides by 3

 Next lets look at b:

 *The 5 b angles = 180 degrees   *Divide BOTH sides by 5

 Putting those values in for a and bwe get:

 *Plug in 60 for a and 36 for b

 Our answer to this problem is 5/3.   Need more help on these topics?   Basic Geometry and Operations with Algebraic Expressions

 8 - 5.  In the figure above, if XY is a line segment, what is the value of ?  a and b are measured in degrees.

 Answer: D 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:

 *The 3 a angles = 180 degrees   *Divide BOTH sides by 3

 Next let's look at b:

 *The 5 b angles = 180 degrees   *Divide BOTH sides by 5

 Putting those values in for a and b we get:

 *Plug in 60 for a and 36 for b

 Our answer to this problem is 4.   Need more help on these topics?   Basic Geometry and Operations with Algebraic Expressions

 9 - 1.

 Column A Column B

 Answer: C Using the distributive for Column A we get:

 *distributive property *commutative property

 is the same as .    Need more help on these topics?   Multiplying Polynomials

 9 - 2.

 Column A Column B

 Answer: C Factoring Column A we get:

 *Factor the difference of two squares

 is the same as .    Need more help on these topics?   Factoring

 9 - 3.

 Column A Column B

 Answer: D Squaring Column A we get:

 *Squaring x + y

 It is real tempting to say that Column A is greater than Column B at this point, but keep in mind that there were no stipulations on what x or y could be.  This means they can be ANY real number.  So if there product is positive, then Column A would be greater, but if there product is negative, then Column B would be greater.  The relationship cannot be determined from the information given. Need more help on these topics?   Multiplying Polynomials

 9 - 4.

 Column A Column B

 Answer: D Cubing Column B we get:

 *Cubing x + 3

 It is real tempting to say that Column B is greater than Column A at this point, but keep in mind that there were no stipulations on what x could be.  This means it can be ANY real number.  So if  is positive, then Column B would be greater, but if it is negative, then Column A would be greater.  Both are possible.    The relationship cannot be determined from the information given. Need more help on these topics?   Multiplying Polynomials

 9 - 5.

 Column A Column B

 *Factor the Perfect Square Trinomial *The sq. root of an expression squared is the abs. value of that expression

 If  is positive, then the two values are the same.  However, if it is negative then, Column A will be greater.  The relationship cannot be determined from the information given. Need more help on these topics?   Factoring and Square Root

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