gre practice questions- quantitative

7/11/14, 2:59 PMGRE Preparation - Part 2 (Quantitative)

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Lesson 11: Printer Friendly

Quantitative Reasoning Practice – Part 1

Chapter 1

Introduction

Wow. Here we are at Lesson 11. You've come a long way and have done some very valuable work.

This lesson and Lesson 12 bring everything you've learned together. Today you'll get to practice your achievements by taking a full lengthquantitative reasoning section test, 20 questions in 35 minutes. After the practice test, we'll go through the steps together as we review theanswers one by one.

Here's how we'll accomplish this. In our lesson today, we'll cover the first 10 questions. They begin with a set of seven quantitative comparisonproblems followed by three standard math questions. Then, in Lesson 12, we'll go over the remaining seven standard math questions and theset of three data interpretation questions.

Well, that's enough talking about it, let's do it. First, click the practice test icon below. A new browser window or tab will open that contains thePDF. Please print out the test now. Oh, and don't forget scratch paper.

Click this icon to open the Practice Test PDF

You'll probably want to use a calculator to help you with the calculations, but remember that the GRE computer calculator will be a little differentthan yours. If you'd rather recreate a tangible test calculator (a good idea), or if you don't have access to one that observes the order ofoperations, consider using the calculator in the POWERPREP II software. To find out how to access it, see the FAQs for today's lesson.

Give yourself 35 minutes to answer the questions. Set a timer so that you'll have the actual experience of working against a clock (this wouldbe good to practice several times before the actual GRE test so that you'll be more comfortable and thus more relaxed, when confronted withthe ticking clock.) Read the test instructions and then start the timer. When the alarm sounds, lay that pencil down and stop; you're done. Then come back to our lesson and we'll examine the first 10 answers together.

Ready? Then go for it! I'll be here when you get back.

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Chapter 2

Explanations for Questions 1-4

How'd you do? Still feeling a little rusty? If so, let yourself relax and follow the explanations in today's lesson. And please bear in mind, thesequestions will definitely become easier to answer the more you do them. Remember, all mastery takes practice—and that especially applies tomanaging the GRE. So just be patient with this part of the process.

Okay, then. Let's review how to answer the first four quantitative comparison questions. Keep your printed test in front of you and use it tofollow along with the lesson.

Question 1

The test starts off simply. The first question regards basic statistics.

The arithmetic mean of x and y is 22, and v = 25 and z = 27.

Quantity A Quantity B

24.5 Average of x, y, z, and v

The problem gives you four variables. You know the average (arithmetic mean) of two of them and the values of the other two. You have all theinformation you need to find the value of Quantity B and, therefore, compare the two quantities, so right away you know the answer isn't D. Linethat one out.

You may be able to figure out the average of the four variables in your head. The average of v and z is easy. You don't need to add thevariables and divide by two to know that their average is the value between them, 26.

Once you know that the average of v and z is 26 and the average of x and y is 22, you can quickly find the average of all four values—again,without adding the values and dividing by two. The value that's smack in the middle of 22 and 26 is 24. Note that their average is also theirmedian. The average of the four values is 24.

If you don't feel comfortable answering the question by eying the values, you can solve the problem by setting up an equation. Remember theformula: the average is the sum of the values divided by the number of values. When you plug the known values into the formula, you get this:

You don't have an exact value for x + y. But, there's still a way to figure it out. Knowing the average of x and y allows you to determine the valueof x + y. Here's how:

Create another average formula using what you know about x and y:

Multiply both sides by 2 to solve for x + y.

44 = x + y



Then, you replace the value for x + y into the original average formula and solve:

To use the calculator in the software, you'd enter (44 + 25 + 27) ÷ 4 = and you'd get 24.

Whether you solve for it the quick way or the long and sure way, you come up with Quantity A is greater than Quantity B. The correct answer isA.

Question 2

The second question looks more complicated than it is.

(x + 3y)(x - 3y) = 6


6 x2 – 9y2

The first thing to notice is that the first terms in the given equations are the same except for the operation. The first term uses addition and thesecond, subtraction. The product of two binomials that are the same except for their operations is the difference of perfect squares. So, (x + 3y)(x - 3y) is the same as x2 – 9y2. From here on it's a piece of cake. If (x + 3y)(x - 3y) = 6, then x2 – 9y2 has to be 6, too. The quantities are equaland the answer is C.

Two down, eight to go!

Question 3

The third question addresses coordinate geometry.


The slope of a horizontalline

The slope of a line with points (2,3) and(-1,1)

Apply what you know about slope. A horizontal line has a slope of zero. So, if Quantity B has a positive slope, it's greater. If it has a negativeslope, Quantity A is larger. You know you can find the slope of a line when you know two of its points. It's possible to evaluate the quantities, soD can't be the correct answer. Scratch that one.

You find slope by taking the difference between the y values of the two points and dividing by the difference between the x values of the points,like this:



Note that subtracting the negative number in the denominator is like adding it. Knowing how to subtract a negative number is crucial to solvingthis equation. The slope in Quantity B is positive, so Quantity B is greater than Quantity A.

You could also solve this problem by drawing the points on a graph on your scratch paper to see which way the line slopes.

The line slopes up from left to right, so its slope is positive.

Any way you look at it, the answer is B

Feeling pretty good? Make a quick fist pump, but don't relax just yet. There are still more questions to go.

Question 4

You've been able to solve the previous questions by focusing on just one of the quantities. You'll have to figure out both quantities to solve thisone.

A rectangular box with dimensions of 18 feet by 15 feet by 9 feet sits beside aquantity of smaller square boxes, each measuring a cubic yard.


Volume in cubic feet of the Greatest number of smaller boxes that



larger box divided by 27 can fit inside the larger box

The problem gives you the box's dimensions, so you can solve for its volume and get a defined value for Quantity A. Once you know the box'svolume, you can also figure out how many cubic yards it's made up of. Each quantity has a defined value, so D's not the correct answer.

Be careful, though. Take the time to figure both values. You may be tempted to quickly choose B. The number of smaller boxes that fit into thelarger box seems to indicate the box's volume. Because Quantity A divides the volume by 27, it seems that it must be smaller than B.

Don't be fooled! The problem gives the box dimensions in feet and the smaller boxes are measured in yards. You have to make themeasurements equal to compare them.

Start with the volume of the box. Volume is equal to the product of the length, width, and height (V = lwh),so V = 18 x 15 x 9. V = 2,430 cubic feet. Divide that by 27 to get a value of 90 for Quantity A.

To find the value of Quantity B, convert feet to yards. There are three feet in a yard and 27 cubic feet in acubic yard (33 = 27). So just divide 2,430 by 27. Sound familiar? It's the same operation you performed toget the value in Quantity A. So 90 boxes fit into the larger box.

You also could've figured out the volume in cubic yards by dividing the initial values by three before youmultiplied them together:

V = (18 ÷ 3) x (15 ÷ 3) x (9 ÷ 3)

You would enter the numbers into the computer's calculator using the parentheses keys. The resultinganswer is 90.

The two quantities are equal and the answer is C.

So far so good? That's over half of the quantitative comparison questions. Why not take a short break before we move on to the remainingones?

Chapter 3

Explanations for Questions 5 – 7

Welcome back! The next three questions complete the set of quantitative comparison questions in the section.

Question 5

How about a little probability?

A child has a green, blue, yellow, red, and purple block that she keeps in anopaque container. She takes one block out of the container at random, thenplaces it back in the container and removes another block.

Quantity A Quantity



B

Probability of the child's picking thepurple block twice in a row.

5%

To find the probability of picking the same block twice in a row, find the probability of picking the block one time and multiply that by picking itone time again.

The probability of picking the purple block one time is 1 out of 5 because there is one purple block in the container of 5 total blocks. Theprobability of putting the purple block back and picking it again is also 1 out of 5. Multiply them together to find the probability of picking thepurple block twice in a row.

Divide to convert to a decimal: 1 ÷ 25 = 0.04 or 4%.

You could've converted to decimals before you multiplied by clicking on the following keys on the calculator:

(1 ÷ 5) x (1 ÷ 5)

The answer would come up 0.04, which you'd then convert to 4% and determine that Quantity B is greater than Quantity A.

Another correct answer, B. Let's move on to the question 6.

Question 6

y < 0 < x


xy

Don't be put off by the lack of numbers in this question. Just start with what you know. The question tells you that y is less than 0 and x isgreater than 0. Therefore, y is negative and x is positive.

Pick some values for x and y that meet the specifications. Say that y is -1 and x is 1. Write y = -1 and x = 1 on your scratch paper so you won'tforget.

Substitute the values in the two quantities. Quantity A would be . Quantity B would be 1 x -1 = -1. The two values are equal.



Don't choose C and move on, though. You're not done yet. Before you select C, you must try some other values to make sure that thequantities are equal in all cases.

Let's say that y = -2 and x = 3. Quantity A would be , and Quantity B would be 3 x -2 = -6. Now you know the answer has to beD. See how you have to know more about x and y to figure out how they're related?

You'd click the oval next to answer D. And you'd score!

Question 7

Take a look at the last quantitative comparison:


Area of the triangle

This question asks you to compare the area of the triangle with the equation in Quantity A.

What do you need to know to answer this question? You need the area of the triangle in terms of its coordinates.



Here's what you do know:

The area of a triangle is 1/2 its base times its height.

You have the measurements for the base and the height in the form of their coordinates. The base of our right triangle ABC is the valueof A1 less the value of C1. So, base = A1 – C1.

Likewise, the height of the triangle is the value of A2 less the value of B2. So, height = A2 – B2.

Note that you only need the x-coordinates for the base because you just need to know the length along the x-axis. And you only need the y-coordinates for the base because you just need to know the length along the y-axis.

So, the area of triangle ABC is :

Okay. How does this compare with the value in Quantity A?

Because multiplication is commutative (you can swap numbers and still get the same answer), the order of multiplication is unimportant.Therefore, the numerators are the same. But, if you multiply the denominators in the expression in Quantity A, you get a value of 4. Since adenominator of 4 is greater than a denominator of 2, the value in Column A must be less than the value in Column B because you're dividing bya larger number.

The correct answer is B.

The next three questions in the test are standard math questions. But before we move on to our discussion, take a little stretch-and-yawnbreak. Maybe have a glass of water or juice. We'll continue when you're ready.

Chapter 4

Explanations for Questions 8 - 10

Now that you're rested and ready, let's take a look at the last three questions (standard math type) in this first half of the practice test.

Question 8

This question involves finding distance and knowing the common ratios of right triangles.

Katie and Aaron leave school at the same time and walk for two hours. Katiewalks due west at an average rate of four kilometers per hour, and Aaronwalks due south at three kilometers per hour. What is the straight-linedistance between them, in kilometers, at the end of the two hours?

You don't have answers to choose from for this question, so you're on your own. Start by drawing the distances on your scratch paper.

Put a point at the school. Katie walks for two hours at a rate of four kilometers per hour, so she walked a distance of 2 x 4 kilometers to thewest. Draw a line from the school to a point directly to the left of the school's point. This line shows Katie's walk. Designate the line with adistance of 8 km.



For Aaron, draw a point directly below the school's point. Connect the points with a line that measures the distance of 2 x 3, or 6 km. Then drawa line from the point where Katie ended her walk to the point where Aaron stopped. The length of this line is the distance you're supposed tofind, x. Your drawing should look a little like this:

That's a right triangle! So you could use the Pythagorean theorem to find the measure of x, but you'll save time if you notice that the legs of thetriangle are multiples of 3 and 4. What you've got here is a 3-4-5 triangle times two. Therefore, you know that the other side is the multiple of 5times 2, or 10.

So you'd type 10 in the box and go on to the next question.

Question 9

This question regards coordinate geometry.

Which of the following is an equation of a line that passes through the origin ofthe coordinate plane and is parallel to the line 3x – y = 6?

(A) 3x – y = 6

(B) x – y = 0

(C) 3x + y = 0

(D) 3x – y = 0

(E) x = 3y

You can eliminate A because it's the same equation as the one in the question. Two lines with the same equation wouldn't be parallel to eachother; they'd be on top of each other!


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The equation of a line (or slope intercept form) is y = mx + b, where m represents the slope and b represents the y-intercept. Start by puttingthe equation in the question in the slope intercept form:

-y = -3x + 6

y = 3x – 6

So the slope of the line is 3 and the y-intercept is 6. Because parallel lines have the same slope, the correct answer will have a slope of 3 and ay-intercept of 0.

When you put B in the slope intercept form, you see that it has a slope of 0:

x – y = 0

-y = -x + 0

y = x + 0

This line has a y-intercept of 0, but its slope is 1. Cross out B on your scratch paper.

Choice E has a slope of 1/3: -3y = -x; y = -1/3 x. So it can't be right either. Scratch E.

Try C. 3x + y = 0 becomes y = -3x + 0. The slope is 3 – but negative 3 rather than positive 3. Cross out C.

It's got to be D. When you put D in slope intercept form, you get –y = -3x + 0, which becomes y = 3x + 0. Now you have a line with a slope of 3like the one in the question and a y-intercept of 0.

Definitely D.

Question 10

Here we are at the last question for today!

The area of a circle is less than 35π. The circumference of the circle could be:

Select all that apply.

This question asks you to recognize the relationship between the area and circumference of a circle. Therefore, you must be able to manipulateboth of these formulas. You know that the circumference of a circle is 2rπ and the area of a circle is πr2. When you know these formulas, youcan calculate the radius.

You're told that the area of the circle is less than 35π: A < 35π.

Because the area of a circle is πr2, you now know that the radius is less than the square root of 35.



You'd use the calculator to figure out that the square root of 35 is 5.92, which is just under 6.

Utilize this information to determine the range of the circumference. You know that the circumference must be less than 12π becausecircumference is 2rπ. If the radius is less than 6, then the circumference must be less than 2 x 6π: C < 12π

And, yes. You'd click on every answer that's less than 12π. Only A and B fit the bill!

That's certainly enough for today, don't you think? We'll continue our discussion of the remaining half of the test in Lesson 12.

Chapter 5

Summary

Congratulations. You've made it midway through the practice test and are closing in on Lesson 12. I'm sure you can see that the more mathproblems you do, the easier they become. If you have any questions, though, about anything we've covered, please stop by the DiscussionArea.

Until we meet again in Lesson 12, review what we've gone over today. You might also want to reorganize and recopy your Things toRemember review sheet or note cards to help solidify the concepts. And be sure to set aside some time to complete the quiz and do theassignment.

Good luck. I'm looking forward to seeing you next time!

Supplementary Material

GRE Mathematical Conventions

http://www.ets.org/s/gre/pdf/gre_math_conventions.pdf

This booklet provides an overview of the conventions the GRE observes and the assumptions it makes in the quantitative reasoning sections.

FAQs

Q: How can I get practice using the GRE's computer calculator?

A: The computerized GRE provides a calculator within the software. You learned in Lesson 2 that it works a little differently than most personalcalculators, so it's a great idea to practice with it before the exam. If you've downloaded the POWERPREP II software from the link in theSupplemental Material for Lesson 2, you have access to the calculator just as it appears on the GRE. Here's how to get to it:

1. Open the POWERPREP II software.

2. Access the Test Preview Tool.

3. Click Exit Section until you get to Section 3, Quantitative Reasoning.

4. Click Continue to enter the section.

5. From the toolbar at the top of the page, click Calc.

http://www.ets.org/s/gre/pdf/gre_math_conventions.pdf



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The calculator opens in a separate page that you can drag around your computer screen with your mouse. It stays on top of the other pages onyour computer unless you minimize it. So you can use it while you read through today's lesson. Just minimize the other pages ofthe POWERPREP II software until you can see the lesson.

Assignment

Download the GRE Mathematical Conventions booklet from the Supplemental Material for today's lesson. Read through the entire booklet.Take out your Things to Remember sheet or note cards and jot down any information from the booklet that you think is particularly important toremember for the exam.

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