Welcome to the Magoosh GMAT Quantitative practice test with answer explanations. This is one of Magoosh’s many free GMAT practice tests designed to help you predict your GMAT scores.

This diagnostic GMAT exam includes both Data Sufficiency and Problem Solving questions, and covers the most frequently tested GMAT Quant concepts. To test your Verbal skills, go to our Magoosh GMAT Verbal Diagnostic. We recommend taking both of these together.

## Take the Magoosh GMAT Diagnostic Test

For real GMAT exam-like pacing, **give yourself 25 minutes to complete this GMAT practice quiz**; this will help ensure that the GMAT scores on this diagnostic test are accurate. This GMAT practice exercise can be seen as a “micro test” version of the real GMAT test– fewer questions, but the pacing is the same. The mix of question formats and concepts is also the same as the real test from the Graduate management Admissions Council, with Data Sufficiency and Problem Solving questions that cover all of the major GMAT exam math topics. The answer explanations you see at the end will help you learn even more about these question formats and math concepts.

Our diagnostic GMAT test assumes you are already familiar with the basic question formats. But if you need to, you can read a brief description of those two GMAT test Quantitative question types before you start the quiz. (NOTE: This is one of two free GMAT practice tests from Magoosh; we recommend taking our GMAT exam Verbal diagnostic test along with this one.)

*This quiz has 10 questions…. Take a deep breath and do your best.*

## GMAT Problem Solving and Data Sufficiency: An Overview

There are two question formats on the GMAT test’s Quantitative section: Problem Solving and Data Sufficiency. Problem Solving is just what it sounds like: you’re given a Quant problem and asked to choose the solution from the answer choices. Data Sufficiency is a little different, and is unique to the GMAT exam. Data Sufficiency is more oriented toward strategy and logical thinking than toward calculating a final answer. This format is unique to the GMAT exam, and contributes to 40% or so of your GMAT scores in Quant. (This ratio is also reflected on our diagnostic test.) So let’s quick take a closer look at Data Sufficiency.

### What is GMAT Data Sufficiency?

Data sufficiency is an essential part of any GMAT study plan. When you include this type of question in your GMAT practice, bear in mind that GMAT exam Data Sufficiency questions have a much more predictable structure than Problem Solving ones. Data Sufficiency problems will always contain the following components:

1) An initial math question.

2) Two statements that give additional information related to the math question.

3) Answer choices that ask you to decide whether one or both statements gives you the information you need to answer the question.

Note that you don’t select the actual answer to the math problem. You just decide whether you have enough information– *sufficient data*— to solve the problem. That’s the nice thing about Data Sufficiency on the GMAT exam– often you don’t need to work out the entire problem step-by-step. You only need to figure out if you *can* solve the problem.

Although each Data Sufficiency problem presents a different math question, there is– in a sense– just one Data Sufficiency question: *Can you solve this problem? Why or why not?* This is ultimately a very strategy-oriented question, so be sure to check out the strategy tips for Data Sufficiency in the answer explanations that come with your diagnostic test results.

If you want to experience the GMAT exam’s Data Sufficiency question format in greater depth before you take the Diagnostic test, check out this set of Data Sufficiency GMAT practice questions, with answer explanations. Understanding this format is crucial to good GMAT scores, both during your study plan and on test day.

### A Word on Word Problems

Word problems are by far the most commonly-tested math concept in GMAT Quantitative. Both Data Sufficiency and Problem Solving questions can also be word problems.

In fact, at least half of all Quant questions on a given GMAT exam are word problems, a statistic also reflected in our Quant Diagnostic test. (For more statistics on word problem frequency, see Magoosh’s breakdown of GMAT Quant concepts. Not that both of our free GMAT practice tests simulate real GMAT concept breakdowns.) You’ll see several word problems on the 10 question quiz above. Sharp word problem skills are great for your GMAT scores, so focus on word problems in your GMAT practice study plan.

**And on that note… take the quiz!**

## Diagnostic GMAT Scores, Answer Explanations, and Study Plan Recommendations

After you take the quiz, enter your email [optional] to get a copy of your Diagnostic GMAT scores along with answer explanations and custom recommendations for your GMAT exam prep. The custom recommendations can also be found at this direct link to our main GMAT Diagnostic test page. These recommendations divide test-takers into four different “buckets,” based on their abilities in both Quant and Verbal. These buckets are labeled Group 1, Group 2, Group 3, and Group 4. Each group comes with its own special recommendations for GMAT practice.

The GMAT prep recommendations will include a recommended study plan and additional tips and advice, based on your performance on the free GMAT practice tests. The study plans we assign to each score group are all three months long. This, typically, is the amount of prep time that most test-takers need in order to get excellent GMAT scores. With that in mind, if you feel three months isn’t the right timeline for you, you can pick a different study plan from the Magoosh GMAT exam study plan page.

## How to Use these Free GMAT Practice Tests

As mentioned above, this GMAT Quant quiz should be taken with the GMAT Verbal Quiz, and you should follow the recommendations for your score group.

Beyond that, these quizzes are a great way to start identifying your strengths and weaknesses on the GMAT exam. Rather than simply looking at your score on these free GMAT practice tests, you should carefully examine exactly which questions you missed, and why. The answer explanations in the summary you receive at the end of the test can really help you understand which concepts are in play for each question, and can give you insight into the kinds of things you should be studying. You may find you need to focus on Data Sufficiency, or on algebra, or integer properties, and so on.

Above all, remember that the GMAT scores you get today are not the GMAT scores you’re stuck with. If you scored low on this diagnostic test, don’t feel bad! This test is meant to be a starting point toward your best possible GMAT scores. And that road to better scores includes many additional materials, such as full-length free GMAT practice tests from the Graduate Management Admissions Council, and other materials, both official and unofficial. Good luck on your road to GMAT exam success!

Hey, I took this diagnostic test and scored 8 out of 10. Thanks for designing this well structured test. I wanted to know how close are the difficulty levels aligned to actual GMAT exam. The questions with level tagged as Hard and Very Hard – What would be the number of such questions on the actual day of the exam? suppose I keep on giving right answers, will I then only get such hard level of questions?

Thanks in advance

S

Hi Shalini,

We try to make our questions as similar as we can to the actual GMAT. Therefore, you could expect “Hard” and “Very Hard” questions to be similar to the more difficult questions that you’ll see on test day. As far as knowing exactly how many difficult questions you’ll get on the exam, it depends. This is because the test is adaptive! For more information on this, check out our blog post here:

Computer Adaptive Testing on the GMAT

Hi Mike,

How are you?

I have a question regarding question no 9.

Can it be solved using analytical approach i.e using graphical approach. if so can you please elaborate more on how to combine both the statements

Please see my analysis below

Statement 1

a^6 < a

a^6 -a < 0

a*(a^5 -1) 1 or a < 0

This implies both a and (a^5 -1) have the same sign i.e +ve or -ve. Not sufficient

Statement 2

a^5 < a

a^5 – a < 0

a*(a^4 -1) < 0

(a^2 + 1)*(a – 1)*a*( a+ 1) 1 or -1 < a 1 or a 1 or -1 < a < 0 from statement 2

We can see that a can still lie in either +ve or -ve region. Not sufficient

therefore E is our answer

Please share your inputs for the above solution. Is it correct?

Thanks & Regards,

Arvind

Hello Arvind,

What a great question! That shows you’ve really put some thought into this problem. Good job! 🙂

Yes, we can perform a degree of analysis on these two inequalities. I would not necessarily recommend that as the default approach for problems like this, because you can spend a lot of time and wind up at a dead end. On the test, that can be very discouraging.

In our case, though, we can draw some definite conclusions from the inequalities.

Statement (1) leads us to conclude, as you observed, that a(a^5 – 1) > 0 and therefore a and a^5 – 1 must have the same sign.

– Option 1: a is positive => a^5 – 1 is positive. So a^5 > 1. This is true for all positive numbers greater than 1.

– Option 2: a is negative => a^5 – 1 is negative. So a^5 < 1. This is true for all negative numbers. - possible outcomes of Stmt(1): a < 0 OR a > 1. So (1) is indeed insufficient.

Statement (2) leads us to conclude that a(a^4 – 1) > 0. Our knowledge of exponents should put us on watch for different outcomes because even and odd exponents can have different consequences when it comes to sign. But again, a and a^4 – 1 must have the same sign.

– Option 1: a is positive => a^4 – 1 is positive. So a^4 > 1. This, too, is true for all numbers greater than 1. So a > 1.

– Option 2: a is negative => a^4 – 1 is negative. So a^4 < 1. An even power can never yield a negative result, so we are restricted to results between 0 and 1. Our options here are -1 < a < 0. - possible outcomes of Stmt(2): -1 < a < 0 OR a > 1. And (2) is also insufficient.

Can we consider the two statements together? There’s no direct way to combine both inequalities into one inequality because we have no idea whether a^5 or a^6 is greater. But we can use our results above and look for overlap between the outcomes of (1) and (2).

(1) => a < 0 OR a > 1

(2) => -1 < a < 0 OR a > 1

What a values do these have in common? Either -1 < a < 0 OR a > 1. Therefore, the two results combined do not adequately determine whether a is positive. Using (1), (2), or both combined, we could have an a value that is positive or negative. So the correct answer is (E).

If you really want to visualize this, then replace a with x and plot the expressions x^6 – x and x^5 – x on a graphing calculator. You will see that the domains over which BOTH are positive are between -1 and 0 and greater than 1.

I hope that helps! 🙂