Data Suffiency

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The Data Sufficiency Section

Introduction

GMAT test writers use data sufficiency questions to test your ability to "reason quantitatively." This stands in

sharp contrast to the problem solving section, which is designed to test how well you manipulate numbers. If you

find yourself doing a lot of number crunching on the data sufficiency questions, you are doing something wrong.

Math Concepts You Should Know

The data sufficiency questions cover math that nearly any college-bound high school student will know. In

addition to basic arithmetic, you can expect questions testing your knowledge of averages, fractions, decimals,

algebra, factoring, and basic principles of geometry such as triangles, circles, and how to determine the areas

and volumes of simple geometric shapes.

The Answer Choices

GMAT data sufficiency questions will all have the exact same answer choices. Memorize these answer choices

before you take the exam. It will help you better utilize your time in the quantitative section. The answer choices

are summarized below as you will see them on the GMAT exam.

A. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.

B. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.

C. Both statements 1 and 2 together are sufficient to answer the question but neither statement is

sufficient alone.

D. Each statement alone is sufficient to answer the question.

E. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to

answer the statements.

Use Process of Elimination

If statement 1 is insufficient, then choices A and D can immediately be eliminated.

Similarly, if statement 2 is insufficient, then choices B and D can immediately be eliminated.

If either statement 1 or 2 is sufficient on its own, then choices C and E can be eliminated.

A Simple 4 Step Process for Answering These Questions

Many test takers make the mistake of not arming themselves with a systematic method for analyzing the answer

choices for these questions. Overlooking even one step in the process outlined below can make a big difference in

the final quantitative score you will be reporting to your selected business schools.

1.) Study the questions carefully. The questions generally ask for one of 3 things: 1) a specific value, 2) a

range of numbers, or 3) a true/false value. Make sure you know what the question is asking.

2.) Determine what information is needed to solve the problem. This will, obviously, vary depending on

what type of question is being asked. For example, to determine the area of a circle, you need to know the

circle's diameter, radius, or circumference. Whether or not statements 1 and/or 2 provide that information will

determine which answer you choose for a data sufficiency question about the area of a circle.

3.) Look at each of the two statements independently of the other. Follow the process of elimination rules

covered above to consider each statement individually.

4.) If step 3 did not produce an answer, then combine the two statements. If the two statements

combined can answer the question, then the answer choice is C. Otherwise, E.


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Data Sufficiency Tips and Strategies

Use only the information given in the questions. The GMAT CAT seeks to measure your abili ty to distinguish

facts from careless assumptions. Do notrely on a visual assessment of a diagram accompanying a geometry

question to determine angle sizes, parallel lines, etc. In addition, do not carry any information over from one

question to the next. Each question in the data sufficiency section of the GMAT stands on its own. You can count

on seeing at least a few questions where a wrong answer choice tries to capitalize on this common fallacy.

Do not get bogged down with complicated or lengthy calculations. As we stated before, these questions

are designed to test your ability to think conceptually, not to solve math problems.

Use process of elimination. This GMAT section lends itself perfectly to using the process of elimination. If time

becomes an issue, you can always look at the 2 statements in either order. Remember, the order you analyze the

two statements in doesn't matter, so long as you begin by looking at them individually. If you find statement 1

confusing, you can save time by skipping to statement 2 and seeing whether it can help you eliminate incorrect

answer choices.

Be on the lookout for statements that tell you the same thing in different words. When the 2

statements convey the same exact information, you will know, through process of elimination, that the correct

answer choice is either D or E. A favorite ploy of GMAT testers is to mix ratios and percentages. Here is an

example where Statement 2 simply states backwards the exact same information provided by Statement 1.

1. xis 50% ofy

2. the ratio ofy:xis 2:1

Make real-world assumptions where necessary. You must assume that, in certain abstract questions such

as "What is the value ofx?", thatxmight be a fraction and/or a negative number.

Practice, practice, practice. The more time you spend practicing data sufficiency questions, the better able

you will be to internalize the tips and strategies given above. You will also become very comfortable with the type

of questions from this portion of the test, and will quickly realize if there are any math areas, such as geometry

or algebra where you need to brush up your skills. When it comes time to sit for the GMAT, you will want to know

key math formulas and data relationships off the top of your head.

GMAT Data Sufficiency Questions

Below is a set of sample data sufficiency questions similar to those found in the GMAT math section. Due to the

relatively small number of questions that we have published here, we strongly recommend that you use these

only to augment your GMAT preparations.

Use the following answer choices for the questions below.

A. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.

B. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.

C. Both statements 1 and 2 together are sufficient to answer the question but neither statement is

sufficient alone.

D. Each statement alone is sufficient to answer the question.

E. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to

answer the statements.

1) If the average size of 3 accounts is $1 million, is the smallest account less than $500,000?


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1. The largest account is $1.3 million.

2. One of the accounts is $0.7 million.

2) Is the product ofxand ygreater than 60?

1. The sum ofxand yis greater than 60.

2. Each of the variables is greater than 2.

3) What is the value ofy?

1. y- 3 = 22. y2 = 25

4) What was the percent increase of Company A's stock between June 1 and June 30, 2000?

1. The stock gained $5 in value during June 2000.

2. The stock rose 12% during the first half of the month.

5) Which company reported the larger dollar increase in earnings?

1. Company A reported that its earnings increased by 5%.

2. Company B reported that its earnings increased by 7%.

6) Is xa prime number?

1. xis an even number.

2. xcan not be divided evenly by an odd number other than 1.

GMAT Data Sufficiency Answers

The following answers are provided by Test Prep New York, a company that has helped hundreds of students

radically improve their scores and gain admission to top schools. The first and only company to employ an

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1) C. Recall that the sum of the 3 accounts is $3 million. If the largest is $1.3 million, then the sum of the other

two accounts must be $1.7 million. Since the second-largest account could be $1.29 million, then the smallest

account could be $0.41 million, which is less than $0.5 million. Hence, Statement 1 by itself is insufficient.

However, if we know the value of 2 of the variables (as we do if we read statements 1 and 2 together), and the

average value of all three variables (as we do from reading the question), then we can determine the value of the

third variable. If the largest account is worth $1.3 million and the smallest is worth $0.7 million, then the third

variable must be $1.0 million. With the value of all 3 variables, we can quickly determine the value of the

smallest variable. Statements 1 and 2 together give us the information needed to answer the question.

2) C. Statement 1 by itself is not sufficient. One of the two variables could be a small fraction. (Think of 500 and

0.01.) Statement 2 by itself could yield the product of 3 and 4. However, the information from both statements is

taken together, we can definitively state that the answer to this question is "true."

3) A. Statement 1 is sufficient to determine thatxequals 5. Statement 2 only tells us thatxcould be +5 or -5.

4) E. The statements, together as well as alone, do not give enough information to answer the question. To

determine the percent change, we would need one of the additional pieces of information:
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a. The beginning stock price for the month.

b. The ending stock price for the month.

c. The percent change in the stock for the second half of the month.

5) E. The question can not be answered with the statements provided. The question asks which company's

earnings increased by more dollars, not which company's earnings increased by a greater percentage. The

different percentage rates of increase tell us nothing about either company's actual (dollar) increase in sales

unless we know each firm's starting baseline.

6) E. The question can not be answered with the statements provided. Becausexcan be an even number and

still be prime (2 is a prime number), statement 1 is insufficient. Additionally, xmight be divisible by even

numbers, so statement 2 is also insufficient.

Here's a list of useful GMAT tips that apply specifically to Data Sufficiency

questions (GMAT Quantitative section):

1. Memorize the five answer choices; they're the same for each and every Data

Sufficiency question.

2. Be careful not to carry over any information from one numbered statement

to another. (Making this mistake is remarkably easy, especially under time

pressure and in a momentary lapse of concentration.)

3. If a question asks for a numerical value (as opposed to a quantitative

expression that includes variables), the question is answerable only if a

numbered statement (1 or 2) yields one and only one possible numerical

answer not a range of values.

4. If you can eliminate either answer choice (A) or (B), then you can also

eliminate answer choice (D).

5. If either numbered statement (1 or 2) alone suffices to answer the question,

then you can eliminate answer choices (C) and (E).

6. In distinct contrast to Problem Solving geometry figures, Data Sufficiency

figures are not necessarily drawn proportionately unless a figure indicates

explicitly that it is drawn to scale. Do NOT rely on your eye to measure angle

sizes, line segment lengths, or areas. Instead, handle any Data Sufficiency

question using your knowledge of mathematics along with the numbers

provided.


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7. Data Sufficiency questions are designed to test you primarily on quantitative

concepts, not on your ability to manipulate numbers (that's what Problem

Solving questions are for). So if you find yourself doing a lot of pencil work,

you're probably on the wrong track.

8. Just as in Problem Solving questions, in Data Sufficiency questions cast in a

real-world setting you should make reasonable real-world assumptions.

Don't split hairs by looking for subtle meanings or ambiguous language. The

test-makers are not out to trick you in this way.

Here's a list of useful GMAT tips that apply specifically toProblem Solving questions (GMAT Quantitative section):

1. If the question asks for a numerical value, the answer choices will either increaseor decrease in value as you read down the list. So if you estimate roughly the sizeof number the question asks for, then you can more easily zero in on the most

viable answer choices.

2. Always look for a shortcut to crunching numbers a more intuitive way of

getting to the right answer. The typical Problem Solving question is designed toallow for a longer way as well as a shorter way of solving it. So if you find

yourself doing a lot of pencil work, then there's probably an easier way.

3. Geometry figures are drawn proportionately unless a figure indicates explicitlythat it is not drawn to scale. Nevertheless, don't rely on your eye to measure angle

sizes, line segment lengths, or areas. Instead, use your knowledge of mathematics

along with the numbers provided to solve the problem. Believe me: The test-makers are careful to ensure that no problem can be solved merely by visual

measurement or estimation.

NOTE: The one exception involves Data Interpretation questions that require you

to interpret bar graphs and line charts; you can (and should) rely on visualestimation for these questions.

4. If you're stuck, many questions allow you to work backwards by assuming

hypothetically that each answer choice in turn is the correct one, then testing it by

"plugging it in."

5. Use pencil and scratch paper for all calculations, and always check yourcalculations before confirming your response. Remember: Wrong answer choices

will anticipate commonly made computational errors, and careless errors are the#1 cause of incorrect answers in GMAT Problem Solving.

6. In handling word problems (math problems cast in a real-world setting), make

reasonable real-world assumptions. Don't split hairs by looking for subtle

meanings or ambiguous language. The test-makers are not out to trick you in thisway.


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Data Sufficiency Format, Skills Tested, and DirectionsHere are the key "specs" for GMAT Data Sufficiency questions:

How many: 13-14 questions

Where: In the 75-minute Quantitative Ability section, mixed with Problem

Solving questions

Format: Multiple-choice. A question is followed by two numbered statements,which provide specific information. You select one of 5 choices by clicking on an

oval. The 5 answer choices are the same for every Data Sufficiency question.

Skills tested: Your ability to understand arithmetic, algebra, and geometryconcepts, and your ability to reason logically about quantitative problems.(List of specific areas covered)

Directions: The following directions will appear on your screen just before

your first Data Sufficiency question (and you can access them while tackling anyData Sufficiency question by clicking on the HELP button):

Directions: This problem consists of a question and two statements, labeled (1) and (2), in

which certain data are given. You have to decide whether the data given in the statements

are sufficient for answering the question. Using the data given in the statements plus yourknowledge of mathematics and everyday facts (such as the number of days in July or the

meaning of counterclockwise), you must indicate whether:

o statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

to answer the question asked;

o statement (2) ALONE is sufficient, but statement (1) alone is not sufficient

to answer the question asked;

o BOTH statements (1) and (2) TOGETHER are sufficient to answer the

question asked, but NEITHER statement ALONE is sufficient;

o EACH statement ALONE is sufficient to answer the question asked;o statements (1) and (2) TOGETHER are NOT sufficient to answer the

question asked, and additional data specific to the problem are needed.

Numbers: All numbers used are real numbers.

Figures: A figure accompanying a data sufficiency problem will conform to theinformation given in the question, but will not necessarily conform to the additional
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information in statements (1 and 2).

Lines shown as straight can be assumed to be straight and lines that appear jagged canalso be assumed to be straight.

You may assume that positions of points, angles, regions, etc., exist in the order shownand that angle measures are greater than zero.

All figures lie in a plane unless otherwise indicated.

Note: If the data sufficiency problem asks you for the value of a quantity the data given

in the statements are sufficient only when it is possible to determine exactly one

numerical value for the quantity.

To review these directions for subsequent questions of this type, click on HELP.

Sample Data Sufficiency Question

Here's a typical GMAT-style Data Sufficiency question:

Are the majority of salespeople employed by XYZ Company commissioned?

1. The number of salespeople employed by XYZ Company exceeds the number of

employees at XYZ Company who are not salespeople.

2. The percentage of XYZ Company's salespeople who are commissioned exceedsthe percentage of employees at XYZ Company who are salespeople.

o Statement 1 ALONE is sufficient to answer the question, but statement 2 alone isNOT sufficient.

o Statement 2 ALONE is sufficient to answer the question, but statement 1 alone is

NOT sufficient.

o BOTH statements 1 and 2 TOGETHER are sufficient to answer the question, but

NEITHER statement ALONE is sufficient.o Each statement ALONE is sufficient to answer the question.

o Statements 1 and 2 TOGETHER are NOT sufficient to answer the question.

Quick Tip for Sample QuestionAsk yourself what specific information you need in order to answer the question posed.

As you consider each of the two numbered statements independently of each other, ask

yourself whether the statement provides any such information.

Analysis of Sample Question

This problem involves the concept of proportion. During the GMAT, expect to encounterat least two proportion questions (either Problem Solving or Data Sufficiency) altogether.

Notice that no arithmetical calculations are required here. That's because Data


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Sufficiency problems are designed to test you primarily on concepts, not on your ability

to solve a problem by working to a quantitative solution. (That's what Problem Solving

questions are for.)

In order to answer the question posed here, you need information about the number of

commissioned salespeople relative to the number of non-commissioned salespeople.Statement (1) alone provides no such information. [You can eliminate the first and fourth

answer choices (A and D).]

Statement (2) alone provides a meaningless comparison between percentages of two

different "wholes"; the statement provides no information about the number of

commissioned salespeople relative to the number of non-commissioned salespeople (the

"whole" being the total number of salespeople). Thus, statement (2) alone is insufficientto answer the question. [You can eliminate the second answer choice (B).]

Considered together, however, statements (1) and (2) do suffice to answer the question.

The correct response is the third answer choice (C). Statement (1) provides that morethan 50% of the employees are salespeople. Statement (2) adds that this percentage is less

than the percentage of salespeople who are commissioned. Thus, the percentage of

salespeople who are commissioned must exceed 50%, and the answer to the question

itself must be "yes." (In other words, you can answer the question considering the twostatements together.)

Data sufficiency tutorialLast updated: 13 Oct 2008

Data sufficiency questions account for about 1/3, i.e. 12 to 13, of the questions in the

quantitative section.

These questions are about working out what is necessary and sufficient data to be able toanswer a question which is very different from the usual problems solving questions you

have faced.

Once you are familiar with the format then this will make complete sense.

In this tutorial we will look at the key strategies for tackling data sufficiency questionsand work through some examples of standard 'tricks' that are used to catch you out in this

type of question.

You are expected to have completed thefractions,exponents, ratios and percents,

geometryandproperties of numbers tutorials before starting this tutorial.
http://www.prepfortests.com/gmat/tutorials/fractionshttp://www.prepfortests.com/gmat/tutorials/fractionshttp://www.prepfortests.com/gmat/tutorials/exponentshttp://www.prepfortests.com/gmat/tutorials/exponentshttp://www.prepfortests.com/gmat/tutorials/exponentshttp://www.prepfortests.com/gmat/tutorials/geometryhttp://www.prepfortests.com/gmat/tutorials/geometryhttp://www.prepfortests.com/gmat/tutorials/numberpropertieshttp://www.prepfortests.com/gmat/tutorials/fractionshttp://www.prepfortests.com/gmat/tutorials/exponentshttp://www.prepfortests.com/gmat/tutorials/geometryhttp://www.prepfortests.com/gmat/tutorials/numberproperties


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Next page: What is a data sufficiency question

What is a data sufficiency question

Last updated: 13 Oct 2008

Each data sufficiency question consists of 3 parts

The question

Statement (1)

Statement (2)

You are asked to determine which combination of the two statements is necessary andsufficient to answer the question.

Answers A-E answers for data sufficiency problems are always the same.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE

is sufficient

4. EACH statement ALONE is sufficient

5. Statements (1) and (2) TOGETHER are NOT sufficient

Data sufficiency questions are unlike most of the math questions in that you don't have to

answer the question in the first part of the problem, rather you have to work out what

information is sufficient to solve the question.

This is probably easiest to see if we look at an example.

Example data sufficiency problem

Last updated: 23 Nov 2008

This is an example of a data sufficiency problem.

Is ?

1.2.



3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONEis sufficient

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Remember, each data sufficiency problem is made up of the question,

Is ?

And two statements,

1.2.

You are asked to decide which combination of the statements is is required to answer the

question.

Have a go at this question before we look at the answer on the next page.

Explanation for example problem


Now lets work through this example of a data sufficiency problem together.

Is ?

1.

2.



3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONEis sufficient4. EACH statement ALONE is sufficient


To answer this we will have to examine each statement separately.


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Is statement (1) sufficient to answer the question?

Statement (1) tells us that .

This is true of any non-zero value of x, so x could be positive e.g. which is greater

than zero, but it could also be negative e.g. which is also greater than zero.

Therefore statement (1) is not sufficient to answer the question.



A cubing a number does not change it's sign so if cubed is positive then is positive.

Therefore statement (2) is sufficient to answer the question.

Putting it all together

We have just shown that statement (2) is sufficient to answer the question but statement

(1) is not.

This matches answer B which must be the correct answer.

In answering this question we already are starting to make use of the key strategies for

tackling data sufficiency problems so lets look at them in more detail.

Explanation for example problem


Now lets work through this example of a data sufficiency problem together.

Is ?

1.

2.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient

3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE

is sufficient4. EACH statement ALONE is sufficient


To answer this we will have to examine each statement separately.


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This is true of any non-zero value of x, so x could be positive e.g. which is greater

than zero, but it could also be negative e.g. which is also greater than zero.

Therefore statement (1) is not sufficient to answer the question.



A cubing a number does not change it's sign so if cubed is positive then is positive.

Therefore statement (2) is sufficient to answer the question.

Putting it all together

We have just shown that statement (2) is sufficient to answer the question but statement

(1) is not.

This matches answer B which must be the correct answer.

In answering this question we already are starting to make use of the key strategies for

tackling data sufficiency problems so lets look at them in more detail.

Strategies for data sufficiency questions


The basic strategies for tackling data sufficiency problems are as follows.

Learn the answer choices

Keep the statements separate

Simplify the question and data

Avoid unnecessary calculations

Use a process of elimination Learn the 'gotchas'

Let us start with learning the answer choices.



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The answers A, B, C, D and E are exactly the same for every data sufficiency question.

However they are quite confusing when you first see them. Therefore it is important the

you learn the choices so that you do not make the mistake a selecting the answer youwant in the real test.

The answers are as follows.



is sufficient



Which sounds complicated but there is a simple phrase to help you remember them, '1-2-

TEN' which stands for...

A. 1 alone is sufficient

B. 2 alone is sufficient

C. Together they are sufficient

D. Either is sufficient

E. Neither is sufficient

As you practice data sufficiency questions test your recall of the answer choice for each

possible combination of statements.



When you first start working on data sufficiency problems you will find it very easy tofall into the trap of mixing up the data statements.

To ensure you don't fall into this trap you should tackle every data sufficiency questions

in the same way.

1. Write 1 & 2 on your noteboard2. Work out whether statement 1 alone is sufficient to answer the question.

3. Mark 1 on your board with a tick or a cross depending on whether you could

answer the question with 1 alone.

4. Work out whether statement 2 alone is sufficient to answer the question.5. Mark 2 on your board with a tick or a cross depending on whether you could

answer the question with 2 alone.

6. Then work out which is the appropriate answer using the table below.


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Statement 1 Statement 2 Answer

A

B

D

C or E

You can see that in the case where neither statement is sufficient on it's own the answer

could be C, i.e. both statements together can answer the question, or E, i.e. even with

both statements together you cannot answer the question.

Therefore in this case you will need to do some more work out whether the question can

be answered with both statements.

Next page: Data sufficiency mini quiz (part I)

Data sufficiency mini quiz (part I)


To help you practice keeping the data statements separate when working on datasufficiency problems we will do the problems in this mini quiz in two parts.

In this first part of the quiz consists you are faced with a set of problems with the first

data statement and then the same set of problems again but this time with the second data

statement.

For each question/statement combination below, decide whether the statement provides

you with sufficient information to answer the question.

Statement 1

# Question Data statement Is the data sufficient?

1 What percentage of is ?

2Is an integer?

is an even number

3 Is an even number? is even
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4 What is the value of

5 Is an odd number? is an even number

Statement 2

# Question Data statement Is the data sufficient?

1 What percentage of is ?

2Is an integer?

is a multiple of

3 Is an even number? is odd

4 What is the value of

5 Is an odd number? is divisible by 3

Try answering these before we look at the answers.

Mini quiz answers (part I)


These are the answers to thedata sufficiency mini quiz (part I).

Statement 1

# Question Datastatement

Is the data sufficient?

1

What

percentage of

is ?

Yes. This gives you the ratio between and so you can

work out what percentage of is .

2Is an integer?

is an evennumber No. being an even number tells you nothing about

3Is an even

number?is even

Yes. An even times an even is even BUT an odd times

and odd is odd, so if is even then must be even. Seetheproperties of numbers tutorial for more detail.

4

What is the

value of

No. This tells you nothing about a which could be any

number so you cannot tell the value of

5Is an oddnumber?

is an evennumber

No. is even just tells you that is an integer, but itcould still be odd or even.

Statement 2

# QuestionData

statementIs the data sufficient?

1 What No. This tells you nothing about the ratio between and
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percentage of

is ?

. For example could be 1 and could be 4 which would

give you one percentage but equally could be 97 and

100 which would give a totally different percentage.

2 Is an

integer?

is amultiple of

Yes. If is a multiple of then it must be divisible by

and will be an integer.3

Is an even

number?is odd Yes. If is odd then must be even.

4What is thevalue of

No. Knowing the value of does not enable you towork out .

5Is an odd

number?

is divisible

by 3

No. could still be odd or even. For example could be 9

which is odd and divisible by 3 but it could also be 6

which is even and divisible by 3.

Now to answer the questions.

Next page: Data sufficiency mini quiz (part II)

Data sufficiency mini quiz (part II)


Inpart I of the data sufficiency mini quizwe looked at each data statements in turn forthe questions below.

Now we will look at the both statements together with each question.

Fill in the "Is 1 sufficient?" and "Is 2 sufficient?" columns with "yes" or "no" to indicate

whether each data statement is sufficient to answer the question. If you can't remember

what you answered previously then work it out again (it should not take you long).

Then fill in the "Answer" column with one of the the following GMAT answer choices.


3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONEis sufficient



If you have trouble remembering the answer choices then remember1-2-TEN.
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We have filled in the first row for you.

# Question Is 1 sufficient? Is 2 sufficient? Answer (A-E)

1

What percentage of is ?

1.

2.

Yes No A

2

Is an integer?

1. is an even number

2. is a multiple of

3

Is an even number?

1. is even

2. is odd

4

What is the value of ?

1.

2.

5

Is an odd number?

1. is an even number

2. is divisible by 3

Try to answer these before continuing the tutorial.

Next page: Mini quiz answers (part II)

Mini quiz answers (part II)


Answers topart II of the data sufficiency mini quiz.

Remind yourself what the answers A-E stand for with1-2-TEN.

# QuestionIs 1

sufficient?

Is 2

sufficient?Answer (A-E)

1 What percentage of Yes No A (1 alone)
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is ?

1.

2.

2

Is an integer?

1. is an even

number

2. is a

multiple of

No Yes B (2 alone)

3

Is an even number?

1. is even

2. is odd

Yes Yes D (Either)

4

What is the value of

?

1.

2.

No No.

Since neither on it's own can answer the

question the answer to the questioncould be C (Together) or E (Neither).

In this case using both pieces of

information you can work out what

and are and so discover the value of.

Therefore the answer is C.

5

Is an odd number?

1. is an even

number

2. is divisible

by 3

No No

Since neither on it's own can answer the

question the answer to the questioncould be C (Together) or E (Neither).

In this case even using both pieces of

information together you can't work outwhether y is odd.

Therefore the answer is E.

Next page: Simplify questions and data statements

Simplify questions and data statements

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You will find that the question and data statements are sometimes written in a way which

deliberately obscures a fairly simple meaning.

In these cases you will find it useful to simplify the statements or question to make itclearer what information you are provided or what the question you are asked is.

Example problem to simplify

If n is a positive integer, is ?

1.

2. n > 2




is sufficient4. EACH statement ALONE is sufficient


Have a go at this question before reading the explanation below.

Simplify the question

The question in this problem can be simplified.

If n is a positive integer, is ?

Firstly we can express both sides of the inequality in similar ways because we know that

So we can write the question as

But since the bases for both exponents are the same this can be simplified further to just

compare the powers.

Which means can simplify what looks like quite a complex question to, "If n is a positive

integer, is n > 3?"


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Simplify the data statements

We can also simplify the first data statement

If we take cube roots of both sides of the equation we get

Statement 2 cannot be simplified further

Solve the problem

Once you have simplified this data sufficiency problem it is easy to solve

Statement 1 tells you which is greater than 3 and so is sufficient to answer the

question.

Statement 2 tells you that which is insufficient to answer the question.

Therefore the answer is A.

Next page: Avoid unnecessary calculations

Comments (4):

1. If n is larger than 2, and n is an integer. . wouldn't that make it 3 or bigger? Then

wouldn't this be enough info to solve question for statement 2?

Anonymous on 29 Oct 2007 (permalink)

2. You know that n is an integer and n > 2 and you need to know whether n > 3.

There are two possibilities n is 3 in which case it IS NOT greater than 3 or n is 4

or more in which case it IS greater than 3.

Therefore statement 2 is not enough to answer the question.

joel on 1 Nov 2007 (permalink)

3. why isnt it n LESS THAN 3, why is it n GREATER THAN 3

Anonymous on 10 Nov 2007 (permalink)

4. I agree, n should be LESS THAN 3.
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Avoid unnecessary calculations


You are so used to working out the answer in math questions and that when you first startdata sufficiency questions it is easy to find yourself doing unnecessary calculations to

work out the answers from the data you are given.

In fact if you find yourself doing lots of calculations on a data sufficiency question then

you are almost certainly approaching it in the wrong way.

For example

What is the area of rectangle ABCD?

1. AB is 6.125cm long2. BC is 12.375 cm long



is sufficient

4. EACH statement ALONE is sufficient5. Statements (1) and (2) TOGETHER are NOT sufficient

It should be obvious to you that you need both the length and width of the rectangle to

find the area and therefore that the answer is C.

However you do not have to multiply 6.125 x 12.375 to work out the area.

Early on you will be tempted to do the calculations to find the answer in data sufficiencybecause you will lack confidence in your answers.

This is a habit that you must break as soon as possible.

You should aim to spend significantly less time on data sufficiency questions than you do

on problem solving questions because you rarely have to do any calculations.

Once you are well practiced it should take you on average about 1.5 minutes per datasufficiency question which will leave you nearer 2.5 minutes per problem solving

question.

Those extra seconds on the problem solving questions are invaluable if you are to scorewell in the quantitative section of the GMAT.

Next page: Process of elimination
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Process of elimination


If you get stuck on a data sufficiency question then you can often use a process ofelimination to give yourself a reasonable chance of getting the questions right anyway.

For example, if you have found that statement 1 is sufficient to answer the question and

you are not sure about statement 2 then you can eliminate all the answers except A (1alone) and D (Either). Even if you guess at this point you have a 50-50 chance of getting

the question right.

Similarly, if you have already found that statement 2 is sufficient to answer the question

and you are not sure about statement 1 then you can eliminate all the answers except B (2alone) and D (Either). Again this gives you a 50-50 chance of getting the question right.

On the other hand, if you have found that statement 1 is not sufficient to answer the

question and you are not sure about statement 2 then you can eliminate all the answers

except B (2 alone), C (Together) and E (Neither). Even if you guess at this point youhave a one third chance of getting the question right.

I will leave it as an exercise for you to work out which answers remain if you have

already found that statement 2 is not sufficient to answer the question.

Next page: Data sufficiency 'gotchas'

Data sufficiency 'gotchas'


There are lots of tricks or 'gotchas' that are used commonly in GMAT data sufficiency

questions to catch you out and you need to learn to spot these.

There are too many of these to list in this tutorial and learning these is a case of tryinglots of practice questions.

Once you have reviewed 100 or more practice questions you will become very familiar

with these 'gotchas' and you should aim not to fall for the same trick twice.

However, there is one 'gotcha' that is worth covering in this tutorial.
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The answer can be no

Although the data statements will never contradict one another, they may sometimes lead

to a negative answer.

Lots of beginners get caught out by data sufficiency questions where the answer is no,and mark no against the data statement without thinking.

For example

Is x even?

1. 2x is even2. x + 1 is even



is sufficient



You should be able to see that first statement does not answer the question for you. Evenif 2x is even, x could still be even or odd. So you can mark statement 1 as 'no'.

The second statement however tells you that x is odd and therefore you know that the

answer to the question is no. Be careful here, you may be tempted to mark statement 2 as

'no' but statement 2 has given you enough information to answer the question so youmust mark it as 'yes'.

Since the second statement answers the question alone and the first statement does not the

answer is B.

Next page: Summary of data sufficiency

Summary of data sufficiencyLast updated: 13 Oct 2008

We looked at some examples of data sufficiency questions and also covered the basic

strategies for data sufficiency questions.

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This will keep you from making mistakes in the real test when selecting your

answer.

Remember1-2-TEN


This is the key strategy for data sufficiency.

Study each statement separately and use your noteboard to keep a record of

whether statement 1 and/or statement 2 is sufficient to answer the question.

Simplify

When you are faced with complex looking questions or data statements it is worthspending a short time simplifying them to work out what you are really being

asked and what data you are being provided with.

Avoid unnecessary calculationsYou can save lots of time on data sufficiency questions because you usually don't

have to do any calculations.

Use a process of elimination

You can eliminate many of the answers to improve your chances of getting thequestion right even if you get stuck assessing one of the statements.

Learn the 'gotchas'

There are lots of standard tricks that are used in GMAT data sufficiency questionsto catch you out and you should learn to spot these.

Further reading

Data sufficiency posts from Jeff Sackmann's GMAT Daily Tips

Introduction to data sufficiency from Bell Curves

Data sufficiency tips from AdmissionsConsultants

Quick data sufficiency tips from Mark Alan Stewart

Next page: Practice Questions
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Data Suffiency

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