7040279 Data 20 Sufficiency 1

8/8/2019 7040279 Data 20 Sufficiency 1

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The MBA Center Data Sufficiency


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ReadyPart One


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Beginningof section

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Hi, my name is Jeff.

Ill be your instructor for todays lesson, Da ta Sufficiency .

The speed of this lesson is up to you.

Click on the yellow action buttons at the bottomof each screen to move forward or backward

The buttons on the far right and far left take you to the next or to theprevious s ection .

Click on the forward ( Next Screen ) button to begin the lesson.


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Hey you! What happened?

I hope you were just playing.

Click on the P revious Screen button and try again.


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AimPart Two


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N ot Only M at h, bu t al s o Logic

Like Problem Solving, Data Sufficiencyquestions test basic math skills - arithmetic,algebra, geometry and word problems.

The strategies discussed in the Problem Solvinglesson are applicable here in Data Sufficiency

questions as well.But your approach will be quite different.

Data Sufficiency tests not only math, but also logic skills.

To crack them, youll need the following:1. The ability to distinguish between relevant and irrelevant data.2. The ability to determine whether you have enough information to

answer a question.

In this section, youll be provided with strategies that will give you thenecessary logic skills to solve Data Sufficiency questions.


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1. The q uestion will either ask for the value of a variable or for an answer to a yes-or-no question. Well discuss these twotypes of DS questions in a moment.

2 . Each DS problem contains two statements . These representpieces of information which can be added in order to answer the question. One or both of the statements may or may not

be sufficient to answer the question. Thats what youll beasked to determine!

3. Answer choices are the same for all Data Sufficiencyquestions. As you practice, youll become familiar with thestandard set of choices , and youll soon have them memorizedwithout even trying. But do make sure you truly have the

answer choices memorized! Youll waste a great deal of timereading through the same set of answer choices for everyData Sufficiency question.

A Data Sufficiency question is made up of three parts:


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What is x + 5 ?C an you an sw e r t h i s qu e s tion?

No way!

To do so, you need to know the value of x.

x 2 = 1

Thats no good. (1 )2 = 1, but ( 1 )2 = 1 too!

x 2 + 5 x 6 = 0

Remember the quadratic equations we looked at in the ProblemSolving lesson?

If neither the first nor the second piece of information enables you toanswer the question, combine the two and see what you can do.

Lets look at this again as a Data Sufficiency question...

W hat if I gave you t h i s piece of info rm ation?

T r y s olving t he e qu ation w it h only t h i s piece of info rm ation


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Click on the oval that corresponds with the correct answer choice.

Wh a t is x + 5 ?

(1) x 2 = 1(2 ) x 2 + 5 x 6 = 0

(A) Statement (1 ) BY ITS ELF is sufficient, but statement (2 ) byitself is not sufficient.

(B) Statement (2 ) BY ITS ELF is sufficient, but statement (1 ) byitself is not sufficient.

(C ) NE ITHER statement BY ITS ELF is sufficient, but the twostatements COMBI NE D are sufficient.

(D) E AC H statement BY ITS ELF is sufficient.(E) Statement (1 ) and statement (2 ) COMBI NE D are not

sufficient.


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Hey, way to go! Thats right, the answer is (C ).Try another one...


Wh a t is x + 5 ?

(1) x 2 = 1(2 ) x 2 2 x + 1 = 0



(C) NE ITHER statement BY ITS ELF is sufficient, but the twostatements COMBI NE D are sufficient.


sufficient.


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Sorry, the correct answer is (C ). Click on the expl a n a tion icon to seehow the previous question is done.

Then try another one...


Wh a t is x + 5 ?

(1) x 2 = 1(2 ) x 2 2 x + 1 = 0





sufficient.


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G ood job! Try one more...


Wh a t is 3 x 4 + 5 ?

(1) x 2 = 1(2 ) x 2 + 5x 6 = 0

(A) Statement (1 ) BY ITS ELF is sufficient, but statement (2 ) byitself is not sufficient.(B) Statement (2 ) BY ITS ELF is sufficient, but statement (1 ) by

itself is not sufficient.(C) NE ITHER statement BY ITS ELF is sufficient, but the two

statements COMBI NE D are sufficient.(D) E AC H statement BY ITS ELF is sufficient.

(E) Statement (1 ) and statement (2 ) COMBI NE D are notsufficient.


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Wh a t is 3 x 4 + 5 ?

(1) x 2 = 1(2 ) x 2 + 5x 6 = 0




(D) E AC H statement BY ITS ELF is sufficient.(E) Statement (1 ) and statement (2 ) COMBI NE D are notsufficient.

Sorry, the correct answer is (B ). Click on the expl a n a tion icon to seehow the previous questions done.

Then try one more...


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The correct answer to the last question is (A ).

Click on the E xpl a n a tion icon to see why.

Ask yourself this: Can the first statement find one (and just one ) valuewhich can be placed in the original question? If the answer is no, thenits not sufficient. If yes, then it is.

Then move on to statement number two. Ask yourself the samequestion for the second statement.

If necessary combine both statements and ask the question one moretime.

The preceding quadratic equations were allexamples of value q uestions .

Value questions ask for one, and only one,single value for x.


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This is a value question. A statement is not sufficient if it contains morethan one value for the variable x .

Look at each statement separately

St a tement 2

x2 + 5x - 6 = 0

Factor the equation:

(x 3 )(x 2 ) = 0

x could be 3 x 3 = 0or x could be 2 x 2 = 0

two values, not sufficient

St a tements 1 a nd 2

There is no one common variable that links the two equations.

x = 1 or x = 1 or x = 2 or x = 3

The statements combined are not sufficient .

St a tement 1

x2 = 1

x could be 1 (1 )2 = 1

x could also be 1 (1 )2 = 1


Wh a t is x + 5 ?


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T h e a nswer is (B ).

St a tement ( 2 ) BY IT S ELF is sufficient to solve t h e problem .

St a tement 1

x2 = 1

x could be 1 (1 )2 = 1

x could also be -1 (-1 )2 = 1


St a tement 2

x2 - 2 x + 1 = 0


(x - 1 ) (x - 1 ) = 0

x could be 1 x - 1 = 0or x could be 1 x - 1 = 0

one value, sufficient

Wh a t is x + 5 ?


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St a tement 1

x 2 = 1

x could be 1 (1 )2 = 1 x could also be -1 (-1 )2 = 1

two values but remember our original equation:

Wh a t is 3 x 4 + 5 ?

K no w t he r u les of parity .

If (-1) 2 = 1 then (-1) 4 = 1 also.

Statement (1 ) is sufficient!

St a tement 2

x 2 + 5 x - 6 = 0


( x - 3) ( x - 2) = 0

x could be 3 x - 3 = 0or x could be 2 x - 2 = 0


T h e a nswer is (A ).

St a tement ( 1) a lone is sufficient to solve t h e problem .

Wh a t is 3x 4 + 5 ?


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Now take a look at this one

Wh a t is t h e a re a of a rect a ngul a r la wn?

(1) 7 5 percent of t h e l a wn is mowed .(2 ) A rect a ngul a r region, 10 meters by 12

meters, is mowed, a nd t h e rest is unmowed .

(A) Statement (1 ) ALONE is sufficient to answer thequestion, but statement (2 ) alone is sufficient.

(B) Statement (2 ) ALONE is sufficient to answer thequestion, but statement (1 ) alone is not sufficient

(C) Statements (1 ) and (2 ) COMBI NE D aresufficient to answer the question, but neither alone is sufficient.

(D) Each statement BY ITS ELF is sufficient.

(E) Statements (1 ) and (2 ), alone or combined, arenot sufficient to answer the question.



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The correct answer is (C ).

Click on the E xpl a n a tion icon to see how its done.

At no time will you ever be asked to actually s olve a DS problem.Youre only asked to determine which statements are sufficient toanswer it.

The best timesaving device you have when tackling Data Sufficiencyquestions will be your ability to determine if there is or is not enoughinformation to answer a question without actually answering thequestion.

Use the Da ta Sufficiency flowc h a rt to eliminate wrong answer choices.

And whats the total area of the lawn?

If you dont know, dont worry. You dontneed to know. In fact, If you can tell me thelawns area, then youve gone too far.

Never solve a Data Sufficiency problem!


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Understand that this is a value question, so youll need to knowthe area of the enti r e la w n to answer it.

We still havent eliminated four

answer choices, so combineStatements 1 and 2.

Statement 1 :

mowed = 75% of total

Statement 1: not suff .Eliminate (A ) and (D ).Statement 2: not suff .Eliminate (B ). Statement 2 :

120 = x % of total

St a tements 1 a nd 2 :

120 = 75% of total

Combined: Sufficient!Eliminate ( E) .

Now, examine each statement separately, eliminating answer choices as you go.

a re a mowed = x% of tot a l a re a


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Because answer choices for all DS questions are always the same, thechart will apply for all DS questions in the G MAT!

As with all question types in the G MAT, eliminating some wrong answer choices is always better than eliminating none. It also improves your chances of guessing the correct answer.

P r oce ss of E rr or I dentification

The flow c ha r t helps you to use the Process of E rror Identific a tion as you work your waythrough Data Sufficiency questions.

Determining if a statement is, or is not, sufficientwill automatically rule out a number of answer

choices.


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E limin a te A, D

E limin a te B, C, E

E limin a te B

Answe

r B

Answe

r D

Answe

r A

Answe

r E

Answe

r C

SufficientInsufficient

Insufficient Sufficient Insufficient Sufficient

T h en try st a tement ( 2 )T h en try st a tement ( 2 )

Insufficient Sufficient

Consider bot h st a tements toget h er

Use t h is flowc h a rt to

elimin a tewrong a nswer c h oices w h enyou ex a mine

th est a tements .

Begin wit h st a tement ( 1)


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Begin wit h st a tement ( 2 )

E limin a te B, D

E limin a te A, C, E

E limin a te A

Answe

r A

Answe

r B

Answe

r D

Answe

r E

Answe

r C

SufficientInsufficient

Insufficient Sufficient Insufficient Sufficient

T h en try st a tement ( 1)T h en try st a tement ( 1)

Insufficient Sufficient

Consider bot h st a tements toget h er

T h e flowc h a nges if you beginwit h th e

secondst a tement .


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The MBA Center ApproachPart Three


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Following the MBA Center approach is a proven method which helpsyou:save time,avoid common ETS traps, andimprove your chances of guessing (if necessary ) the rightanswer.

MBA C ente r A ppr oac h

Follow the MBA Center approach to DataSufficiency questions every time to assure youwont be tripped up by ETS traps.

Work systematically through each problem.Read and understand the question first. Thenstart with one statement and move to the next,eliminating wrong answer choices as you go.Finally, look at both statements combined, if necessary, to determine the correct answer choice.


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Step 1: Read and understand the question before you move on to thestatements

Ask yourself, What information do I need in order toanswer the question?

Step 2 : Examine the statements separately, eliminating wronganswer choices

Step 3 : If necessary, consider the statements together

MBA C ente r A ppr oac h


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Use the MBA Center approach on the following Data Sufficiencyquestions

If x a nd y a re positive integers, w h a t is t h e v a lue of x + y?

(1) x2 = y(2 ) x > 16

(A) Statement (1 ) ALONE is sufficient to answer the question,but statement (2 ) alone is sufficient.

(B) Statement (2 ) ALONE is sufficient to answer the question,but statement (1 ) alone is not sufficient

(C) Statements (1 ) and (2 ) COMBI NE D are sufficient to answer the question, but neither alone is sufficient.


(E) Statements (1 ) and (2 ), alone or combined, are not sufficientto answer the question.


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G ood job. Now try this one

If x a nd y a re positive integers, is x + y less t h a n 2 0 ?

(1) x2 = y(2 ) x > 16



(C) Statements (1 ) and (2 ) COMBI NE D are sufficient to answer the question, but neither alone is sufficient.


(E) Statements (1 ) and (2 ), alone or combined, are notsufficient to answer the question.



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Sorry, the correct answer is ( E) . Click on the expl a n a tion icon to seehow its done. Then try this one

If x a nd y a re positive integers, is x + y less t h a n 2 0?

(1) x2 = y(2 ) x > 16



(C) Statements (1 ) and (2 ) COMBI NE D are sufficient toanswer the question, but neither alone is sufficient.





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To answer the question, you would need to be able to determine thevalues of two variables: x and y .

St a tement 1

x2 = y

x could be any number, as could

y .not sufficient

St a tement 2

x > 16

x could be any number greater

than 16not sufficient

St a tements 1 a nd 2

Together, we still dont know much. We cant determine the value of xand, therefore, we dont know y either.

Not sufficient .

If x a nd ya re

positiveintegers,wh a t is

th e v a lueof x + y ?


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The correct answer to the last question is (A ).

Did you see the difference between those last two questions?

Its not necessary to find one value for the variable in a yes-or-noquestion. Only determine whether the answer to the question isdefinitely yes or definitely no.

Take a look at the following yes-or-no questions

Underst a ndth e me a ning

of sufficient

If x a nd y a re positive integers, w h a t is t h e v a lue of x + y ?If x a nd y a re positive integers, is x + y less t h a n 2 0 ?

The first, a va lue question , should be familiar toyou by now.

The second question asked only for a yes-or-noanswer and is, therefore, a yes-or-no question .

Take a look at them again...


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For value q uestions :

A statement is sufficient if, and only if, it gives you enough informationto narrow down the answer to exactly one numerical value.

For yes-or-no q uestions : A statement is sufficient if, regardless of the values, you can answer the question with either a yes or a no.

D efinition of Su fficiency


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A statement in a yes-or-no question is su fficient if it can be answeredwith a yes or a no.


Is t h e odd integer x a prime number?

(1) x + 2 is a prime number .(2 ) x 3 is a prime number .







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G ood job! Try another one


Is t h e integer m odd ?

(1) m is a multiple of bot h 3 a nd 7.(2 ) m - 7 is a n odd integer .







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The correct answer is (B ).

Statement (1 ) says that m is a multiple of both 3 and 7.

O nly an odd integer can satisfy the statement.

3 * 7 = 21 ( odd number )

Double that and youve got 42,an even number.

Statement (1 ) is not sufficient!

Statement (2 ) alone is sufficient to answer the question.

So is m odd?

Its not important, but, no, m is an even number.

Click on the forward Next Screen button to try some Data Sufficiencyquestions on your own.


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The correct answer is (C ).

Statement (1 ) simply has too many variables.

So Does a = 1 ?

Its not important, but, yes, a = 1

G o through the lesson again if youre having trouble.Or, if youre ready, click on the forward Next Screen button to try someData Sufficiency questions on your own.

Statement (2 ) gives us the value of b . Thisdoesnt help at all!

Combine the two and were gettingsomewhere.

Statements (1 ) and (2 ) combined aresufficient to answer the question.


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Fire!Part Four


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If L ydi a is ex a ctly 1.5 times a s old a s F r a ncis, h ow old isF r a ncis?

(1) Seven years ago Lydia was exactly twice as old asFrancis.

(2) Fourteen years from now Lydia will be exactly 25percent older than Francis.

(A) Statement (1 ) ALONE is sufficient to answer the question, butstatement (2 ) alone is sufficient.

(B) Statement (2 ) ALONE is sufficient to answer the question, butstatement (1 ) alone is not sufficient

(C) Statements (1 ) and (2 ) COMBI NE D are sufficient to answer thequestion, but neither alone is sufficient.

(D) Each statement BY ITS ELF is sufficient.(E) Statements (1 ) and (2 ), alone or combined, are not sufficient to

answer the question.

Now its time for some tough ones!

Remember, because Data Sufficiency questions rely on logic as wellas math, a systematic approach is critical.

F i r e !


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G ood job. Now try this one

Wh a t is t h e tot a l a re a of t h e rect a ngle a bove ?

(1) T h e sum of t h e a re a s of rect a ngles I a nd II is 28 .(2 ) T h e sum of t h e a re a s of rect a ngles II a nd III is 2 4 .



(C) Statements (1 ) and (2 ) COMBI NE D are sufficient to answer thequestion, but neither alone is sufficient.

(D) Each statement BY ITS ELF is sufficient.(E) Statements (1 ) and (2 ), alone or combined, are not sufficient to

answer the question.

IIII II


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Sorry, the correct answer is (D ). Try this one


T h e v a lue of a cert a in c a r depreci a tes by 10

percent e a c h ye a r . Wh a t w a s t h e origin a l price of th e c a r?

(1) T h e c a r w a s purc h a sed 2 ye a rs a go, a ndits present v a lue is $ 10,000 .

(2 ) T wo ye a rs a fter t h e c a r w a s purc h a sed,its

depreci a ted v a lue w a s 8 1% of its origin a lprice .


(B) Statement (2 ) ALONE is sufficient to answer thequestion, but statement (1 ) alone is not sufficient


(D) Each statement BY ITS ELF is sufficient.(E) Statements (1 ) and (2 ), alone or combined, are not

sufficient to answer the question.


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Way to go! Try one more

In t h e multiplic a tion problem s h own a bove, e a c hof t h e symbols , , , a nd represents apositive digit (not including 0 ); If > a nd > ,

wh a t is t h e v a lue of ?

(1) = 8(2 ) = 3


(B) Statement (2 ) ALONE is sufficient to answer thequestion, but statement (1 ) alone is not sufficient(C) Statement (1 ) and (2 ) COMBI NE D are sufficient to

answer the question, but neither alone is sufficient.(D) Each of statements (1 ) and (2 ), alone or combined, are

not sufficient to answer the question.(E) Statements (1 ) and (2 ), alone or combined, are not

sufficient to answer the question.

x


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Sorry, the correct answer is ( E) . This ones a bit easier

If n is a n integer, is 3 n less t h a n 100 ?

(1) 3n + 1 > 100(2 ) 3n - 1 = 3n - 162



(C) Statement (1 ) and (2 ) COMBI NE D are sufficient to answer the question, but neither alone is sufficient.

(D) Each of statements (1 ) and (2 ), alone or combined, arenot sufficient to answer the question.



A credit c a rd comp a ny offered a promotion in 199 5


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A credit c a rd comp a ny offered a promotion in 199 5suc h

th a t a ll users of credit c a rd X would get a tr a velvouc h er

a t t h e end of t h e ye a r equ a l in v a lue to a fixedpercent a ge of t h e a mount of money c h a rged on t h ecredit c a rd for t h a t ye a r . Mr . P a vlov c h a rged d doll a rs

oncredit c a rd X a nd Mrs . P a vlov c h a rged 3, 4 00 doll a rs oncredit c a rd X . If Mr . P a vlov got a tr a vel vouc h er equ a l

inva lue to 3 8 0 doll a rs, w h a t w a s t h e v a lue of Mrs .

P a vlovstr a vel vouc h er?

(1) T h e vouc h ers were equ a l in v a lue to 0 .05doll a rs for e a c h doll a r c h a rged to credit c a rd Xin 199 5.

(2 ) d = 7 ,600



(C) Statement (1 ) and (2 ) COMBI NE D are sufficient to answer thequestion, but neither alone is sufficient.

(D) Each of statements (1 ) and (2 ), alone or combined, are not

sufficient to answer the question.(E) Statements (1 ) and (2 ), alone or combined, are not sufficient to

T h a ts rig h t! Youre onefor one . T ryone more ...


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Sorry, the correct answer is (A ). This ones easier

If a a nd b a re positive integers, w h a t percent of a is b ?

(1) 3a = 5b(2 ) a + b = 8 0



(C) Statement (1 ) and (2 ) COMBI NE D are sufficient to answer the question, but neither alone is sufficient.

(D) Each of statements (1 ) and (2 ), alone or combined, arenot sufficient to answer the question.




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Ahh! I got you that time.

The correct answer is (D ).

Download more Data Sufficiency questions from our web site, andorder our textbook for comprehensive coverage of all question types

within theG

MAT

F i r e !


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F i r e !

You got two out of three correct.

Thats not bad .


within theG

MAT


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F i r e !

Sorry, the correct answer is (B ).

You got the first question correct, but you missedthe next two .


within theG

MAT


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F i r e !

G ood job.

You got the first one wrong, but you pulled it upwith the next two.

Remember: in the actual exam, it is the earlyquestions that hold the greatest point value.

Read about the Computer-adaptive test (CAT ) inthe I nt r od uction lesson .


within theG

MAT


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F i r e !

Sorry, the correct answer is (D ).

You got the second question right, but youmissed the other two.


within theG

MAT


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F i r e !


within theG

MAT

G ood job.

You missed the first two questions, but you gotthe last one right.


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F i r e !

Then download more Data Sufficiency questions from our web site.Our textbook offers comprehensive coverage of Data Sufficiency and

all question types within theG

MAT.

Oops, the correct answer is (A ).

Take some time to review your math skills andtry this lesson again .


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Summary

Part Five


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Su mm a r y

Data Sufficiency answer choices are always thesame. Memorize them! Dont waste timereading them during the actual test.

DS questions are especially tricky and itsimportant that you closely follow the MBA Center 3-step approach to each question.

Click on the MBA Center logo to end this lesson and return to the MBACenter home page.

Step 1: Read and understand the question before you move to thestatements.

Step 2: Examine each statement separately, using the Process of

Error Identification to eliminate wrong answer choices.Step 3: Second, if necessary, consider the two statements

together.

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7040279 Data 20 Sufficiency 1