Introduction To Data Sufficiency

Introduction:

DS means Data Sufficiency. Data Sufficiency is a unique question type: it consists of a question followed by two statements. Our job is to decide whether the information provided in the statements (considering each alone or both combined) is sufficient to answer the question. The most interesting and peculiar thing about Data Sufficiency is that the answer choices are standardized – they are the same for every single DS question. This does not make the questions, easier, however.

A) Statement 1 is sufficient to answer the Question.

B) Statement 2 is sufficient to answer the Question.

C) IF Statement 1 & Statement 2 are taken together, then only it is sufficient to answer the Question.

D) Statement 1 & Statement 2, each alone is sufficient to answer the Question.

E) EVEN IF Statement 1 & Statement 2 are taken together, it is not sufficient to answer the Question.

With the answer choices in mind , let’s try a SIMPLE one :

Question 01: What is the value of x ?

(1) x +1 = 2 - 3x

(2) 1/(2x) = 2

Solution : Statement 1 : x +1 = 2 - 3x --> 4x = 1 --> x = 1/4. …………Sufficient.

Statement 2 : 1/(2x) = 2 --> 4x = 1 --> x = 1/4. …………….Sufficient.

Answer : Now, As Statement 1 & Statement 2 each alone are sufficient to answer the question, the answer would be Choice D.

MAIN GOAL is to determine the sufficiency of the statements, together or alone. (The most interesting aspect, is that we do not need to determine the answer, rather we need to determine if we can answer the question with 100% certainty based on each statement provided or taken together. Data Sufficiency questions are famous for tricking users)

Saying that, let’s try a more challenging one:

Question 02: If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

Solution : Statement 1 :

−4x−12y=0−4x−12y=0

or x+3y=0x+3y=0

or x=−3yx=−3y ==> xx and yy have opposite signs . Hence, either |x|=x|x|=x and |y|=−y|y|=−y OR |x|=−x|x|=−xand |y|=y|y|=y

Implies that , either |x|+|y|=−x+y=3y+y=4y=32|x|+|y|=−x+y=3y+y=4y=32: y=8y=8, x=−24x=−24, xy=−24∗8xy=−24∗8

.................OR |x|+|y|=x−y=−3y−y=−4y=32|x|+|y|=x−y=−3y−y=−4y=32: y=−8y=−8, x=24x=24, xy=−24∗8xy=−24∗8, same answer. Sufficient.

Statement 2 :

|x|−|y|=16|x|−|y|=16. Sum this one with the equations given in the stem ==> 2|x|=482|x|=48 ==> |x|=24|x|=24, |y|=8|y|=8. xy=−24∗8xy=−24∗8 (x and y have opposite sign) or xy=24∗8xy=24∗8 (x and y have the same sign). Multiple choices. Not sufficient.

Answer: Now, As only Statement 1 is sufficient to answer the question, the answer would be Choice A.

Working With The Options(example) :

Until the answer choice selection becomes a second habit, we can follow the structure below:

Step 01: Options : ( A B C D E )

Step 2A: If Statement 01 is sufficient. Strike out B, C & E. ( A

~~B~~ ~~C~~ D

~~E~~ )

Step 2B: If Statement 02 is sufficient. Strike out A. Answer is D (

~~A~~ ~~B~~ ~~C~~ D

~~E~~ )

Step 2C: If Statement 02 is not sufficient. Strike out D. Answer is A ( A

~~B~~ ~~C~~ ~~D~~ ~~E~~ )

Step 3A: If Statement 02 is sufficient. Strike out A & D. Answer is B (

~~A~~ B C

~~D~~ E )

Step 3B: If Statement 02 is not sufficient. Strike out B. (

~~A~~ ~~B~~ C

~~D~~ E )

Step 4A: If Statements 01 & 02 together is sufficient. Strike out E. Answer is C (

~~A~~ ~~B~~ C

~~D~~ ~~E~~ )

Step 4B: If Statements 01 & 02 together is not sufficient. Strike out C. Answer is E (

~~A~~ ~~B~~ ~~C~~ ~~D~~ E )

To Start With:

This is a non-traditional idea. Thus, to get a hang of it one may go through the link below and try some 500-level questions:

500-level DS question CollectionThe Most Important Stuff:

1 . Definitely the basic need is the quant concepts. Below is the link for all you need for GMAT Quant.

Ultimate GMAT Quantitative Megathread2. Please practice the questions at different levels (Recommendation: Once your accuracy is >75% at 500-level , move to 600-level. And once you reach the accuracy >75% at 600-level , move to 700-level )

DS Question Directory by Topic and DifficultyOther Important DS Links:

PS : This document is an effort by GMAT CLUB Community to get the beginners going in terms of DATA SUFFICIENCY (DS) Questions. Special Thanks to Bunuel , bb , pushpitkc & GMAT CLUB Community.
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