# CAT Data Sufficiency Questions and Answers Set-3 PDF

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Data Sufficiency is a vital topic in the Quantitative Aptitude (QA) section of the CAT exam. These questions test the candidate’s ability to analyze information and determine whether the data provided is sufficient to answer the given question. As such, it is essential for CAT aspirants to be familiar with various types of data-sufficiency questions and develop the necessary skills to solve them. To aid in this preparation process, we are offering Set-3 of Cat Data Sufficiency Questions and Answers in PDF format. In this article, we will provide you with the most important questions to prepare for the CAT exam with detailed solutions.

Instructions:Â Â 1Â toÂ 6

EachÂ ofÂ theÂ questionsÂ belowÂ consistsÂ ofÂ aÂ questionÂ andÂ twoÂ statementsÂ numberedÂ 1Â andÂ 2Â givenÂ belowÂ it.Â YouÂ haveÂ toÂ decideÂ whetherÂ theÂ dataÂ providedÂ inÂ theÂ statementsÂ areÂ sufficientÂ toÂ answerÂ theÂ question.

QuestionsÂ 1:

NÂ isÂ 2Â digitÂ numberÂ suchÂ thatÂ itÂ hasÂ anÂ oddÂ numberÂ ofÂ factors.Â WhatÂ isÂ theÂ sumÂ ofÂ theÂ digitsÂ ofÂ N?

StatementÂ I.Â TheÂ sumÂ ofÂ theÂ digitsÂ isÂ notÂ divisibleÂ byÂ 3
StatementÂ II.Â TheÂ sumÂ ofÂ theÂ digitsÂ isÂ even

a)Â IfÂ theÂ dataÂ inÂ statementÂ IÂ aloneÂ isÂ sufficientÂ toÂ answerÂ theÂ questionÂ whileÂ theÂ dataÂ inÂ statementÂ IIÂ aloneÂ isÂ not.
b)Â IfÂ theÂ dataÂ inÂ statementÂ IIÂ aloneÂ isÂ sufficientÂ toÂ answerÂ theÂ questionÂ whileÂ theÂ dataÂ inÂ statementÂ IÂ aloneÂ isÂ not.
c)Â IfÂ theÂ dataÂ inÂ bothÂ theÂ statementsÂ togetherÂ isÂ sufficientÂ toÂ answerÂ theÂ question.
d)Â IfÂ theÂ dataÂ inÂ eitherÂ statementÂ aloneÂ isÂ sufficient.
e)Â IfÂ theÂ dataÂ evenÂ inÂ bothÂ statementsÂ togetherÂ isÂ notÂ sufficientÂ toÂ answerÂ theÂ question.

QuestionÂ 2:

IsÂ theÂ positiveÂ integerÂ XÂ divisibleÂ byÂ 12?
StatementÂ I.Â WhenÂ XÂ isÂ dividedÂ byÂ 16Â theÂ remainderÂ isÂ 4
StatementÂ II.Â WhenÂ XÂ isÂ dividedÂ byÂ 18Â theÂ remainderÂ isÂ 6

a)Â ifÂ theÂ dataÂ inÂ statementÂ IÂ aloneÂ isÂ sufficientÂ toÂ answerÂ theÂ questionÂ whileÂ theÂ dataÂ inÂ statementÂ IIÂ aloneÂ isÂ not.
b)Â ifÂ theÂ dataÂ inÂ statementÂ IIÂ aloneÂ isÂ sufficientÂ toÂ answerÂ theÂ questionÂ whileÂ theÂ dataÂ inÂ statementÂ IÂ aloneÂ isÂ not.
c)Â ifÂ theÂ dataÂ inÂ bothÂ theÂ statementsÂ togetherÂ isÂ sufficientÂ toÂ answerÂ theÂ question.
d)Â ifÂ theÂ dataÂ inÂ eitherÂ statementÂ aloneÂ isÂ sufficient.
e)Â ifÂ theÂ dataÂ evenÂ inÂ bothÂ statementsÂ togetherÂ isÂ notÂ sufficientÂ toÂ answerÂ theÂ question.

QuestionÂ 3:

InÂ aÂ schoolÂ 40%Â ofÂ theÂ studentsÂ inÂ 12thÂ standardÂ areÂ inÂ CommerceÂ streamÂ andÂ theÂ restÂ inÂ ScienceÂ stream.Â IfÂ 20%Â ofÂ theÂ studentsÂ inÂ ScienceÂ streamÂ areÂ females,Â whatÂ isÂ theÂ percentageÂ ofÂ malesÂ inÂ theÂ commerceÂ stream?
StatementÂ I.Â TheÂ numberÂ ofÂ femalesÂ inÂ theÂ ScienceÂ streamÂ isÂ 36Â lessÂ thanÂ theÂ numberÂ ofÂ boys
StatementÂ II.Â forty-percentÂ ofÂ allÂ studentsÂ inÂ 12thÂ standardÂ areÂ females

a)Â ifÂ theÂ dataÂ inÂ statementÂ IÂ aloneÂ isÂ sufficientÂ toÂ answerÂ theÂ questionÂ whileÂ theÂ dataÂ inÂ statementÂ IIÂ aloneÂ isÂ not.
b)Â ifÂ theÂ dataÂ inÂ statementÂ IIÂ aloneÂ isÂ sufficientÂ toÂ answerÂ theÂ questionÂ whileÂ theÂ dataÂ inÂ statementÂ IÂ aloneÂ isÂ not.
c)Â ifÂ theÂ dataÂ inÂ bothÂ theÂ statementsÂ togetherÂ isÂ sufficientÂ toÂ answerÂ theÂ question.
d)Â ifÂ theÂ dataÂ inÂ eitherÂ statementÂ aloneÂ isÂ sufficient.
e)Â ifÂ theÂ dataÂ evenÂ inÂ bothÂ statementsÂ togetherÂ isÂ notÂ sufficientÂ toÂ answerÂ theÂ question.

QuestionÂ 4:

InÂ theÂ decimalÂ representationÂ ofÂ a,Â whereÂ 0Â <Â aÂ <Â 1,Â isÂ theÂ digitÂ inÂ tenthsÂ placeÂ aÂ non-zeroÂ number?
StatementÂ I:Â 16aÂ isÂ anÂ integer
StatementÂ II:Â 32aÂ isÂ anÂ integer

a)Â IfÂ theÂ dataÂ inÂ statementÂ IÂ aloneÂ isÂ sufficientÂ toÂ answerÂ theÂ questionÂ whileÂ theÂ dataÂ inÂ statementÂ IIÂ aloneÂ isÂ not.
b)Â IfÂ theÂ dataÂ inÂ statementÂ IIÂ aloneÂ isÂ sufficientÂ toÂ answerÂ theÂ questionÂ whileÂ theÂ dataÂ inÂ statementÂ IÂ aloneÂ isÂ not.
c)Â IfÂ theÂ dataÂ inÂ bothÂ theÂ statementsÂ togetherÂ isÂ sufficientÂ toÂ answerÂ theÂ question.
d)Â IfÂ theÂ dataÂ inÂ eitherÂ statementÂ aloneÂ isÂ sufficient.
e)Â IfÂ theÂ dataÂ evenÂ inÂ bothÂ statementsÂ togetherÂ isÂ notÂ sufficientÂ toÂ answerÂ theÂ question.

QuestionÂ 5:

IsÂ x(y+2)Â anÂ oddÂ number,Â whereÂ xÂ andÂ yÂ areÂ distinctÂ integers?
StatementÂ I:Â xÂ andÂ yÂ areÂ primeÂ numbers
StatementÂ II:Â y>11

a)Â IfÂ theÂ dataÂ inÂ statementÂ IÂ aloneÂ isÂ sufficientÂ toÂ answerÂ theÂ questionÂ whileÂ theÂ dataÂ inÂ statementÂ IIÂ aloneÂ isÂ not.
b)Â IfÂ theÂ dataÂ inÂ statementÂ IIÂ aloneÂ isÂ sufficientÂ toÂ answerÂ theÂ questionÂ whileÂ theÂ dataÂ inÂ statementÂ IÂ aloneÂ isÂ not.
c)Â IfÂ theÂ dataÂ inÂ bothÂ theÂ statementsÂ togetherÂ isÂ sufficientÂ toÂ answerÂ theÂ question.
d)Â IfÂ theÂ dataÂ inÂ eitherÂ statementÂ aloneÂ isÂ sufficient.
e)Â IfÂ theÂ dataÂ evenÂ inÂ bothÂ statementsÂ togetherÂ isÂ notÂ sufficientÂ toÂ answerÂ theÂ question.

QuestionÂ 6:

TwoÂ personsÂ AÂ andÂ BÂ areÂ standingÂ someÂ distanceÂ apartÂ andÂ startÂ movingÂ towardsÂ eachÂ other.Â TheyÂ meetÂ afterÂ aÂ timeÂ â€˜tâ€™Â seconds.Â WhatÂ wasÂ theÂ distanceÂ betweenÂ themÂ beforeÂ theyÂ startedÂ movingÂ towardsÂ eachÂ other?

StatementÂ 1:Â TheÂ speedsÂ ofÂ AÂ andÂ BÂ areÂ â€˜v1â€™Â andÂ â€˜v2â€™Â respectively.
StatementÂ 2:Â TheÂ speedsÂ ofÂ AÂ andÂ BÂ areÂ inÂ theÂ ratioÂ 2:3.

a)Â IfÂ theÂ dataÂ inÂ statementÂ IÂ aloneÂ isÂ sufficientÂ toÂ answerÂ theÂ questionÂ whileÂ theÂ dataÂ inÂ statementÂ IIÂ aloneÂ isÂ not.
b)Â IfÂ theÂ dataÂ inÂ statementÂ IIÂ aloneÂ isÂ sufficientÂ toÂ answerÂ theÂ questionÂ whileÂ theÂ dataÂ inÂ statementÂ IÂ aloneÂ isÂ not.
c)Â IfÂ theÂ dataÂ inÂ bothÂ theÂ statementsÂ togetherÂ isÂ sufficientÂ toÂ answerÂ theÂ question.
d)Â IfÂ theÂ dataÂ inÂ eitherÂ statementÂ aloneÂ isÂ sufficient.
e)Â IfÂ theÂ dataÂ evenÂ inÂ bothÂ statementsÂ togetherÂ isÂ notÂ sufficientÂ toÂ answerÂ theÂ question.

SolutionsÂ (1Â toÂ 6)Â

WeÂ areÂ givenÂ thatÂ NÂ isÂ aÂ twoÂ digitÂ numberÂ havingÂ oddÂ numberÂ ofÂ factors.
SoÂ weÂ canÂ sayÂ thatÂ NÂ isÂ aÂ perfectÂ square.
2Â digitÂ perfectÂ squaresÂ areÂ 16,Â 25,Â 36,Â 49,Â 64,Â 81
TheÂ sumÂ ofÂ theÂ digitsÂ ofÂ theseÂ numbersÂ isÂ asÂ follow
16Â –Â 7
25Â –Â 7
36Â –Â 9
49Â –Â 13
64Â –Â 10
81Â –Â 9
FromÂ statementÂ IÂ weÂ canÂ ruleÂ outÂ 9Â butÂ weÂ stillÂ haveÂ 4Â possibilitiesÂ left.Â HenceÂ weÂ cannotÂ answerÂ theÂ questionÂ fromÂ statementÂ IÂ alone.
FromÂ statementÂ II,Â weÂ knowÂ thatÂ theÂ sumÂ ofÂ theÂ digitsÂ isÂ even.Â Thereâ€™sÂ onlyÂ oneÂ sumÂ whichÂ isÂ even.Â i.eÂ 10Â HenceÂ fromÂ weÂ cannotÂ answerÂ theÂ questionÂ usingÂ statementÂ IIÂ alone.

WeÂ haveÂ toÂ findÂ whetherÂ theÂ givenÂ statementsÂ areÂ enoughÂ toÂ findÂ whetherÂ XÂ isÂ divisibleÂ byÂ 12Â i.e.Â XÂ isÂ divisibleÂ byÂ bothÂ 3Â andÂ 4.
FromÂ statementÂ I,Â XÂ isÂ ofÂ theÂ formÂ 16mÂ +Â 4.Â 16mÂ +Â 4Â isÂ divisibleÂ byÂ 4Â butÂ weÂ cannotÂ knowÂ whetherÂ XÂ isÂ divisibleÂ byÂ 3Â orÂ not.Â Thus,Â statementÂ IÂ aloneÂ isÂ notÂ sufficientÂ toÂ answerÂ theÂ givenÂ question.
FromÂ statementÂ II,Â XÂ isÂ ofÂ theÂ formÂ 18kÂ +Â 6.Â 18kÂ +Â 6Â isÂ divisibleÂ byÂ 3Â butÂ weÂ cannotÂ knowÂ whetherÂ XÂ isÂ divisibleÂ byÂ 4Â orÂ not.Â Thus,Â statementÂ IIÂ aloneÂ isÂ notÂ sufficientÂ sufficientÂ toÂ answerÂ theÂ givenÂ question.
IfÂ weÂ combineÂ bothÂ theÂ statementsÂ weÂ findÂ thatÂ XÂ isÂ divisibleÂ byÂ bothÂ 3Â andÂ 4.Â Thus,Â bothÂ statementsÂ togetherÂ canÂ answerÂ ifÂ XÂ isÂ divisibleÂ byÂ 12.Â Thus,Â CÂ isÂ theÂ rightÂ choice.

Let the total number of students in 12th standard be x. Then total students in Commerce = .4x and students in Science = .6x
Number of females in the Science stream = .6x \timesÃ—2 = .12x Thus, no. of males in the Science stream = .48x
From Statement I, .48x – .12x = 36
=> .36x = 36. Thus, x = 100. From this we cannot find the percentage of males in Commerce stream.
From statement II, Total girls in 12th = .4x
Thus, total girls in Commerce stream = .4x – .12x = .28x
Thus, total males in Commerce stream = Total students in Commerce – girls in Commerce = .4x – .28x = .12x
From this we can find the percent of male students in Commerce. Thus, B alone is enough to answer the given question.

I: If 16a is an integer, a can be 1/2, 1/4, 1/8, 1/16 or 0.5, 0.25, 0.125, 0.0625
Thus, from this statement, we canâ€™t infer that the tenth decimal digit is non-zero.
II: If 32a is an integer, a can be 1/2, 1/4, 1/8, 1/16, 1/32 or 0.5, 0.25, 0.125, 0.0625, 0.03125
Thus, from this statement, we canâ€™t infer that the tenth decimal digit is non-zero.
If both statements are used, we can infer that â€˜aâ€™ is one among 0.5, 0.25, 0.125, 0.0625.
But, even then we canâ€™t conclude that the tenth decimal digit is non-zero since 0.0625 has 0 has tenth decimal digit.

x(y+2)
I: x and y are prime.
So, if any of x and y is 2, x(y+2) is a even number. While, when both are odd x(y+2) is also odd.
II: y>11
This is clearly not sufficient as even y will yield even number and odd x and y will yield odd number.
Using I and II together:
So, x=2 then the number is even, and when x is odd prime number, the number is odd.
Thus, the question cannot be answered even by using both statements together.