ENGINEERING APTITUDE · ENGINEERING APTITUDE (QUANTATIVE APTITUDE AND ANALYTICAL ABILITY) Salient Features : • 171 topics under 25 chapters in 5 units • 531 theoretical examples

https://iesmasterpublications.com/engineering-aptitude-quantitative-aptitude-and-analytical-ability-ese-gate-psus-2019

ENGINEERING APTITUDE(QUANTATIVE APTITUDE AND ANALYTICAL ABILITY)

Salient Features :

• 171 topics under 25 chapters in 5 units• 531 theoretical examples for comprehensive understanding• 388 chapterwise solved examples for practice• 633 Questions segregated chapterwise from last 38 years of UPSC/GATE/ESE

Exams with detailed solutions

(For ESE & GATE Exam)

(CE, ME, PI, CH, EC, EE, IN, CS, IT)

Office : Phone : F-126, (Lower Basement), Katwaria Sarai, New Delhi-110016 011-26522064Mobile : E-mail:

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First Edition : 2018

Typeset at : IES Master Publication, New Delhi-110016

IES MASTER PUBLICATIONF-126, (Lower Basement), Katwaria Sarai, New Delhi-110016Phone : 011-26522064, Mobile : 8130909220, 9711853908E-mail : [email protected], [email protected] : iesmasterpublications.com, iesmaster.org

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Copyright © 2018, by IES MASTER Publications. No part of this booklet maybe reproduced, or distributed in any form or by any means, electronic,mechanical, photocopying, recording, or otherwise or stored in a database orretrieval system without the prior permission of IES MASTER, New Delhi. Violatesare liable to be legally prosecuted.

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PREFACE

Union Public Services Commission (UPSC) in its quest for best engineering minds looks for the very basic prideof an engineer, which it tests through your quantitative and analytical abilities. The profession itself calls for puttingyou in situations, both human and technical, where things are tied into hundred knots. As an engineer you areexpected to think critically, detect systematic themes while analysing data, and achieve thoroughness with accuracyin deriving solutions under challenging circumstances.

To test these qualities in an ESE aspirant, in the year 2016, UPSC introduced Engineering Aptitude as a part ofthe syllabus for common paper of ESE in 2016. With an objective to develop these abilities, IES Master has comeup with this Engineering Aptitude book that brings you face-to-face with thousands of problems under various sub-heads such as probability, polynomials, speed-time, work-time, clock and calendar, as well as geometry andmeasurements that you might encounter as a professional. Covering 171 topics under 25 chapters in 5 units, thisbook is an effort by IES Master to expose you to the complete theory of ESE syllabus along with previous yearsquestions from UPSC (last 38 years), GATE (last 9 years), and ESE (last 2 years).

As you flip through the pages of this book, it captures your imagination with subtleness, and exposes you to morethan 1,200 problems, enough to give your pen the required strength to take on any competitive exams includingESE, GATE and PSUs.

Under the expert guidance of Mr Kanchan Kumar Thakur (Ex-IES), Mr Puneet Sharma, who has more than 14years of teaching, has tamed the tornado that will blow you away, with its concept clarity and conciseness. Havinggone through it, we hope that as your fingers follow your command, the brain will engineer solutions no matter howdifficult the challenge is.

IES Master PublicationNew Delhi

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CONTENTS

UNIT 1 : QUANTITATIVE REASONING

1.1 Number System .................................................................................................. 01–40

(i) Number Line ..................................................................................................... 01

(ii) Definition of Various Types of Numbers .......................................................... 01

(iii) Various forms of Number Tree ......................................................................... 02

(iv) Concept of Prime and Composite Numbers .................................................... 04

(v) Factorization ...................................................................................................... 06

(vi) Factorial ............................................................................................................ 06

(vii) Factorization of Factorial .................................................................................. 07

(viii) Last Digit Problems .......................................................................................... 09

(ix) Number of Zeros at the End of any Product .................................................. 10

(x) Divisibility Rules ................................................................................................ 11

(xi) Relations between Dividend, Divisor and Quotient ......................................... 13

(xii) Successive Division .......................................................................................... 14

(xiii) Remainder Theorem ......................................................................................... 15

(xiv) LCM and HCF................................................................................................... 18

(xv) Indices or Powers ............................................................................................. 24

(xvi) Surds ................................................................................................................. 25

(xvii) Simplification ..................................................................................................... 28

Solved Examples ........................................................................................................ 31

Previous Years Questions UPSC/GATE/ESE ............................................................ 34

1.2 Ratio and Proportion ......................................................................................... 41–54

(i) Ratio .................................................................................................................. 41

(ii) Proportion .......................................................................................................... 43

(iii) Partnership ........................................................................................................ 46

Solved Examples ........................................................................................................ 47


VI | ENGINEERING APTITUDE GS AND ENGINEERING APTITUDE

1.3 Percentage........................................................................................................... 55–68

(i) Percentage ........................................................................................................ 55

(ii) Concept of Multiplying Factors ........................................................................ 56

(iii) Successive Percentage Change ...................................................................... 57

Solved Examples ........................................................................................................ 60


1.4 Profit and Loss................................................................................................... 69–82

(i) Profit or Gain .................................................................................................... 69

(ii) Loss ................................................................................................................... 69

(iii) Concept of Multiplying Factor Related to Profit and Loss ............................. 69

(iv) Discount ............................................................................................................ 73

(v) Three Special Cases of Profit and Loss ......................................................... 74

Solved Examples ........................................................................................................ 76


1.5 Simple Interest and Compound Interest ......................................................... 83–90

(i) Simple Interest .................................................................................................. 83

(ii) Compound Interest ........................................................................................... 83

(iii) Difference between CI and SI for First Two Years ......................................... 85

Solved Examples ........................................................................................................ 87


1.6 Average and Alligation .................................................................................... 91–116

(i) Average ............................................................................................................. 91

(ii) Problems based on Ages ................................................................................. 93

(iii) Weighted Average ............................................................................................ 95

(iv) Alligation ............................................................................................................ 96

(v) Problems based on Mixture of Two Liquids .................................................. 101

(vi) Addition of Pure Solution in a Mixture .......................................................... 102

(vii) Removal and Replacement ............................................................................ 103

Solved Examples ...................................................................................................... 107

Previous Years Questions UPSC/GATE/ESE ...........................................................111

GS AND ENGINEERING APTITUDE CONTENTS | VII

1.7 Time and Work ............................................................................................... 117–134

(i) Concept of Variation ....................................................................................... 117

(ii) Work-Time ....................................................................................................... 119

(iii) Men Days ........................................................................................................ 119

(iv) Types of Questions ......................................................................................... 120

Solved Examples ...................................................................................................... 125

Previous Years Questions UPSC/GATE/ESE .......................................................... 129

1.8 Speed, Distance and Time ............................................................................ 135–162

(i) Speed .............................................................................................................. 135

(ii) Analysis of Speed, Distance and Time Relationship .................................... 136

(iii) Average Speed ............................................................................................... 138

(iv) Relative Speed ................................................................................................ 140

(v) Boats and Streams ......................................................................................... 141

(vi) Linear and Circular Races ............................................................................. 142

Solved Examples ...................................................................................................... 147


1.9 Geometry and Mensuration........................................................................... 163–218

(i) Basic Concepts ............................................................................................... 163

(ii) Polygon ........................................................................................................... 167

(iii) Triangle ........................................................................................................... 170

(iv) Triangle Classification .................................................................................... 171

(v) Similar Triangles ............................................................................................. 177

(vi) Quadrilaterals .................................................................................................. 182

(vii) Perimeter and Areas of Quadrilaterals .......................................................... 184

(viii) Hexagon .......................................................................................................... 186

(ix) Circle ............................................................................................................... 186

(x) Properties of Circle ......................................................................................... 187

(xi) Mensuration ..................................................................................................... 193

Solved Examples ...................................................................................................... 198


VIII | ENGINEERING APTITUDE GS AND ENGINEERING APTITUDE

UNIT 2 : ANALYTICAL REASONING

2.1 Ranking Test ................................................................................................... 219–224

(i) Introduction...................................................................................................... 219

Solved Examples ...................................................................................................... 221


2.2 Dices and Cubes ............................................................................................ 225–242

(i) Cubes .............................................................................................................. 225

(ii) Types of Problems .......................................................................................... 225

(iii) Type 1 : Counting of Cubes .......................................................................... 225

(iv) Type 2 : Concept of Dice/Cube with Numbers ............................................. 226

(v) Type 3 : (Unfolded Cube/Dice) ...................................................................... 228

(vi) Type 4 : (Maximum Number of Pieces with ‘x’ Cuts) ................................... 229

(vii) Type 5 : (Minimum Number of Cuts with ‘n’ Pieces) .................................... 230

(viii) Type 6 : (Colouring of Cubes) ....................................................................... 231

Solved Examples ...................................................................................................... 235


2.3 Direction Sense .............................................................................................. 243–262

(i) Introduction...................................................................................................... 243

(ii) Reference Compass ....................................................................................... 243

(iii) Problem Solving Technique ............................................................................ 243

(iv) Types of Problems .......................................................................................... 244

(v) Type I : Shortest Distance Based Questions ................................................ 244

(vi) Type II : Direction Based Questions ............................................................. 247

(vii) Type III : Shadow Based Questions .............................................................. 248

(viii) Type IV : Clocks Based Questions ................................................................ 249

(ix) Type V : Faulty Compass Based Questions ................................................. 250

(x) Type VI : Rotation Based Questions ............................................................. 250

Solved Examples ...................................................................................................... 254


GS AND ENGINEERING APTITUDE CONTENTS | IX

2.4 Blood Relationship......................................................................................... 263–276(i) Introduction...................................................................................................... 263(ii) Symbols Used in Family Diagram ................................................................. 263(iii) Types of Questions ......................................................................................... 264(iv) Blood Relation Based on Conversation ......................................................... 264(v) Blood Relation Based on Puzzle ................................................................... 267(vi) Coded Blood Relationship .............................................................................. 268

Solved Examples ...................................................................................................... 271


2.5 Seating Arrangement ..................................................................................... 277–294(i) Introduction...................................................................................................... 277(ii) Linear Seating Arrangements ......................................................................... 277(iii) Circular Arrangement ...................................................................................... 281(iv) Two Row Sitting Arrangements ...................................................................... 283(v) Complex Arrangements ................................................................................... 285

Solved Examples ...................................................................................................... 287


2.6 Coding Decoding............................................................................................ 295–304(i) Introduction...................................................................................................... 295

(ii) Type I : Change in Relative Position of Letters ........................................... 295

(iii) Type II : Shifting of Letters to Form New Word ........................................... 295

(iv) Type III : Coding Letter to Numbers.............................................................. 297

(v) Type IV : Substitution Based Coding ............................................................ 298

(vi) Type V : Mixed Number Coding .................................................................... 298

(vii) Type VI : Mixed Letter Coding ....................................................................... 299(ix) Type VII : Direct Letter Coding ...................................................................... 300

(x) Type VIII : Mixed Type Coding ...................................................................... 300

Solved Examples ...................................................................................................... 302


2.7 Puzzles ............................................................................................................. 305–328

(i) Introduction...................................................................................................... 305

Solved Examples ...................................................................................................... 311


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X | ENGINEERING APTITUDE GS AND ENGINEERING APTITUDE

2.8 Clocks .............................................................................................................. 329–340(i) Clocks .............................................................................................................. 329(ii) Types of Problems .......................................................................................... 330(iii) Type 1: Angle Between Two Hands (when time is given) ........................... 330(iv) Type 2 : Time (when angle between two hands is given) ........................... 330(v) Type 3 : Slow and Fast Clocks ..................................................................... 332(vi) Type 4 : Overall Gain or Loss of Time ......................................................... 332(v) Type 5 : Mirror Based Problems ................................................................... 333

Solved Examples ...................................................................................................... 324


2.9 Calendars ........................................................................................................ 341–347(i) Concepts of Extra Days (or) Odd Days ........................................................ 341(ii) Important Points .............................................................................................. 341(iii) Types of Problems .......................................................................................... 342

Solved Examples ...................................................................................................... 345


UNIT 3 : CRITICAL REASONING

3.1 Basic Concepts of Syllogism ....................................................................... 348–372(i) Introduction...................................................................................................... 348(ii) Basic Terminology ........................................................................................... 348(iii) Classification of Propositions ......................................................................... 350(iv) Elimination Techniques of Venn Diagrams .................................................... 353(v) Adjectives in Syllogism ................................................................................... 354(v) Conclusions from Multiple Statements ........................................................... 354(vi) Types of Conclusions ..................................................................................... 355(vii) Special Case (The Case of “EITHER ... OR ...”) ......................................... 356

Solved Examples ...................................................................................................... 358


3.2 Critical Reasoning .......................................................................................... 373–392(i) Introduction...................................................................................................... 373(ii) Basic Terminology ........................................................................................... 373(iii) Steps Followed in Critical Reasoning ............................................................ 373(iv) Types of Questions ......................................................................................... 374

Solved Examples ...................................................................................................... 380


GS AND ENGINEERING APTITUDE CONTENTS | XI

UNIT 4 : MODERN MATHS

4.1 Sequences and Series ................................................................................... 393–422(i) Sequence ........................................................................................................ 393(ii) Series .............................................................................................................. 393(iii) Arithmetic Progression (AP) ........................................................................... 393(iv) Geometric Progression (GP) .......................................................................... 396(v) Arithmetico–Geometric Progression (AGP) .................................................... 400(vi) Harmonic Progression (HP)............................................................................ 401(vii) Sum of General Series ................................................................................... 402(viii) Hidden Sequences.......................................................................................... 405

Solved Examples ...................................................................................................... 406Previous Years Questions UPSC/GATE/ESE .......................................................... 413

4.2 Polynomials ..................................................................................................... 423–458(i) Introduction...................................................................................................... 423(ii) Algebraic Expression and Various Terms ...................................................... 423(iii) Graph of Elementary Functions ..................................................................... 425(iv) Linear Equation ............................................................................................... 426(v) Quadratic Equations ....................................................................................... 428(vi) Roots of a Polynomial of Higher Degree ...................................................... 432(vii) Maximum and Minimum Values of a Polynomial ........................................... 434(ix) Inequalities ...................................................................................................... 435(x) Quadratic Inequalities ..................................................................................... 437(xi) Modulus ........................................................................................................... 439(xii) Logarithms ....................................................................................................... 440(xiii) Logarithmic Inequalities .................................................................................. 443

Solved Examples ...................................................................................................... 445Previous Years Questions UPSC/GATE/ESE .......................................................... 450

4.3 Set Theory ....................................................................................................... 459–478(i) Set ................................................................................................................... 459(ii) Types of Set ................................................................................................... 459(iii) Venn Diagrams of Different Sets ................................................................... 461(iv) Standard Results Based on Venn Diagrams ................................................. 462(v) Algebraic Laws of Sets .................................................................................. 463(vi) Concept of maximizing or Minimizing the Intersection and Union ............... 465

Solved Examples ...................................................................................................... 467


XII | ENGINEERING APTITUDE GS AND ENGINEERING APTITUDE

4.4 Permutation and Combination ...................................................................... 479–518

(i) Fundamental Principle of Counting ................................................................ 479

(ii) Permutation ..................................................................................................... 480

(iii) Combination .................................................................................................... 482

(iv) Total Number of Combinations ....................................................................... 484

(v) Difference between Permutation and Combination ....................................... 485

(vi) Permutation of Alike Items ............................................................................. 487

(vii) Division of Items into Groups of Different Sizes ........................................... 489

(viii) Division of Different Items into Groups of Equal Size .................................. 489

(ix) Distribution of Different Items......................................................................... 491

(x) Distribution of Identical Items into Groups .................................................... 492

(xi) Circular Permutation ....................................................................................... 494

(xii) Sum of all Numbers formed from given Digits .............................................. 495

(xiii) Rank of a Word .............................................................................................. 496

(xiv) Number of Dearrangements ........................................................................... 498

(xv) If Only Selections or Rejections is to be Considered .................................. 499

(xvi) Formation of Words / Formation of Numbers ............................................... 500

Solved Examples ...................................................................................................... 502


UNIT 5 : DATA INTERPRETATION

5.1 Data Interpretation .......................................................................................... 519–562(i) Introduction...................................................................................................... 519(ii) Some Theoretical Concpets ........................................................................... 519(iii) Tables .............................................................................................................. 520(iv) Line Graph ...................................................................................................... 524(v) Bar Graph ....................................................................................................... 527(v) Pie Charts ....................................................................................................... 536(vi) Double pie charts ........................................................................................... 543(vii) Combination of Graphs .................................................................................. 546

Solved Examples ...................................................................................................... 551


NUMBER SYSTEM

NUMBER LINENumber line is a line on which all the positive and negative numbers can be represent in a sequence. It stretches fromnegative infinity to positive infinity.

–3 –2 –1 0 1 2 3+–

DEFINITION OF VARIOUS TYPES OF NUMBERS

Natural NumbersCounting Numbers 1, 2, 3, 4, ..... are called Natural Numbers. The symbolic representation is N, i.e.,N = {1, 2, 3, 4, 5, .....}.

Whole NumbersAll the natural numbers together with ‘0’ are called Whole Numbers and the symbolic representation is W, i.e.,W = {0, 1, 2, 3, 4, .....}

IntegersAn integer is a number that can be written without a fractional component, it is represented by ’Z’.Integers are further classified into positive integers (2, 4, 5 etc.), zero (0) and negative integers (–2, –5 etc.).

Rational Numbers

A number which can be expressed in the form of pq where, p and q are integers and q 0, is called a rational number..

For example : Any integer number is a rational number since, it can be written as the ratio of two integer numbers,one the integer number itself and another number is 1.

Other examples of rational number are 2 3,3 7

,… etc.

Note : A decimal represents a rational number if and only if it has a finite number of digits. But recurring decimalsare exceptions as they are also assumed as Rational Numbers, i.e., all recurring decimals are rational numbers.

Irrational Numbers

A real number, which is not rational, is called irrational number. An irrational number has non-terminating and non-recurring decimal part.Between any two numbers, there are infinite numbers of irrational numbers.

Examples of irrational numbers are : 3 43, 5, 7, 11Numbers and e are also irrational number because both have non-terminating and non-recurring decimal part.

= 3.14159265358979… and e = 2.71828182859045… where, e is called Euler’s number.

1.1

2 | ENGINEERING APTITUDE GS AND ENGINEERING APTITUDE

Note : Any terminating or recurring decimal is a rational number. Any non-terminating and non-recurring decimalis an irrational number.

Example 1

Which one of the following is not a rational number?

(a)38 (b)

11123

(c) 2 (d) None of these

Sol. (c)

The number is option (a) and (b) are rational numbers, as they are the ratio of two integers. The number 2 isnon-recurring, so it is not a rational number.

Real Numbers

The real numbers include all the measuring numbers. The symbol for the real number is R. All the numbers whichcan be represented on the number line are called real numbers.

Complex Numbers

All the numbers that can be represented in a + ib form where a & b are real numbers and i = 1 are called ComplexNumbers.

C = 2{a ib; a, b R & i 1}

VARIOUS FORMS OF NUMBER TREE

Numbers

Complex NumbersReal Numbers

Irrational NumbersRational Numbers

FactionsIntegers

Whole numbers

Natural numbers

Numbers

Integers Decimals

Terminating Non-Terminating

RecurringNon-Recurring

(Irrational Numbers)Rational Numbers

Form - 1 : Form - 2 :

Complex Numbers

Real Number IrrationalRational FractionsIntegers (–ve Integers)

Whole Number

NaturalNumbers

Form - 3 :

GS AND ENGINEERING APTITUDE NUMBER SYSTEM | 3

IES MASTER Publications

Example 2

Consider the following statements :

I. Every natural number is a real number. II. Every real number is a rational number.

III. Every integer is a real number. IV. Every rational number is a real number.

Which of the above statements are correct?

(a) I, II and III (b) I, III and IV (c) II and III (d) III and IV

Sol. (b)

From the number tree, given above, all natural numbers are real numbers but its converse is not true. So, statement(I) is true.

Every real number is not a rational number, some may be irrational numbers. Hence, statement (II) is wrong.

Similarly, from number tree, we can say about statement (III) and (IV) that both the statements are true.

Recurring Decimals

A decimal in which a digit or a set of digits is repeated continuously is called a recurring decimal. For representingrecurring decimal, we place bar on the repeated numbers.

For example : (i) The number 0.247632476324763 can be represented as 0.24763(ii) and similarly, the number 0.1555 can be represented as 0.15

Example 3

Express the recurring decimal 0.230 in the form of a fraction.

Sol.

The given decimal can be written as 0.230 = 0.230230230… …(i)As the bar is placed on three digits, so, we will multiply the above equation by 103

30.230 10 = 230.230230… …(ii)From equation (i) and (ii), we can write

3(10 1) 0.230 = 230 or 0.230 = 3230

10 1 =

230999

Example 4

The value of 1.34 4.12 is

(a)13390 (b)

37190 (c) 2195

990(d) 4615

990

Sol. (d)

The decimal 1.34 can be written as 1.34 = 1.343434… …(i)As the bar is placed on two digits after decimal point, so, we will multiply the above equation by 102

21.34 10 = 134.3434… …(ii)From equation (i) and (ii)

2(10 1) 1.34 = 133 1.34 = 13399

In 4.12 , the bar is place on one digit so it can be written as 4.12 = 4.1222 … …(i)

by multiplying 102 in above equation 24.12 10 = 412.222… …(ii)

34 | ENGINEERING APTITUDE GS AND ENGINEERING APTITUDE

1. Product of 82540027 and 43253 is

(a) 3570403787831 (b) 3570403787832

(c) 3570403787833 (d) 3570403787834

[UPSC–1985]2. In binary system, 1010 is equivalent to

(a) 8 (b) 9

(c) 10 (d) 11 [UPSC–1986]3. If n is an integer between 20 and 80, then any of

the following could be (n + 7) except

(a) 47 (b) 58

(c) 84 (d) 88 [UPSC–1988]4. Zero was invented by

(a) Aryabhata (b) Varahamihira

(c) Bhaskara I (d) An unknown Indian

[UPSC–1995]5. A person has to completely put each of three liquids:

403 litres of petrol, 465 litres of diesel and 496litres of mobil oil in bottles of equal size withoutmixing any of the above three types of liquids suchthat each bottle is completely filled. What is theleast possible number of bottles required?

(a) 34 (b) 44

(c) 46 (d) None of the above

[UPSC–2007]6. Four metal rods of lengths 78 cm, 104 cm, 117cm

and 169 cm are to be cut into parts of equal length.Each part must be as long as possible. What isthe maximum number of pieces that can be cut?

(a) 27 (b) 36

(c) 43 (d) 480 [UPSC–2009]7. Three bells toll at intervals of 9, 12 and 15 minutes

respectively. All the three begin to toll at 8am. Atwhat time will they first toll together again?

(a) 08:45 am (b) 10:30 am

(c) 11:00 am (d) 01:30 pm

[UPSC–2013]8. There are five hobby clubs in a college viz,

photography, yachting, chess, electronics andgardening. The gardening group meets every secondday, the electronics group meets every third day,

the chess group meets every fourth day, the yachtinggroup meets every fifth day and the photographygroup meets every sixth day. How many times doall the five groups meet on the same day within 180days?

(a) 3 (b) 5

(c) 10 (d) 18 [UPSC–2013]

9. A gardener has 1000 plants. He wants to plan themin such a way that the number of rows and thenumber of columns remains the same. What is theminimum number of plants that he needs more forthis purpose?

(a) 14 (b) 24

(c) 32 (d) 34 [UPSC–2013]10. Three persons start walking together and their steps

measure 40 cm, 42 cm and 45 cm respectively.What is the minimum distance each should walkso that each can cover the same distance incomplete steps?

(a) 25.20 m (b) 50.40 m

(c) 75.60 m (d) 100.80 m

[UPSC–2013]

11. Five persons fire bullets at a target at an interval of6, 7, 8, 9 and 12 sec. respectively. The number oftimes they would fire the bullets together at thetarget in an hour is.

(a) 6 (b) 7

(c) 8 (d) 9 [UPSC–2014]

12. The question is followed by two statements I and II.Mark the answer as

(a) if the question can be answered with the helpof statement I alone.

(b) if the question can be answered with the helpof statement II, alone.

(c) if both statement I and statement II are neededto answer the question.

(d) if the question cannot be answered even withthe help of both the statements.

If x, y and z are real numbers, is z – x even or odd?

(I) xyz is odd.

(II) xy + yz + zx is even. [UPSC–2014]

GS AND ENGINEERING APTITUDE NUMBER SYSTEM | 37

IES MASTER Publications

1. (a)In this problem, we will see only last digits. Theseare 7 and 3 respectively. Hence, last digit of theproduct of two numbers will be 1. Hence, option (a)is correct.

2. (c)(1001)2 =1 × 23 + 0 × 22 + 0 × 21 + 1 × 20 = 9

3. (d)Given, 20 < n < 80 So, 20 + 7 < (n + 7) < 80 + 7or, 27 < (n + 7) < 87.Hence, option (d) is not possible.

4. (d)It is not clear whether Brahm Gupta or Aryabhatawas the inventor of zero.So, option (d).

5. (b)The size of bottle required to be filled

= HCF of (403, 465 and 1496 litres)= 31 litres

The minimum possible number of bottles required

= 403 465 49631 31 31

= 13 + 15 + 16 = 44

6. (b)The maximum equal size of each piece = HCF of(78 cm, 104 cm, 117 cm and 169 cm)By factorisation method, HCF can be found as below

78 = 2 × 3 × 13104 = 2 × 2 × 2 × 13117 = 3 × 3 × 13169 = 13 × 13

HCF = 13 cm

The required number of pieces

=

78 104 117 16913 13 13 13

= (6 + 8 + 9 + 13) = 367. (c)

The time direction after which each bell toll= LCM of (9, 12 and 15 min.)= 180 min. = 3 hrs

If all the three begin to toll at 8:00 AM then thenext toll together again = 8 + 3 = 11:00 AM

8. (a)The number of days after which all the five groupsmeet same day= LCM of (2, 3, 4, 5 and 6 days) = 60 days

The number of times all the groups meet on the

same day within 180 days = 18060

= 3 times

9. (b)As the number of columns and rows are sameso, the number of plants will be a perfect square(i.e. n2).The perfect square just greater than 1000 is 1024so, the number of plants needed

= 1024 – 1000= 24 plants

10. (a)The required distance = LCM of (40 cm, 42 cm and45 cm).By factorisation method, the LCM can be found asbelow.

40 = 2 × 2 × 2 × 542 = 2 × 3 × 7

EXPLANATIONS

1. (a)

2. (c)

3. (d)

4. (d)

5. (b)

6. (b)

7. (c)

8. (a)

9. (b)

10. (a)

11. (b)

12. (a)

13. (b)

14. (c)

15. (d)

16. (b)

17. (c)

18. (d)

19. (d)

20. (c)

21. (c)

22. (7)

23. (a)

24. (c)

ANSWER KEY

25. (d)

26. (a)

27. (d)

28. (b)

29. (b)

30. (b)

31. (d)

32. (b)

33. (d)

34. (b)

35. (c)

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ENGINEERING APTITUDE · ENGINEERING APTITUDE (QUANTATIVE APTITUDE AND ANALYTICAL ABILITY) Salient Features : • 171 topics under 25 chapters in 5 units • 531 theoretical examples

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