examrace aptitude sample preview

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Examrace AptitudeSeries|1TABLE OF CONTENTSTable of Contents ...................................................................................................................................... 1Organization of the Book .......................................................................................................................... 7Math Section .......................................................................................................................................................................... 7Verbal Section ........................................................................................................................................................................ 7Basic Know Hows .................................................................................................................................... 7VOLUME I: Basic Num eracy .................................................................................................................... 9CHAPTER 1: Arithmetic ............................................................................................................................ 9Numbers & Counting ............................................................................................................................................................. 9

Lesson 1: Types of Numbers .................................................................................................................................................... 9Lesson 2: Rounding ................................................................................................................................................................10Lesson 3: Basic Arithmetic Operations ................................................................................................................................. 11Lesson 4: Properties of Negative Numbers .......................................................................................................................... 12Tips & Tricks 1: Multiplication Shortcuts ................................................................................................................................13Tips & Tricks 2: Divisibility Tests..............................................................................................................................................14Lesson 5: Simplification ..........................................................................................................................................................15Tips & Tricks 3: Cyclicity of Last Digits of Powers of Numbers ........................................................................................... 16Lesson 6: Factors and Prime Numbers ................................................................................................................................. 16Lesson 7: Special Numbers .................................................................................................................................................... 17Lesson 8: Base Numbers .......................................................................................................................................................18Lesson 9: Base Conversion to & from Decimal .................................................................................................................... 19Lesson 10: Roman Numerals .................................................................................................................................................20Tips & Tricks 4: Calculating Sum of Numbers ...................................................................................................................... 22

Fractions & Decimals...........................................................................................................................................................25 Lesson 11: Fractions ............................................................................................................................................................... 25Lesson 12: Decimals ...............................................................................................................................................................26

HCF and LCM ......................................................................................................................................................................28Lesson 13: HCF & LCM ..........................................................................................................................................................28

Ratio, Proportion & Chain Rule ...........................................................................................................................................33

Lesson 14: Ratio & Proportion ................................................................................................................................................ 33Percents ................................................................................................................................................................................35

Lesson 15: Percentages .........................................................................................................................................................35Tips & Tricks 5: Common Errors ............................................................................................................................................. 35

Exponents, Roots & Logarithms ........................................................................................................................................37Lesson 16: Exponents and Roots .......................................................................................................................................... 37Lesson 17: Surds .....................................................................................................................................................................38Lesson 18: Squares & Cubes ................................................................................................................................................. 38Lesson 19: Logarithms ............................................................................................................................................................40

Basic Statistics .....................................................................................................................................................................42

Lesson 20: Basic Statistics ..................................................................................................................................................... 42Sets & Venn Diagrams .........................................................................................................................................................45

Lesson 21: Sets & Venn Diagram ........................................................................................................................................... 45CHAPTER 2: Num ber Patterns ............................................................................................................... 48 Sequences, Series & Progressions (Arithmetic, Geometric & Harmonic) ......................................................................48

Lesson 22: Progression ........................................................................................................................................................... 48Lesson 23: Arithmetic, Geometric, Harmonic Means .......................................................................................................... 49Tips & Tricks 6: Convert Recurring Decimal to Fraction ...................................................................................................... 49

Odd Man Out .......................................................................................................................................................................52

Number Series .....................................................................................................................................................................53Tips & Tricks 7: Solving Number Series ................................................................................................................................. 53Find Next Number ...................................................................................................................................................................54Find Next Pair of Numbers .....................................................................................................................................................59

Find the Missing Numbers ..................................................................................................................................................63CHAPTER 3: Algebra .............................................................................................................................. 74Expressions ..........................................................................................................................................................................74

Lesson 24: Basic Algebraic Operations ................................................................................................................................ 74Tips & Tricks 8: Simplifying Expressions ...............................................................................................................................74

Functions ..............................................................................................................................................................................75

Lesson 25: Functions ..............................................................................................................................................................75Equations ..............................................................................................................................................................................78

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Examrace AptitudeSeries|2Lesson 26: Equations .............................................................................................................................................................. 78Solve Linear Equations in One Variable ................................................................................................................................. 78Lesson 27: Solving Linear Equations in One Variable .......................................................................................................... 78Solve Linear Equations in Multiple Variables ......................................................................................................................... 82Lesson 28: Solving Two Linear Equations in Two Variables ................................................................................................82Lesson 29: Solving Two Linear Equations in Multiple Variables .......................................................................................... 82Solve Equations by Factoring ................................................................................................................................................. 86Tips & Tricks 9: Solve Equations by Factoring ...................................................................................................................... 86Solve Quadratic Equations .....................................................................................................................................................87Lesson 30: Solving Quadratic Equations .............................................................................................................................. 87

Inequalities ............................................................................................................................................................................89Tips & Tricks 10: Solving Inequalities .....................................................................................................................................89

Absolute Value .....................................................................................................................................................................91Lesson 31: Absolute Value ...................................................................................................................................................... 91

Matrix ....................................................................................................................................................................................92Lesson 32: Matrix ....................................................................................................................................................................92CHAPTER 4: Financial Problems ............................................................................................................ 95

Cost, Income & Expenditures .............................................................................................................................................95Lesson 33: Income and Expenditures ................................................................................................................................... 95

Profit & Loss .........................................................................................................................................................................97Lesson 34: Profit & Loss .........................................................................................................................................................97

Interest Problems .................................................................................................................................................................99Lesson 35: Simple & Compound Interest ............................................................................................................................. 99

Problems on Discounts .................................................................................................................................................... 102Lesson 36: Discount ............................................................................................................................................................. 102Lesson 37: Present Worth & True Discount ....................................................................................................................... 103Lesson 38: Bankers Discount .............................................................................................................................................. 106

Stocks & Shares ............................................................................................................................................................... 108Lesson 39: Shares & Stocks ................................................................................................................................................ 108

Partnership ........................................................................................................................................................................ 110Lesson 40: Partnership ........................................................................................................................................................ 110CHAPTER 5: Comprehension and Problem Solving ............................................................................ 112

Time, Distance & Speed .................................................................................................................................................. 112Lesson 41: Time, Distance & Speed ................................................................................................................................... 112Relative Speed ...................................................................................................................................................................... 121Lesson 42: Relative Speed .................................................................................................................................................. 121Problems on Trains ............................................................................................................................................................... 124Tips & Tricks 11: Problems on Train .................................................................................................................................... 124Problems on Boats & Streams ............................................................................................................................................ 126Tips & Tricks 12: Boats & Streams ...................................................................................................................................... 126

Problems on Unitary Method .......................................................................................................................................... 127Lesson 43: Unitary Method ................................................................................................................................................. 127Problems on Rate ................................................................................................................................................................. 128Tips & Tricks 13: Rate ........................................................................................................................................................... 128Pipes & Cisterns .................................................................................................................................................................... 135Tips & Tricks 14: Pipes Filling the Tank ............................................................................................................................... 135

Problems on Ages ............................................................................................................................................................ 136Problems on Mixtures ...................................................................................................................................................... 139

Lesson 44: Alligation............................................................................................................................................................. 139Calendar and Clocks ........................................................................................................................................................ 142

Tips & Tricks 15: Clock & Time ............................................................................................................................................ 142Tips & Tricks 16: Calendar ................................................................................................................................................... 144

Temperature ...................................................................................................................................................................... 147Lesson 45: Temperature....................................................................................................................................................... 147

Races & Games ................................................................................................................................................................ 148Tips & Tricks 17: Races & Games ....................................................................................................................................... 148

Brain Teasers ..................................................................................................................................................................... 149Tips & Tricks 18: Tournaments ............................................................................................................................................ 150Tips & Tricks 19: Find the Weights ...................................................................................................................................... 152Tips & Tricks 20: Balance Puzzles ....................................................................................................................................... 152

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Examrace AptitudeSeries|3CHAPTER 6: Permutations, Combinations and Probability ................................................................. 157 Permutations & Combinations ........................................................................................................................................ 157

Lesson 46: Permutation ....................................................................................................................................................... 157Lesson 47: Combination ...................................................................................................................................................... 160

Probability .......................................................................................................................................................................... 168Lesson 48: Probability .......................................................................................................................................................... 168VOLUME II: Advanced Mathematics (Introduction) .............................................................................. 181

CHAPTER 7: Geometry ........................................................................................................................ 181 Lines and Angles .............................................................................................................................................................. 181Lesson 49: Angles and Basic Geometry ............................................................................................................................ 181Lesson 50: Lines ................................................................................................................................................................... 183

Polygons ............................................................................................................................................................................ 185Lesson 51: Polygons ............................................................................................................................................................ 185Regular Polygons .................................................................................................................................................................. 187Lesson 52: Regular Polygons .............................................................................................................................................. 187Triangles ................................................................................................................................................................................. 188Lesson 53: Triangles ............................................................................................................................................................. 188Quadrilaterals ........................................................................................................................................................................ 195Lesson 54: Quadrilateral ...................................................................................................................................................... 195Lesson 55: Trapezium .......................................................................................................................................................... 197Tips & Tricks 21: Isosceles Trapezium ................................................................................................................................ 198Tips & Tricks 22: Right Trapezium ....................................................................................................................................... 199Lesson 56: Kite ..................................................................................................................................................................... 199Lesson 57: Parallelogram .................................................................................................................................................... 200Lesson 58: Rhombus ........................................................................................................................................................... 202Tips & Tricks 23: Lozenge .................................................................................................................................................... 204Lesson 59: Rectangle ........................................................................................................................................................... 204Lesson 60: Square ................................................................................................................................................................ 206

Circles, Chords and Tangents ......................................................................................................................................... 208Lesson 61: Properties of Circle, Tangent, Chord & Secant .............................................................................................. 208Tips & Tricks 24: Degrees & Radian Values ........................................................................................................................ 212

Cyclic Quadrilateral, Tangential and Bi-Centric Quadrilateral....................................................................................... 216Lesson 62: Cyclic, Tangential & Bi-Centric Quadrilateral .................................................................................................. 216

3D Shapes: Solids and Cylinders .................................................................................................................................... 218Lesson 63: Introduction to Solids, Their Area & Volume ................................................................................................... 218

Coordinate Geometry ....................................................................................................................................................... 223Lesson 64: Coordinate Geometry ....................................................................................................................................... 223CHAPTER 8: Trigonometry ................................................................................................................... 228Lesson 65: Pythagorean Theorem ...................................................................................................................................... 228Lesson 66: Trigonometric Identities .................................................................................................................................... 228

Heights and Distances ..................................................................................................................................................... 234Tips & Tricks 25: Heights & Distances ................................................................................................................................ 234VOLUME III: Data Interpretation & Sufficiency ..................................................................................... 239 CHAPTER 9: Data Sufficiency .............................................................................................................. 239 Tips & Tricks 26: Data Sufficiency Basics ........................................................................................................................... 239CHAPTER 10: Data Interpretation-Tables ............................................................................................ 244 Tips & Tricks 27: Data Interpretation Basics ....................................................................................................................... 244Tips & Tricks 28: Tabulation Basics ..................................................................................................................................... 244

CHAPTER 11: Data Interpretation-Graphs ........................................................................................... 250 Tips & Tricks 29: Graphical Questions ................................................................................................................................ 250

Bar Graph .......................................................................................................................................................................... 250Line Graph ......................................................................................................................................................................... 253Pie Graph ........................................................................................................................................................................... 255VOLUME IV: Analytical & Logical Reasoning ....................................................................................... 258 CHAPTER 12: Analytical Ability ............................................................................................................ 258

Lesson 67: Analytical Reasoning ........................................................................................................................................ 258Problems on Comparison ................................................................................................................................................ 260

Arrangement of Single Attribute ...................................................................................................................................... 265Arrangement of Multiple Attributes ................................................................................................................................. 274Blood Relations ................................................................................................................................................................. 291

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Examrace AptitudeSeries|4Tips & Tricks 30: Blood Relations ........................................................................................................................................ 291

Directions ........................................................................................................................................................................... 294Tips & Tricks 31: Directions .................................................................................................................................................. 294CHAPTER 13: Logical Reasoning ........................................................................................................ 297 Lesson 68: Logical Reasoning ............................................................................................................................................ 297

Based on Assumptions .................................................................................................................................................... 299Lesson 69: Assumptions...................................................................................................................................................... 299Type I: Statement-Assumption ............................................................................................................................................ 301

Based on Arguments........................................................................................................................................................ 307Lesson 70: Arguments ......................................................................................................................................................... 307Lesson 71: Fallacies ............................................................................................................................................................. 308Type II: Statement-Argument ............................................................................................................................................... 312Tips & Tricks 32: Finding Strong & Weak Arguments ........................................................................................................ 312Type III: Argument Method, Strengthen-Weaken Arguments .......................................................................................... 317Tips & Tricks 33: How to Strengthen-Weaken Arguments ............................................................................................... 317Tips & Tricks 34: Finding Method of Argument .................................................................................................................. 319Type IV: Assorted Argument Questions .............................................................................................................................. 327Tips & Tricks 35: More Argument Questions Types........................................................................................................... 327

Based on Conclusions ..................................................................................................................................................... 340Lesson 72: Conclusion Questions ...................................................................................................................................... 340Type V: Statement-Conclusion ............................................................................................................................................ 341Type VI: Inference .................................................................................................................................................................. 344Type VII: Theme Detection ................................................................................................................................................... 346VOLUME V: Eth ical Decision Making & Logical Problem Solving ........................................................ 354 CHAPTER 14: Logical Problems .......................................................................................................... 354

Logic Games ..................................................................................................................................................................... 354Verification of Truth ........................................................................................................................................................... 361Factual Statements .......................................................................................................................................................... 366CHAPTER 15: Decision Making & Problem Solving ............................................................................. 369

Tips & Tricks 36: Decision Making & Judgment ................................................................................................................ 369Assertion-Reason ............................................................................................................................................................. 369

Tips & Tricks 37: Assertion-Reason Relationships ............................................................................................................ 369Cause & Effect .................................................................................................................................................................. 372

Tips & Tricks 38: Cause-Effect Relationships .................................................................................................................... 372Course of Action ............................................................................................................................................................... 376

Tips & Tricks 39: Course of Action ...................................................................................................................................... 376Decision Making ............................................................................................................................................................... 380Judgment .......................................................................................................................................................................... 384CHAPTER 16: Ethics & Moral Decision Making ................................................................................... 388

Lesson 73: Ethics & Moral Decision Making ...................................................................................................................... 388VOLUME VI: Verbal Aptitude (Mental Ability Part-I) .............................................................................. 394 CHAPTER 17: Playing with Alphabets ................................................................................................. 394 Tips & Tricks 40: Alphabet Series ........................................................................................................................................ 394

Complete the Series ......................................................................................................................................................... 394Graphical Series Completion ........................................................................................................................................... 396Find Missing Alphabet ...................................................................................................................................................... 398CHAPTER 18: Playing with Words ....................................................................................................... 400 Basics ................................................................................................................................................................................ 400

Lesson 74: Linguistic Concepts .......................................................................................................................................... 400Lesson 75: Articles, Vowels & Consonants ........................................................................................................................ 401Tips & Tricks 41: Common Confusing Words .................................................................................................................... 402

Word Meanings ................................................................................................................................................................. 405Tips & Tricks 42: Word List ................................................................................................................................................... 405

Odd Man Out .................................................................................................................................................................... 409Synonyms & Antonyms .................................................................................................................................................... 416

Tips & Tricks 43: Synonyms & Antonyms ........................................................................................................................... 416Synonyms .............................................................................................................................................................................. 416

Antonyms .............................................................................................................................................................................. 418Anagrams .......................................................................................................................................................................... 419

Tips & Tricks 44: Anagram ................................................................................................................................................... 419www.examrace.com


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Examrace AptitudeSeries|5CHAPTER 19: Coding-Decoding ......................................................................................................... 422

Tips & Tricks 45: Coding-Decoding .................................................................................................................................... 422Based on Code & Key Scheme ...................................................................................................................................... 422Based on Letter Coding ................................................................................................................................................... 423Based on Letter Rearrangement ..................................................................................................................................... 426Based on Word Parts ....................................................................................................................................................... 427CHAPTER 20: Analogies ...................................................................................................................... 432

Lesson 76: Deducing Relationships ................................................................................................................................... 432

Word Relations: Type I (Missing Word in Pairs of Words) ............................................................................................. 433Word Relations: Type II (Find Missing Word in Sentence) ............................................................................................. 443Word Relations: Type III (Given One Pair, Find the Missing Pair).................................................................................. 446Word Relations: Type IV (Find Missing Word in Word Triplets) ..................................................................................... 450Word Relations: Type V (Find Two Words to Form an Analogy) ................................................................................... 452Find Essential Element ..................................................................................................................................................... 452CHAPTER 21: Language & Grammar ................................................................................................... 459

Lesson 77: Noun ................................................................................................................................................................... 459Lesson 78: Singular & Plural ................................................................................................................................................ 459Lesson 79: Pronoun ............................................................................................................................................................. 460

Lesson 80: Verb .................................................................................................................................................................... 460Lesson 81: Sentence Structure-Subject, Predicate & Object .......................................................................................... 460Lesson 82: Tenses ................................................................................................................................................................ 462Lesson 83: Adjectives .......................................................................................................................................................... 462Lesson 84: Adverbs .............................................................................................................................................................. 463Lesson 85: Prepositions ....................................................................................................................................................... 463Lesson 86: Conjunctions ..................................................................................................................................................... 463Lesson 87: Interjections ....................................................................................................................................................... 464Lesson 88: Phrases & Clauses ............................................................................................................................................ 464Lesson 89: Verbals-Gerunds, Participles & Infinitives ....................................................................................................... 464Lesson 90: Direct & Indirect Speech................................................................................................................................... 465Lesson 91: Active & Passive Voice ..................................................................................................................................... 466Tips & Tricks 46: Common Punctuation Rules .................................................................................................................. 467Tips & Tricks 47: Common Grammatical Mistakes ........................................................................................................... 469

Sentence Correction ........................................................................................................................................................ 470Tips & Tricks 48: Using s and s ......................................................................................................................................... 470Tips & Tricks 49: Whos versus Whose ............................................................................................................................... 471Tips & Tricks 50: Their versus There ................................................................................................................................... 471Tips & Tricks 51: Correct usage of Was & Were ................................................................................................................ 473Tips & Tricks 52: Correct usage of I & Me .......................................................................................................................... 474Tips & Tricks 53: Correct use of One as a Pronoun .......................................................................................................... 474

Form Paragraphs: Order of Sentences .......................................................................................................................... 475Lesson 92: Order of Sentences ........................................................................................................................................... 475Some Fixed Sentences ........................................................................................................................................................ 477No Fixed Sentences ............................................................................................................................................................. 478CHAPTER 22: General Verbal Reasoning ............................................................................................ 486 VOLUME VII: Non-Verbal & Visual Reasoning (Mental Ability Part-II) .................................................. 494 CHAPTER 23: Abstract (Diagram matic) Reasoning ............................................................................. 494 Lesson 93: Non Verbal Reasoning ...................................................................................................................................... 494Lesson 94: Abstract Reasoning .......................................................................................................................................... 494

Find Missing Figures ........................................................................................................................................................ 495Sequence Completion ..................................................................................................................................................... 504Odd Man Out .................................................................................................................................................................... 509Replace Incorrect Tile ....................................................................................................................................................... 513

Analogies ........................................................................................................................................................................... 514Fitting Pieces ..................................................................................................................................................................... 516Problems Involving Many Shapes .................................................................................................................................. 516CHAPTER 24: Spatial (3-D ) Reasoning ................................................................................................ 518

Tips & Tricks 54: Spatial Reasoning .................................................................................................................................... 5182-D to 3-D .......................................................................................................................................................................... 518Odd Man Out .................................................................................................................................................................... 519Wooden Blocks ................................................................................................................................................................. 519

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Examrace AptitudeSeries|6Dice and Cubes ................................................................................................................................................................ 523

Tips & Tricks 55: Dice Problems .......................................................................................................................................... 523CHAPTER 25: Mechanica l Aptitude ..................................................................................................... 529 VOLUME VIII: Reading Comprehension ............................................................................................... 537 CHAPTER 26: Easy Passages .............................................................................................................. 537 Lesson 95: Reading Comprehension ................................................................................................................................. 537

Passage I ........................................................................................................................................................................... 539Passage II .......................................................................................................................................................................... 539

Passage III ......................................................................................................................................................................... 540Passage IV ......................................................................................................................................................................... 541Passage V .......................................................................................................................................................................... 541Passage VI ......................................................................................................................................................................... 541Passage VII ........................................................................................................................................................................ 542Passage VIII ....................................................................................................................................................................... 542Passage IX ......................................................................................................................................................................... 542CHAPTER 27: Moderately Difficult Passages ...................................................................................... 544 Passage I ........................................................................................................................................................................... 544Passage II .......................................................................................................................................................................... 545Passage III ......................................................................................................................................................................... 545Passage IV ......................................................................................................................................................................... 547Passage V .......................................................................................................................................................................... 548Passage VI ......................................................................................................................................................................... 548Passage VII ........................................................................................................................................................................ 549Passage VIII ....................................................................................................................................................................... 550Passage IX ......................................................................................................................................................................... 550Passage X .......................................................................................................................................................................... 551CHAPTER 28: Advanced Passages ..................................................................................................... 553 Passage I ........................................................................................................................................................................... 553Passage II .......................................................................................................................................................................... 554Passage III ......................................................................................................................................................................... 556Passage IV ......................................................................................................................................................................... 557Passage V .......................................................................................................................................................................... 559Passage VI ......................................................................................................................................................................... 561Passage VII ........................................................................................................................................................................ 562Passage VIII ....................................................................................................................................................................... 564Passage IX ......................................................................................................................................................................... 565Passage X .......................................................................................................................................................................... 566VOLUME IX: Interpersonal & Communication Skills ............................................................................ 568 CHAPTER 29: Communication Skills ................................................................................................... 568

Lesson 96: Communication Skills ....................................................................................................................................... 568CHAPTER 30: Interpersonal Skills ........................................................................................................ 577 Lesson 97: Interpersonal Skills ............................................................................................................................................ 577Appendices ........................................................................................................................................... 586

Appendix I: Word List ....................................................................................................................................................... 586Appendix II: Prefix (Root) Words with Meaning & Examples ........................................................................................ 606Appendix III: Suffix with Meaning and Examples .......................................................................................................... 610Appendix IV: Synonym List .............................................................................................................................................. 611Appendix V: Antonym List ............................................................................................................................................... 613Appendix VI: Comparative & Superlative Forms of Adjective ...................................................................................... 615Appendix VII: Units and Measurements ......................................................................................................................... 616

Basic Terms ........................................................................................................................................................................... 616Numbers ................................................................................................................................................................................ 616Units, Measurement & Conversion ..................................................................................................................................... 616Temperature Conversions .................................................................................................................................................... 617

Appendix VIII: Multiplication Tables 1 to 20 ................................................................................................................... 618Appendix IX: Common Algebraic Errors ........................................................................................................................ 618Appendix X: Animals & Their Sounds ............................................................................................................................. 618Other Books and E-Books by Examrace ............................................................................................. 620

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Examrace AptitudeSeries|8 Eta Theta Iota Kappa Lambda Mu Nu Xi Omicron Pi Rho Sigma Tau Upsilon Phi Chi Psi Omega Symbol for the currency (Indian Rupee) used in the book is `.

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Examrace AptitudeSeries|10Common Fractions: Fractions where denominator is not 10 or multiple of

it. For example,

etc.

Decimal Fractions: Fractions where denominator is 10 or multiple of 10.For example

,

etc.

Proper Fractions:In such fractions, numerator is less than denominator &their value is always less than one, e.g., , etc.

Improper Fractions:In such fractions, numerator is greater than or equalto the denominator & their value is always greater than or equal to one.

For example,

etc.

Irrational Numbers:Irrational number is number that cant be represented aswhere and are integers and is not zero & is an infinite non-recurringdecimal. Example = 3.1416What kind of number is 2?A.Natural B.Rational C. Irrational D. Fraction

Answer: C

Solution:2=1.4142135623thisisanirrationalnumber.What kind of number is

?

A.Natural B.Rational C. Irrational D. FractionAnswer: D

Solution:2=1.4142135623,thisisanirrationalnumber.

What kind of number is 2?A.Natural B.Whole C. Integer D.All of the aboveAnswer: D

Solution:Allnaturalnumberarewholenumbers&allwholenumbersareintegers.2isanaturalnumber&alsowholenumberandinteger.What type of number is ?

A.Natural B.Rational C. Irrational D. FractionAnswer: C

Solution:=3.1415926535,thisisanirrationalnumber.

What type of number is 0?A.Natural B.Rational C. Irrational D. FractionAnswer: B

Solution:Pleaserefertothedefinitionsabove.Lesson 2: RoundingA rounded number has about the same value as the original number, but is lessexact. For example, 300 would be the nearest rounded figure for 342 becausethis value lies closer to 300 than to 400.Rounding Digits: Finding out rounding digit is the first step in rounding. If

rounding to closest tens in case of whole numbers, rounding digit is 2nd

num-ber to left (tens place). In case of rounding to nearest hundred, third digit fromthe left is rounding digit (hundreds place).Rounding Natural Numbers: Once the rounding digit is known use followingrules: Rounding digit dont change, if digit to its right are between 0 to 4. Also, all

digits to its right will become 0.Rounding digit rounds up by one number, if digit to right are between 5 to 9.

All digits to its right will become 0.Rounding Decimals: If rounding numbers require decimals, use following rules:

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Examrace AptitudeSeries|112CHAPTER 5: COMPREHENSION AND PROBLEM SOLVINGTime, Distance & SpeedLesson 41: Time, Distance & SpeedDistanceUnderstanding how far 2 objects are placed numerically is distance, it is phys-ical length, or estimation based on other criteria.

Distance cant be negative Distance travelled never decreases.

Distance is scalar quantity or magnitude, while displacement is vector quan-tity & has both magnitude and direction.

Distance covered along curved path from point A to point B is distinguishedfrom straight-line distance from A to B. E.g., in case of round trip on circledisplacement is zero as one reaches the same point where one starts or inother words end point coincide. Straight-line distance equal distance trav-

elled only if path is straight line. Distance can be expressed in meter, kilometer, feet, miles etc.Time Time is expressed in seconds, minutes, hours or days etc.Speed Speed is distance covered per unit time. If speed is given by , distance by

& time taken by than, Speed, .

Time, . Distance, .

It is directly proportional to distance and inversely proportional to time. It can be in km/hr., m/sec etc.Average Speed: Average speed, is defined as total distance by total time

taken. If is total distance covered in the trip and is the total time taken for the trip, then,

. Note that average speed is not the average of speeds.

Suppose a man covers a certain distance at speed km/hr. and an equaldistance at speed km/hr. Then, the average speed during the whole jour-ney is km/hr.

Conversion between Speed Units: Speed can be converted from one unit toanother using the following formulas:

km/hr. = m/sec

m/s =

km/hr.

km/hr. = ft./sec

Important Problems Solving Concepts For a round trip distance back and forth are equal. Speed and time problems can be solved by drawing table. E.g., if G travels at

12 km/hr. M leaves 20 minutes later & travels at 36 km/hr. At what distancewould M overtake G. To solve this organize data in box with distance, speedand time with rows representing moving objects

Speed Time Speed Time = DistanceG 12 12

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Examrace AptitudeSeries|272Answer questions I to VI based on given information, , , , and travelextensively on business & 4 of them have China visa. All, apart from and ,have visas for Russia. s only visa is for Pakistan, although only and do nothave a visa for Pakistan.I. Who only has visas for China and Pakistan?

A. B. C. D. Answer: D

Solution:Followingtablerepresentsinformation.Itgivesforeachpersonthevisasthattheyhold. China China China China

Pakistan Pakistan PakistanRussia Russia Russia

Fromthetableabove,hasvisasforonlyChinaandPakistan.II. Who has the most visas?

A.

B.

C.

D.None Answer: C

Solution:ReferthetableaboveinhintforquestionI.hasvisasforallthreecountriesIII. Who travels most often?

A. B. C. D.Cannot sayAnswer: D

Solution:Datadoesnotprovideanyinformationonfrequencyoftravel.IV. Who are the two people who have identical visas?

A. & B. & C. & D. & Answer: A

Solution:ReferthetableaboveinhintforquestionI.andhaveidenticalvisas.V. How many visas does the group have between them?

A.4 B.12 C.10 D.17Answer: C

Solution:RefertableaboveinhintforquestionI.Totalnumberofvisasis2+1+3+2+2=10.VI. Which of the following is the most frequented country?

A.Pakistan B.Russia C.China D.Cannot sayAnswer: D

Solution:Datadoesnotprovideanyinformationonfrequencyoftraveltoanyparticularcountry.Answer questions I to II based on given information, , and all take a holi-day by the sea, whilst , and go hiking in the mountains. , and travel byair. , and do not enjoy their holiday.I. Who goes to the sea and does not enjoy the holiday?

A. B. C. D. Answer: B

Solution:Thetablebelowsummarizestheinformation.Sstandsforholidaybythesea,Mstandsforhikinginthemountains,AfortravelbyairandDfordonotenjoytheirholidayPerson Type Person Type Person Type M + A S + D M + A + D S S + A M + D

Itcanbeseenthatgoestotheseaanddoesnotenjoyholidays.II. Who does not travel by air and goes hiking?

A. B. C. D.Answer: D

Solution:Fromthetableabove,goeshikingbutdoesnottravelbyair.www.examrace.com


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Examrace AptitudeSeries|318Sample Stems for Weaken Argument Questions Which one of the following, if true, would most weaken the researchers or

above argument or undermines the conclusion? Prediction end of paragraph would be called into question if it were true that Which one of the following, if true, most calls question into argument that

?

Which one of the following, if true, would be biggest challenge to conclusion?Sample Stems for Strengthen Argument Questions Which one of the following, if established, does most to justify the position

advanced by the passage? Which one of the following, if true, provides the best reason in favor of the

proposal? Which one of the following, if true, most strengthens the argument or sup-

ports the proposal? Which of the following principles, if valid, helps to justify scientists reason-

ing the most? Which one of the following, if true, helps to best support the claim that ?Strategies Identify the key assumptions in the argument. It is important to understand how to strengthen or weaken assumptions, so

being proficient to identify assumptions makes it easy to choose answersthat which support or undermine them.

Correct answer choices undermine or support structurally their respective

conclusions rather than by attacking evidences directly. Finding key assumption in question is much more important than finding

answer directly that will make assumption more likely to be true or less like-ly to be true, whatever the case be.

Strengthening argument makes conclusion more likely to be true while weak-ening argument makes it somewhat less likely to be true.

In weaken questions, sometimes correct answer contradicts the statementmade in original argument.

Also argument weakening doesnt disproving it completely & strengtheningdoesnt prove it beyond doubts, i.e. they dont prove something true or falserather right answer supports or weakens required assumptions, while alsobeing relevant to hypothesis.

Example: More and more computer software that is capable of correcting notjust spelling, but also grammar and punctuation is being developed. There-fore, having good knowledge of grammar and punctuation is unnecessary forworking reporters and writers. Consequently, while training journalists, lessemphasis is placed on grammar & this helps students and professors to con-centrate on other important subjects. Which among the following, if true,weakens the argument the most, given for the recommendation above?A. Effective use of software that corrects grammar and punctuation requires

knowledge of grammatical principles.B. Most software that corrects grammar and punctuation are already in use.C. Developing more complex & ethical guidelines for reporters means that

professors in journalism schools must get time to teach such issues.D. Most of the software that correct grammar and punctuation can be run on

computers available to most of the media outlets.

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Examrace AptitudeSeries|434Solution:Starvationisthelackofnutritionandexhaustionisthelackofenergy.Moon:Satellite::Earth: ?

A.Sun B. Planet C.Solar System D.AsteroidAnswer: B

Solution:MoonisaEarthssatelliteandEarthisaplanet.Forecast:Future::Regret: ?

A.Present B.Atone C.Past D. SinsAnswer: C

Solution:Forecastdealswithfuturehappeningsandregretdealswithpastactions. Influenza: Virus::Typhoid: ?

A.Bacillus B. Parasite C.Protozoa D.BacteriaAnswer: D

Solution:Firsttermgivesthedisease&secondtermgivesitscause.Influenzaiscausedbyviruswhiletyphoidiscausedbybacteria.Fear:Threat::Anger: ?

A.Compulsion B. Panic C.Provocation D. ForceAnswer: C

Solution:Firsttermgivesafeelingwhilesecondtermgivestheactionthatcausessuchafeeling.Feararisingfromthreatandangeriscausedbyprovocationmeaningtoaggravate.Melt:Liquid::Freeze: ?

A.Ice B.Condense C.Solid D.CrystalAnswer: C

Solution:Firsttermgivesprocessofformationofsecondterm.Meltingistheprocess(ofconvertingasolid)toformliquid.Similarlyfreezingistheprocess(ofconvertingaliquid)toformsolid.Clock:Time::Thermometer: ?

A.Heat B.Radiation C. Energy D.TemperatureAnswer: D

Solution:Firsttermgivestheinstrumentusedtomeasurethesecond.Clockmeasurestimewhilethermometermeasurestemperature.Muslim:Mosque::Sikhs: ?

A.Golden Temple B.Medina C.Fire Temple D.GurudwaraAnswer: D

Solution:Secondtermgivestheplaceofworshipforthefirst.MosqueistheplaceofworshipforMuslims,GurudwaraistheplaceofworshipforSikhs(notethatGoldenTemplereferstoaspecificplace)Paw:Cat::Hoof: ?

A.Horse B. Lion C.Lamb D. ElephantAnswer: A

Solution:Firsttermgivesthenameofthefootofthesecond,i.e.,catsfootisknownaspawsimilarlyhorsesfootiscalledhoof.Eye:Myopia::Teeth: ?

A.Pyorrhea B.Cataract C.Trachoma D. EczemaAnswer: A

Solution:Secondtermgivesthediseaseoftheorgangivenbyfirstterm.Myopiaisdiseaseofeyeandpyorrheaisdiseaseofteeth.Tractor:Trailer::Horse: ?

A.Stable B.Cart C.Saddle D. EngineAnswer: B

Solution:Secondtermgivestheobjectthatispulledbythefirst.Astrailerispulledbytractorsimilarly,cartispulledbyhorse.Scribble:Write::Stammer: ?

A.Walk B. Play C.Speak D.DanceAnswer: C

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