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ETYMOLOGY, ROOT WORDS, PREFIXES AND SUFFIXES

Etymology deals with the origin of the words. One of the most effective ways to learn vocabulary is

to understand the roots of the word. Each word has a root which can be either a prefix or a suffix.These roots are derived from various languages like the Greek, Latin, French and even our ownSanskrit. Each root gives you the hint (or in some cases story behind the word) to guess what themeaning of a particular word could be. Below given is a list of few root words and the words thatoriginate from them.

ambi : bothambiguous, ambidextrous, ambivalent

ante : beforeantedate, anteroom

anti : against

antipathy, antagonistauto : self

autocrat, autobiography bene : well

beneficent, benevolent, benefactor brevis : short

brevity, abridge, abbreviate bellum : war, rebellious

belligerent, bellicose bi : two

binoculars, bicameral, bigamy biblios : a book

bibliophile, bibliomaniac, bibliography bio : life

biologycircum : around

circumspect, circumnavigate, circuitouscredo : belief

credulous, credibledis(dif,di) : apart

disjoin, differ

eu : welleulogy, euphony, eugenicsextra : beyond, outside of

extravagant, extraordinary, extrapolate


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STORIES BEHIND FEW WORDS AND PHRASES

Hazard: The word comes from the Arabic al-zahr, which means the dice. In the Western Europethe term came to be associated with a number of games using dice, which were learned during thecrusades whilst in the Holy Land. The term eventually took on the connotation of danger because,from very early on, game suing dice were associated with the risky business of gambling and conartists using corrupted dice.

Alcohol: The word comes from the Arabic al-kuhl, which originally meant a very fine powder of black lead which was used for eye makeup. It was obtained by the process of distillation or veryhigh refining and thus alcohol which is one of the very refined products was thus named.

Hobsons choice: Tobias Hobson was a Cambridge stable manager who lent horses. He insisted that the customers take the horses in the stall closest to the door or take none at all. Hence, themeaning of Hobsons choice is almost no choice at all.

Henry Ford almost gave no choice to his customers. When he introduced the first set of ford cars,he said to the customers, You can get a car of any colour as long as it is black. Isnt that aquintessential example of Hobsons choice?

Hat trick: The term originated from the most famous sport in our country, cricket. In England,when the bowler took three wickets in three successive balls, a hat was presented by the clubcommemorating the effort. The same spread into different sports.

Villain: Would you believe that the roots of the word villain are from the word village? Seems, odd right? Long ago, in England, there was a distinct separation of the class and the common folk. The

people who worked in the fields, the villagers, were thought of as beneath the nobility and wereassociated with theft from the noble. Hence, a sense of bad person came to be associated with the

people from villages. While in the present context, villains are no longer considered to be peoplefrom the villages, the association of the person being bad remained with the word.

Tongue in cheek: The commonly used phrase meaning to speak insincerely, comes from thehabitual gesture of Old ages where it was a practice to signal disregard for someone or something bymaking a bulge in your cheek using your tongue.

Let the cat out of the bag: To let the cat out of the bag is to reveal a secret. In olden days, artfultraders substituted a pig suckling with a cat and placed that in a bag so that the customer would notnotice it. If the cat jumped out of the bag, then the secret was out.


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CONTEXTUAL VOCABULARY

Contextual Vocabulary: As the name suggests it is about understanding the meaning of a word

based on the context.You can guess the meaning of the word based on some clues.

Example : The couple finally secured a table at the popular, crowded restaurant.What comes into your mind when you think of the word secured ?

Secured first rank - obtained Secured 100 marks - scored Is your house secure? - insured/safeIs the car door secure? - locked

But in the above example we are talking about secured a table which means the couple was finallyable to get a table and sit and have food.Clue: Since the words have multiple meanings -understand the meaning based on the

given situation .

Example : The kings laws were often arbitrary ; in other words, he made rules based on how he feltat the moment.in other words connects "arbitrary" and "he is making rules based on what he felt at the moment."Clue: Look for a word that is synonym to the given unknown word.

Example : David was very outgoing as opposed to his coy older sister.As opposed to means Davids character is opposite to that of his sister.

David is outgoing. His sister is not outgoing. So, coy means not outgoing.Clue: Look for a word that is an antonym to the given unknown word .

Example : Abhishek had to duck under the doorway as he walked into the room.We know the word duck means a bird. We also know duck out in cricket.But what does to duck here mean ?We can infer that Abhishek is very tall and he has to bend under the doorwayClue: A meaning may not be explicitly given, you have to infer it.

Understand the meaning of the italic word in the following sentences. The fisherman cast his line. The members of the cast took a bow. They put a cast on my broken arm. The yard is littered with shells cast off by - the cicadas.


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ABDICATE: Abdicate the throne. Abdicate mains to relinquish throne formally (It can never happen in the current politics). It is similar to give up. Antonyms will be related to take.

Relinquish

Hand over

Renounce

UsurpSeize

Besiege(to tryfor a long time)

Abdicate

ABHOR: I abhor that man. You can never imagine humans without likes and dislikes. Abhor means to detest, hate, reject. Antonyms will be related to like. You should understand the intensityvariation between dislike and hate.

Hate

Detest

Strongdislike

Aversion(mild)

Despise

Odious

Abominate(very

strong)

Loathe

ApproveLove

Like

Adore

Relish Abhor


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THE HIGH IMPACT WORD LIST

Word Meaning

AABACUS (n) a frame with balls for calculatingABATE (v) to lessen, to subside******************************************************************Usage : Though the current storm abated, the tourists feared the impending one.* * * * * * * * * ** * * * * * * * * * * * ** * * * * * * * * * * ** * * * * * * * * * * * ** * * * * * * * * ** * * * *ABDICATION (n) giving up control or authorityABERRATION (n) abnormalityABET (v) help or encourage to do something wrongABEYANCE (n) suspended action

ABHOR (v) to hate* * * * * * * * * * * ** * * * * * * * * * * * ** * * * * * * * * * * * * * ** * * * * * * * * * * ** * * * * * * * * * *Usage : She loves dogs, but she abhors cats.********************************************************************ABIDE (v) to endure, be faithfulABJURE (v) promise or swear to give up*****************************************************************Usage : After the chowri-chora incident, Gandhji abjured his non-cooperation movement.*****************************************************************ABRADED (v) rubbed off, worn away by frictionABROGATE (v) nullify by authority

ABSCOND (v) run away to avoid arrest*****************************************************************Usage : The police are after the accountant who absconded with money from the bank.*****************************************************************ABSTRUSE (adj) difficult to under stand *****************************************************************Usage : Geometry is not rocket science. Why do you find it so abstruse ?*****************************************************************ABUT (v) border onABYSMAL (adj) so deep as to be immeasurableACARPOUS (adj) effete, no longer fertile, worn out*****************************************************************Usage: The villagers despised her for being an acarpous woman.*****************************************************************ACCLAIMED (v) welcomed with shouts and approval


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G R E S a m p

l eGRE

Verbal Ability

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INTRODUCTION TO GRE VERBAL SECTION

Introduction to the Verbal Reasoning measure:

The Verbal reasoning measure assesses:

Your ability to analyze and evaluate written material and synthesize information obtained from it.

Analyze relationship among the component parts of a sentence.

Recognize relationships among words and concepts.

Verbal reasoning questions appear in several formats. Each of which is discussed later in this section.About half the measure requires you to read the passage and answer questions on those passages.The other half requires you to read, interpret and complete existing sentences, group of sentences,or paragraphs. Most, but not all, of the questions are standard multiple-choice questions, the differentresponse patterns are:

Select the correct option

Select multiple correct options

Select the correct sentence from the paragraph

The number of choices varies depending on the type of question.

Structure of Verbal Reasoning measure:

The test has 2 sections of Verbal each of approximately 20 Questions per section. Time for eachsection is 30 mins. The directions at the beginning of the section specifies, the number of questionsand time allowed for the section.

There will also be an unidentified unscored section which may be based on Verbal or Quant withapproximately 20 Questions and 30 - 35 mins per section.

Verbal/Quant/unscored sections may appear in any order.


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SENTENCE EQUIVALENCE

Strategies for Sentence Equivalence

Sentence Equivalence questions test your ability to understand the sentence using a variety of clues provided by syntax and grammar to recognize the overall meaning of a sentence. The clues can be punctuation marks, conjunctions etc. You need to choose two words that best complete the blank.

Consider each answer choice carefully and decide which of the two choices complete the sentencein a way that gives the sentence a logically satisfactory meaning that is same and allows it to be read as a stylistically integrated whole. Remember that both the words should produce sentences thatmean the same thing.

Approaches to crack the questions

1. Fill the blanks with your own words

Before reading the answer choices, you may find it helpful to fill in the blanks with a word or words of your own that complete the meaning of the sentence. Then examine the answer choicesto see if one of them parallels your own completion of the sentence.

Example: Our bookshelves at home display a range of books on wide-ranging subjects and inmany languages, reflecting the ____ tastes of our family members.

A. anomalous B. limited C. diverseD. arcane E. furtive F. eclectic

The sentence speaks about wide range of books. Thus, the family must have wide rangingtastes. The blank takes in a word which indicates variety. So from the given options eclectic

which means taking things from a wide range of sources, must be the answer. So eclectic and diverse will be the answer (anomalous = abnormal; arcane = esoteric; furtive = stealthy)

2. Read the sentence and understand the mood or toneAdjectives and Adverbs in a sentence will help you to understand the mood or tone. For example,Melancholy, dull, gloomy express a negative mood. Excited, enthusiastic etc express a positiveand happy tone. So, if you pay attention on words you can understand whether the tone issad, happy, sarcastic, ironic etc.

Example: Dejected by having performed poorly in the final match, Venniza began to questionher abilities. Her self confidence was _________

A. appeased B. destroyed C. placated D. elevated E. sustained F. down

The word dejected implies a negative tone. So the blank also indicates that her self confidenceis down. So down and destroyed will be the most suitable answers.


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TEXT COMPLETION

Text completion questions test your ability to read, interpret, evaluate and reason from the content

you have read and guess the remaining information in the paragraph.These questions will have one to five lines; and one to three blanks. If it has one blank then there will

be five options. Else for each blank there will be three options. You are required to construct ameaningfully coherent paragraph.

Approaches to crack the questions

1. Read through the passage to get an overall sense of it.Certain keywords in a sentence give you an idea about the authors tone, mood and style of writing and helps you to make the correct guess for the possible answer.

Example: Women squat, heads covered, beside huge piles of limp fodder and __________ oillamps, and just above all the cows in the three towns converge upon this spot. Sinners, supplicantsand yes, even scallywags hand over a few coins for a crack at redemption and handful of grass.

A. shining B. bright C. sputtering D. effulgent E. radiant

The words squat , beside limp fodder , sinners, redemption indicate a negative dull tone.So shining, bright, radiant, effulgent do not fit. Sputtering is to make a noise as if spitting (light

popping sound of flame which is dying out).(Effulgent=radiant, refulgent)

2. Think up your own words to fill the blanksAs human beings we have a natural tendency to force ourself to accept a particular option as ananswer, our inclination towards a word may not be correct. So first start with reading the paragraph,guess the words in the blanks and then proceed to the options.

Example: In parts of the Arctic, the land grades into the land fast ice so _______ that you canwalk off the coast and not know you are over the hidden sea.

A. permanently B. imperceptibly C. irregularly D. precariously E.slightly

The words so walk off coast gives you the clue. The ice on the sea is frozen and you canwalk on it without realizing the same. The word in the blank could be related to not knowingly.So imperceptibly is the answer.(precariously = dangerously, not safe)


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READING COMPREHENSION

Reading comprehension (RC) questions measure your ability to read with understanding, insight and

discrimination. This type of question explores your ability to analyze a written passage from several perspectives. These include your ability to recognize both explicitly stated elements in the passageand assumptions underlying statements or arguments in the passage as well as the implications of those statements or arguments.

There will be around 10 passages throughout your exam. The topics will be varied. These questionsmay have one option or more than one option correct. You will also be asked to highlight a particular line in the paragraph that explains the given question.

Lets understand what can hinder your performance and what can boost your performance in RC.

How to improve reading

To perform better in RC you have to read a lot and across various topics.

Reading speed is very important because the faster you read the less time you consume from thetotal exam time. It also helps you to focus better and avoid distractions.

Note: Reading fast alone is not sufficient, you have to be an active and effective reader.

Factors influencing Reading Speed:

a. Eye span & fixation points

b. Vocalization & Sub vocalization

c. Mouse / Hand pointersd. Regression

a. Eye span & fixations: Eye-span is referred to the amount of text someone takes in at oneglance. The period of time during which an eye rests on a word is called fixation.

A speed reader reads many words in one fixation and moves on very quickly to the next set of words.

Read the passage given below and realize the variation your reading speed.

As a child at the age of three, my sister and I had pictures taken together. My sister

and I are ten months and three weeks apart. In this special family picture we look identical. Our big, dark blue and brown eyes and smile resemble twocalm little girls, enjoying the moment with peaceful smiles on our faces. In our long, dark red and blue dresses we sit straight up in front of a warm red fireplace surrounded by green plants.


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l e1. If at all theres one thing he can be ridiculed for, its for making some ______________bad

choices in his career that have resulted in some great flops of the millennium, but tell me of onegood actor whos not made bad acting choices and Ill take all my words back.A. artificially B. monumentally C. enormouslyD. trivially E. arduously F. implicitly

2. The ________ little fact that the new age directors are only self-aggrandizing, over-exaggerated pompous clones with neither the vision nor the courage to make movies that dont play to thegallery, prohibits us from expecting something new or sensible from a movie, how much ever hyped it is.A. irksome B. wrenching C. nascentD. imposing E. interesting F. vexing

3. As an austerity measure, a _________of up-market party hosts who regularly hold parties atthe festival, have decided not to hold lavish bashes this year.A. minuscule B. zealot C. slewD. volume E. paltry F. sheaf

4. The pictures and videos from Abu Ghraib did bring home what was happening there in a waythat nothing else could have done, and promoted a great wave of _________ and humanitarianconcern that helped to get the place closed down.A. revulsion B. benevolence C. aversion

D. turpitude E. anachronism F. sympathy

5. Though James Oliver entered with the __________ conviction that he would make it big inHollywood, he realized within a short while that American entertainment is a cut-throat business.A. sophisticated B. naive C. guilelessD. professional E. cynical F. uninhibited

6. She gasped when she saw that her parents home was _________with ketchup, chocolatesyrup and eggs.A. florid B. ornate C. deluded D. splattered E. adorned F. dabbled

SE CLASS EXERCISE 4


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G R E S a m p

l eAnalytical Writing Assessment

(AWA)

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INTRODUCTION

The Analytical Writing Assessment (AWA) is one of the most neglected yet one of the most important

sections of the GRE Exam. The GRE AWA section has two tasks. One task tests your ability toexpress your views on an issue. You will have two options to choose from. The second task testsyour ability to think critically and analyze a logically flawed argument. Both the tasks are for 30 mins.The AWA section has scores ranging from 0 to 6, 6 being the highest. A well written and coherentessay with relevant examples would get a score of no less than 4.5. Papers awarded 6s areconsidered to be outstanding , 5s are strong , 4s are adequate , 3s are limited , 2s are seriously

flawed , and 1s are fundamentally deficient .

Your Issue and Argument scores are combined into one average score that is reported to the colleges.Although you can view your math and verbal scores at the test center shortly after the test, your analytical writing score will not be available until 1015 days after the test.

The best part of good preparation for the AWA section is that it also helps in your TOEFL examwhich invariably every one of you will be taking as part of your admission process.

It is our endeavor that all the students take the AWA section seriously and score a minimum of 3.5,which is a cutoff for few of the very good colleges in the United States of America.

The GRE AWA tests your skills on

Ability to articulate complex ideas clearly and effectively

Ability to examine claims and accompanying evidence

Ability to support ideas with relevant reasons and examples

Ability to sustain a well-focused, coherent discussion

Ability to control the elements of standard written English.

The crux of the GRE AWA is about constructing an essay with coherent ideas. Before we go into thedetailed discussion of what are the strategies to be used to construct a well written issue or anargument. Let us first see few tips to write a very good essay.


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ESSAY WRITING BASICS

The scorers/evaluators/readers of your essays have a huge task of reviewing hundreds of essays of

fellow GRE test takers. So you should make a conscious effort of writing a captivating essay. Buthow do you write a captivating essay? Are there any rules that make your essay stand out in a lot?

Having good knowledge of various topics, and to go with it, there are a few tips or strategies thatyou can use to construct a well written essay.

1. Have a good beginning.What better than having a gripping start to a story? As we mentioned earlier, the scorers have atedious task of reviewing hundreds of essays. So when you make your essay start in an interestingway, it always captivates the attention of the scorers. You can start your essays with a quote or an anecdote. An anecdote is a short story about a particular topic. You can also pose a questionto keep the reader engaged, so that he keeps reading to find an answer.

2. Do not maintain the same tone all throughout your essay. Bring in some rhythm and cadence toyour writing.It is always better to use transitional words and phrases and figurative speech in your essay.Transitional words and phrases are helpful not only in linking your ideas between sentences, butalso in providing cohesiveness from paragraph to paragraph. In addition to, furthermore, it isevident that, however, on the contrary, sadly enough, as a result, vicariously, in the hind sight etcare examples of transitional phrases and words. Usage of figurative speech like hyperbole,simile, metaphor etc makes your essay flowery.

3. Maintain consistency in person. Based on the topic of the essay choose a person and stick tothe same.

4. Avoid redundancy. Never belabor or beat around the bush while writing about a topic. You cansometimes restate to emphasize, make sure that it never is tautological.

5. Avoid grammatical mistakes. You will lose marks for improper usage of words and word forms.So, if you are not sure about the usage of a particular word, try to find a replacement for that.

6. The GRE AWA exam has a simple word processor. It does not have a spell check. So when you practice for your AWA section, practice in notepad rather than Microsoft word. Avoid incorrectspellings which would certainly have a negative impact on your score.

7. Use proper punctuation. Improper usage of punctuation could completely change the meaningof the sentence.


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ANALYTICAL WRITING

The Analytical Writing measure assesses your critical thinking and analytical writing skills. It assesses

your ability to articulate and support complex ideas, construct and evaluate arguments, and sustaina focused and coherent discussion. It does not assess specific content knowledge.

The Analytical Writing measure consists of two separately timed analytical writing tasks:

a 30-minute Analyze an Issue task

a 30 minute Analyze an Argument task

Overview of the Analytical Writing Measure

The Issue task presents an opinion on an issue of broad interest followed by specific instructionson how to respond to that issue. You are required to evaluate the issue, considering its complexities,and develop an argument with reasons and examples to support your views.

The Argument task presents a different challenge from that of the Issue task: it requires you toevaluate a given argument according to specific instructions. You will need to consider the logicalsoundness of the argument rather than to agree or disagree with the position it presents.

The two tasks are complementary in that one requires you to construct your own argument bytaking a position and providing evidence supporting your views on the issue, whereas the other requires you to evaluate someone elses argument by assessing its claims and evaluating the evidenceit provides.

Preparing for the Analytical Writing Measure:

The basic guidelines one must keep in mind before approaching the Writing tasks are: (theseguidelines will hold good for both the tasks)

1. For every point you make in a GRE essay, always provide a reason and/or an example tosupport that point. (This is the cardinal rule for writing GRE essays)

2. Use transition words and phrases to help the reader follow the flow of your discussion eg. in-addition, moreover, furthermore, finally etc..

3. Try to include brief introductory and concluding paragraphs, which are consistent with eachother and with the paragraphs in the body of your essay. Such lines will help your essay appear

well-organized.

4. Compose your introductory remarks last after youve completed the rest of your essay.Why? Your essay might evolve different from your initial thesis; if youve composed your introduction first, you might need to rewrite it.


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ANALYZE - ISSUE TASK

The Analyze an Issue-task assesses your ability to think critically about a topic of general interest

according to specific instructions and to clearly express your thoughts about it in writing. Each issuetopic makes a claim that test takers can discuss from various perspectives and apply to manydifferent situations or conditions. The issue statement is followed by specific instructions . Your task is to present a case for your own position on the issue according to the specific instructions.Before beginning your written response, be sure to read the issue and instructions carefully and think about the issue from several points of view, considering the complexity of ideas associated withthose views. Then, make notes about the position you want to develop and list the main reasons and examples that you could use to support that position.

It is important that you address the central issue according to the specific instructions. Each task isaccompanied by one of the following sets of instructions.

Specifications for the Issue Task Essay:

Write a response in which you discuss the extent to which you agree or disagree with thestatement and explain your reasoning for the position you take. In developing and supportingyour position, you should consider ways in which the statement might or might not hold true and explain how these considerations shape your position.

Write a response in which you discuss the extent to which you agree or disagree with therecommendation and explain your reasoning for the position you take. In developing and supporting your position, describe specific circumstances in which adopting the recommendationwould or would not be advantageous and explain how these examples shape your position.

Write a response in which you discuss the extent to which you agree or disagree with the claim.In developing and supporting your position, be sure to address the most compelling reasonsand/or examples that could be used to challenge your position.

Write a response in which you discuss which view more closely aligns with your own positionand explain your reasoning for the position you take. In developing and supporting your position,you should address both of the views presented.

Write a response in which you discuss the extent to which you agree or disagree with the claimand the reason on which that claim is based.

Write a response in which you discuss your views on the policy and explain your reasoning for the position you take. In developing and supporting your position, you should consider the


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l eGRE

Quantitative Ability

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l eDo you go numb when you see questions on number system? Do you get scared when somebodyasks you the last digit of 2376 raised to the power of 2376? Do you fail to see the rationale behind denoting a rational number in terms of decimals and percentages?

Lets unravel the mysteries behind these seemingly threatening questions. In fact we will go ahead and make number systems your favourite topic by the end of this chapter.

What do you understand by the term number ? (It is certainly not the comparative degree of numb :)

A number is a symbol that represents a particular quantity. Different number systems have different

ways of representing these symbols. The most commonly used number system is the Arabic number system which has numbers like 1, 23, 45, 678 etc. You must have read other forms of representa-tions like the Roman system where English letters are used as symbols to represent numbers. For example, X, VI, C, LX etc.

While, there exist various number systems we primarily work on the Arabic system which is themost popularly followed system.

Let us dig deep into this system and learn more about numbers.

On a broad scale, numbers can be divided into two categories, the real and the imaginary.

Real numbers: Real numbers are those numbers which can be represented on the number line. Anumber line is a line containing all the positive and negative numbers ranging from negative infinity tothe positive infinity. Numbers like -4.5, 67/89, 9 etc are real numbers.

-5 -4 -3 -2 -1 0 1 2 4 5

Imaginary numbers: Imaginary numbers, on the contrary, cannot be represented on the number line. For example numbers like 1- , 2- etc are imaginary. .

Real numbers can be further be divided into two parts. They are the Rational numbers and

irrational numbers.

NUMBER SYSTEMS


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l eThe figure represented above is the Number tree. You can see how different numbers have beenevolved from the others and the various classifications are also provided.Example 1: Which of the following numbers is a prime number?A. 234 B. 675 C. 123 D. 631 E. 290

Solution: As mentioned earlier, except 2 all other even numbers are composite. So, options A and E are eliminated straight away. The number in the option B ends with 5 and thus has 5 as a factor.So, option B is ruled out.

123 is divisible by 3, so the only number left is 631. Thus the answer is (D).

Alternative method: Checking whether all the numbers from 1 to 631 are factors of 631 are notis a tedious process and might take ages. God bless mathematicians as they gave us an easier wayto find whether a number is a prime number or not.

Check whether any of the numbers from 2 to the 631 (nearest value = 26) divides the number 631

or not. If any of these numbers divides the number then it is not a prime number. In this case none of them divides 631 completely, so 631 is the answer.

Relation between Odd and Even numbers:

Odd + Even = Odd Odd Even = Odd Odd x Odd = Odd Even + Odd = Odd Even Odd = Odd Odd x Even =EvenOdd + Odd = Even Odd Odd = Even Even x Odd= Even

Even + Even = Even Even Even = Even Even x Even= Even

Odd even = Odd Odd odd = Odd Even even = Even Even odd = Even

Real Numbers

Natural NumbersRational

Numbers

Irrational Numbers

Integers

Fractions

Whole Numbers


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Concept of multiplying factor:

Consider the following example; Sachin scored 500 runs in IPL 2. He scored 10% more runs in IPL

3. What is the total number of runs he scored in IPL3 ?

The answer for this can be easily calculated by the principles discussed earlier in this chapter.

The total number of runs scored by sachin in IPL3 = 500 + (10/100) x 500 = 500 + 50 = 550.The same can be done this way 500 + (10/100) x 500 = 500 (1+ 0.1)=500x1.1 = 550

If we see clearly, we are multiplying the number of runs Sachin scored in IPL 2 by a factor 1.1 to getthe runs he scored in IPL 3. This factor of multiplication is called the multiplying factor.

The multiplying factor corresponding to an increase of x% is nothing but 1 + (x/100) and for adecrease of x%, 1-(x/100)

Multiplying Factor (M.F)We could simply say, it is (1+ k), where k is percentage change expressed in decimal

We have discussed earlier about how percentages, fractions/ratios, or decimals are inter-convert-ible and interchangeable. For easy calculations in GRE, it is advisable for the students to learn themultiplication tables upto 20, squares upto 30 and cubes upto 20.

Few of the very commonly used percentages and their corresponding fractional values are given.

1/2 = 50% 1/3 = 33.33% 1/4 = 25% 1/5 = 20%1/6 = 16.67% 1/7 = 14.28% 1/8 = 12.5% 1/9 = 11.11%2/5 = 40% 3/5 = 60% 1/11 = 9.09% 1/12 = 8.33%1/15 = 6.66% 1/16 = 6.25% 3/8 = 37.5% 5/8 = 62.5%7/8 = 87.5% 1/20 = 5%

Example 2: If three fourth of students in the class have motor bikes and half of the bike ownersown a Hero Honda bike, what fraction of the class has Hero Honda bike? Also, represent thesame in terms of percentage.Solution : The fraction of the class owning a Hero Honda bike = x = 3/8

As mentioned above, the percentage equivalent to that is = 37.5 %.

The same problem can be solved using percentages instead of fractions. Try it for yourself.


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Harmonic Progression

If the reciprocals of a progression form an AP, then that progression is called a HarmonicProgression.

The Harmonic mean of 2 numbers is given by HM= 2ab/a+b

For any two numbers a and b, AM GM HM

Some Important Formulae

( 1)2

n nn 2

( 1)(2 1)6

n n nn

2 23 ( 1)

4n n

n

Example : The 20 th term of the series 3, 5, 7, 9

Solution: The above series is an arithmetic progression (AP). We can see that the commondifference of the above series is 2.

Thus the 20 th term of the series is given by, T 20 = a + 19 d

T20 = 3 + 19 2 = 3 + 38 = 41.

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A polynomial of degree two is called a quadratic equation. A standard quadratic equation is of theform a x2 + b x + c = 0, where a, b, c are all real and a 0. A quadratic equation has two roots.

The roots of the quadratic equation could be as followsa. Real and different

b. Real and equalc. Imaginary

The nature of roots of a quadratic equation a x2 + b x + c = 0 is governed by a value called thediscriminant (D). Discriminant is expressed as ( b2 - 4ac). Shown below is the nature of roots based on the discriminant value.

D = b2-4ac

If D = 0 D > 0 If D < 0(Rational and equal) (Roots are complex or imaginary)

D is Perfect square D is not Perfect square(Rational and unequal) (Irrational conjugate pairs)

Example 1: What is the nature of roots of 3 x2 - 5 x + 3 = 0?

A. Real and equal B. Real and unequal C. Rational D. Imaginary E. Irrational

Solution: To find the nature of the roots, we have to find the discriminant D = b2 - 4ac = (-5)2 +4x3x3 = 25 - 36 = -9. If the discriminant value is negative, then the roots are complex or imagi-nary.

Roots of the Quadratic Equation

If a x2 + b x + c=0, then the roots of the quadratic equation are2 4

2b b ac

a

. The roots are commonly represented by and .

Sum of roots ( + )=b

a , Product of the roots ( )=

ca


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l eGraph of the curve y=(x+k) 2 Graph of the curve y= x 2-k

Graph of the curve y= x 3 Graph of the curve y= -x 3

Graph of the curve y=x 2 Graph of the curve y= -x 2


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Normal Distribution

Many natural processes yield data that have a relative frequency distribution shaped somewhat likea bell as shown below with mean m and standard deviation d .

Such data are said to be approximately normally distributed and have the following properties.1. The mean, median, and mode are all nearly equal.2. The data are grouped fairly symmetrically about the mean.3. About two-thirds of the data are within 1 standard deviation of the mean.4. Almost all of the data are within 2 standard deviations of the mean.

As stated above, you can always associate a random variable X with a distribution of data by letting X be a randomly chosen value from the distribution. If X is such a random variable for the distributionabove, we say that X is approximately normally distributed. Just as a data distribution has a meanand standard deviation, the normal probability distribution has a mean and standard deviation. Also,the properties listed above for the approximately normal distribution of data hold for the normaldistribution, except that the mean, median, and mode are exactly the same and the distribution is

perfectly symmetric about the mean.

A normal distribution, though always shaped like a bell, can be centered around any mean and can be spread out to a greater or lesser degree, depending on the standard deviation.


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l e1. Crafty Tara decides to make each of her friends a light box. To let the light out, she removes aright triangle from each side of the box such that the area of each face of the box is the same.

What is the remaining surface area of the box if each edge of the box measures 4 feet and thearea of each triangle measures 6 square feet?A. 60 sft B. 55 sft C. 50 sft D. 28 sft

2. The 25th Annual Go-Cart Race is just around the corner, and Dave needs to build a platform for the winner. In honor of the traditions longevity, Dave wants the platform to be special. So, he willcover all the exposed surfaces of his platform in red velvet. If the base step measures 15 feet by7 feet by 1 foot, and each consecutive step is uniformly 1 foot from the edge of the last step, howmuch exposed surface area must Dave cover?

A. 340 sft B. 318 sft C. 254 sft D. 328 sft

3. The area of the base of a tank is 100 sq. ft. It takes 20 seconds to fill the tank with water poured at rate of 25 cubic feet per second. What is the height (in feet) of the rectangular tank?A. 0.25 B. 0.5 C. 1 D. 5

4. Water is poured into an empty cylindrical tank at a constant rate. In 10 minutes, the height of thewater increased by 7 feet. The radius of the tank is 10 feet. What is the rate at which the water is poured in cubic feet per minute?A. 11 /8 B. 11 /3 C. 7 /60 D. 70

5. A closed rectangular tank contains a certain amount of water. When the tank is placed on its 3 ft by 4 ft side, the height of the water in the tank is 5 ft. When the tank is placed on another side of dimensions 4 ft by 5 ft, what is the height, in feet, of the surface of the water above the ground?A. 2 B. 3 C. 5 D. 4

6. A, B, and C are three unequal faces of a rectangular tank. The tank contains a certain amount of water. When the tank is based on the face A, the height of the water is half the height of the tank.The dimensions of the side B are 3 ft 4 ft and the dimensions of side C are 4 ft 5 ft. What is

MENSURATION & TRIGONOMETRY


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22. The box-and-whisker plot below shows the amount of calories present in some bakery items.

What is the IQR (Inter Quartile Range)?

What is the average of the median and the lower quartile?

If the Lower and the Higher values increase by 50 calories each,what happens to themedian?

In that case what happens to the lower quartile?

And the upper quartile?

23. The following box plot shows the weight of Rugby players (both Male & Female). Answer the questions below.


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Directions for questions 5 to 7: The information below shows the details of value of Indian Rupeeagainst the US Dollar from 09th July to 08th August, 2011. Answer the questions based on thegraph.

5. On which day shown on the graph did the value of the US dollar increase against the Rupee bythe greatest amount?A. July 10 B. July 14 C. July 21 D. July 23 E. Aug 4

6. John had 100 dollars. The exchange rate converts the amount in US dollars to a number in IndianRupees by directly multiplying by the value of the exchange rate. By what amount did Johns$100 increase in terms of Indian Rupees from July 9th to August 8th?A. 5 B. 10 C. 15 D. 35 E. 55

7. On August 8th, the dollar value was approximately what percent of the dollar value on July9th?A. 1.28 B. 12.8 C. 101.07 D. 112.8 E. 128

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