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GMAT Flashcards 2008 Beat The GMAT | http://www.beatthegmat.com Last Updated: August 3, 2008 During my GMAT preparation, I made close to 300 flashcards to help me stay fresh on the strategies and materials I had studied over the course of 5 months. This document contains the digitized version of my flashcards please use them as a study aid. Best of luck! Eric Beat The GMAT | http://www.beatthegmat.com _______ Codes On the top left corner of each flashcard, you will find a code. This code will help you classify the information on each flashcard, telling you: which section of the GMAT the information on the card pertains; the problem type; and the question type. For example, if you were to encounter the following code: V: SC: Idiom You would know that the information on the given flashcard pertains to the verbal section of the GMAT, addresses a sentence correction problem type, and specifically relates to idiom questions. Abbreviations V Verbal Section SC Sentence Correction CR Critical Reasoning RC Reading Comprehension Q Quantitative Section DS Data Sufficiency 10% Test Prep Company Discounts Get 10% off when using these discount codes for online purchases at the following test prep websites. A portion of every purchase made using these discount codes will fund the Beat The GMAT Scholarships! Kaplan 10% discount code: BEAT10 Discount applies to all courses, services, and products More info: http://www.beatthegmat.com/kaplan-gmat-discount.html Manhattan GMAT 10% discount code: BTGMG07 Discount applies to all courses, services, and products More info: http://www.beatthegmat.com/discounts.html Veritas Prep 10% discount code: BTG9311 Discount applies to all courses, services, products, and admissions consulting More info: http://www.beatthegmat.com/veritas-gmat-discount.html Stacy Blackman MBA Admissions Consulting Up to $200 select hourly consulting services: BTG2008 More info: http://www.beatthegmat.com/stacy-blackman-consulting-discount.html Sentence Correction Flashcards 2008 Beat The GMAT | http://www.beatthegmat.com V: SC: Agree V: SC: in that vs. because Agree with another person. - I agree with you on this one. in that is usually better than because Agree to something inanimate. - I agree to your proposal. Beat The GMAT | http://www.beatthegmat.com V: SC: Pronoun Errors Pronoun reference error - Samantha and Jane went shopping, but she couldn t find anything she liked. (Incorrect) Pronoun number error - The average moviegoer expects to see at least one scene of violence per film, and they are seldom disappointed. (Incorrect) Beat The GMAT | http://www.beatthegmat.com V: SC: Parallel Construction Beat The GMAT | http://www.beatthegmat.com V: SC: Misplaced Modifiers Coming out of the department store, John s wallet was stolen. (Incorrect) - 2 ways to fix this misplaced modifier: - Change 2nd half of sentence. - Change first half of sentence into adverbial clause, which contains its own subject. Beat The GMAT | http://www.beatthegmat.com V: SC: Tense A sentence that begins in one tense should generally stay in that tense. Series of actions set off by commas. - Spot these problems by finding a series of actions, lists, or sentences divided into parts. - Usually related to parallel construction questions. - EXCEPTION: Past perfect - Action set in the past perfect must have another action that comes after it set in the simple past. - He had ridden his motorcycle for 2 hours when it ran out of gas. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC V: SC: Apples and Oranges Comparison of nouns: - The people in my office are smarter than those in other offices. Politics Singular word Comparison of actions People Plural word - Synthetic oils burn less efficiently than do natural oils. Compare like things/actions to like things/actions. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: Correct Sentences V: SC: Quantity Words On the flight to LA, Nancy had to choose between two dinner entrees. Countable Items Non- Countable Items Fewer Less Number Amount, quantity Many 1/5 of SC sentences are correct on the GMAT. Much Beat The GMAT | http://www.beatthegmat.com V: SC: 3-Step Method 1) Read original sentence carefully. 2) Scan answer choices for differences that will help identify errors being tested. 3) Eliminate a choice as soon as you find an error. Beat The GMAT | http://www.beatthegmat.com - About 3 questions per test. Beat The GMAT | http://www.beatthegmat.com V: SC: Agreement Verbs must agree with subjects. - Watch for collective nouns - audience, committee are singular - Either, or; neither, nor - Verbs agree with whatever follows or/nor Beat The GMAT | http://www.beatthegmat.com V: SC: Modifiers V: SC: Pronoun A pronoun must agree with its antecedent and refer to only one antecedent. Modifiers should be as close as possible to the word or clause it modifies. - 2 types of errors: reference, agreement - that is singular - those is plural Beat The GMAT | http://www.beatthegmat.com V: SC: -ing Beat The GMAT | http://www.beatthegmat.com V: SC: Verb Tense Verb tense must reflect the sequence of events. When the GMAT gives you a choice between one verb tense that uses an ing form and another that doesn t, usually the ing form is wrong. - 2 reasons to use ing form: emphasize continuing nature of an action or to emphasize that two actions are occurring simultaneously. - Use simple past tense instead of had + past tense. Beat The GMAT | http://www.beatthegmat.com V: SC: Similar Items Similar elements with the same importance and function should be expressed in the same grammatical form. Compare people to people, groups to groups, attributes to attributes. Beat The GMAT | http://www.beatthegmat.com V: SC: Like Things Compare like things only. Comparison words: like, as, compared to, less than, more than, other, that of, those of. Parallel similar elements in a sentence. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: like, such as V: SC: like, as like = similar to Use like for comparing nouns. such as = for example Use as for comparing actions. Beat The GMAT | http://www.beatthegmat.com V: SC: Idioms involving as Beat The GMAT | http://www.beatthegmat.com V: SC: None/No one Memorize: as is usually preferred over like None can be singular or plural. - regarded as (don t use to be) - as long as No one is always singular. - such questions as - plays as Beat The GMAT | http://www.beatthegmat.com V: SC: Passive Construction Avoid passive verbs! Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: Active Tense Active tense is preferred in sentence correction questions. Beat The GMAT | http://www.beatthegmat.com V: SC: Idiom V: SC: Idiom Agree that When rates means price charged, it should be followed by for Rates for Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: Idiom V: SC: Idiom Distinguish between X and Y. Beat The GMAT | http://www.beatthegmat.com V: SC: Idiom Likely to be Beat The GMAT | http://www.beatthegmat.com V: SC: Greater than/More than Greater than is appropriate when describing numbers alone. - Greater than 100 Same to X as to Y. More than should be used when describing the numbers of objects or when making comparisons. - More than 100 fish. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: Subordination, Coordination V: SC: Participles Coordination - Equal emphasis and, or, but Subordination Adjectives formed from verbs - Peter, distracted by his cat and wanting to do his work - Emphasize other part although, while, since Beat The GMAT | http://www.beatthegmat.com V: SC: Ellipsis Put omitted pieces back into sentence to see if it makes sense. Beat The GMAT | http://www.beatthegmat.com V: SC: Less Less is a word used to describe non-count nouns, but also used for sums of money, periods of time and distance, and citations of numerical/statistical data. - It s less than 20 miles to Dallas. - We spent less than $20. - The town spent less than 4% of its budget. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: Passive Passive voice does not itself contribute an error. Eliminate passive if there is a grammatically correct alternative in the active voice. Beat The GMAT | http://www.beatthegmat.com V: SC: One of the One of the + PLURAL NOUN + that/who/ + PLURAL VERB - He is one of the persons who make money. - This is one of the cars that run on hydrogen. Beat The GMAT | http://www.beatthegmat.com V: SC: Consider V: SC: Ellipsis When consider means regard as, as should not be present with consider in the sentence. Consider is also not followed by an infinitive like to be. - Critics consider facilities to be an integral part (Incorrect) Most of the time when we use a comparison using than or as, we leave words out. - He is taller than she. - He is as happy as they. - Critics consider facilities an integral part (Correct) Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: Idiom V: SC: Idiom Deciding that Just as so Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: Idiom V: SC: Strategy Not so much as Beat The GMAT | http://www.beatthegmat.com When the entire sentence is underlined in the question, the answer has a higher probability of being D or E . Beat The GMAT | http://www.beatthegmat.com V: SC: Idiom V: SC: If/Whether X forbids Y to do Z Whether is correct when you re discussing two options. X prohibits Y from doing Z If is correct for more than 2 options. Beat The GMAT | http://www.beatthegmat.com V: SC: Singular or Plural The following can be singular or plural pronouns, depending on the noun it refers to: Beat The GMAT | http://www.beatthegmat.com V: SC: Less, Fewer Less = not as much - Some - More Fewer = not as many - Most - All Beat The GMAT | http://www.beatthegmat.com V: SC: Compare Use compare to for unlike things - He compared her to a summer day. Use compare with for like things - The police compared the forged signature with the original. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: Comparison Words Like used to express similarity, normally between two nouns - Lemons are like limes. As normally used to compare two clauses, NOT two nouns - He looks as if he is drunk. Such as normally used to give examples. Beat The GMAT | http://www.beatthegmat.com V: SC: Number V: SC: Idiom A number requires a plural verb. - A number of people are waiting for the bus. So X as to be Y The number requires a singular verb. - The number of cars in the city is decreasing. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: Idiom V: SC: Idiom Same as X as to Y Beat The GMAT | http://www.beatthegmat.com V: SC: Infinitives to Avoid Just as so too Beat The GMAT | http://www.beatthegmat.com V: SC: Pattern to Avoid To include is wrong. - Including is correct. To implement is wrong. Avoid any sentence construction with: PREPOSITION + NOUN + PARTICIPLE - with child-care facilities included. (Incorrect) - Implementing is correct. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: being, to be V: SC: Idiom Paired Coordinates Avoid being and to be, if possible. Not X, but rather Y - Both forms are considered passive. Beat The GMAT | http://www.beatthegmat.com V: SC: Idiom - Target Target at Beat The GMAT | http://www.beatthegmat.com V: SC: Idiom Between and - The shoe company targeted its advertising at high-school kids. Beat The GMAT | http://www.beatthegmat.com V: SC: they Beat The GMAT | http://www.beatthegmat.com V: SC: Comparison of actions Watch out for comparison of actions: - French wines taste better than Australian wines. (Incorrect) Always be suspicious of the pronoun they. - French wines taste better than Australian wines do. (Correct) - French wines taste better than Australian wines taste. (Correct) - French wines taste better than do Australian wines. (Correct) Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: Pronoun Rules Each pronoun must agree in number (plural or singular) with the noun it replaces. Each pronoun must refer directly and unambiguously to the noun it replaces. Beat The GMAT | http://www.beatthegmat.com V: SC: -ing The ing (present participle) form introduces an action that is simultaneous with the action of the main clause. Beat The GMAT | http://www.beatthegmat.com V: SC: During During + TIME PERIOD is wrong. - During two hours, I felt sleepy. (Incorrect) - During the last two hours, I have felt sleepy. (Correct) Beat The GMAT | http://www.beatthegmat.com V: SC: Phrase, Clause You can change a misplaced modifier into a legal sentence by changing a phrase into a clause. - While leaving the bank, Evelyn s purse was stolen. (Incorrect, underlined portion is a phrase) - As she was leaving the bank, Evelyn s purse was stolen. (Correct, underlined portion is a clause) Beat The GMAT | http://www.beatthegmat.com V: SC: Numbers Greater than 1 Numbers greater than 1 are plural. - Three out of every four automobile owners in the US also own a bicycle. Beat The GMAT | http://www.beatthegmat.com V: SC: Quantifiers With fractions, percentages, and indefinite quantifiers, the verb agrees with the preceding noun or clause. With singular or non-count nouns or clauses, use a singular verb. Beat The GMAT | http://www.beatthegmat.com V: SC: Hopefully Hopefully is almost always wrong on the GMAT. Avoid sentence choices with this word. Beat The GMAT | http://www.beatthegmat.com V: SC: Thinking Words V: SC: Having Having + past participle - Used to express actions that are finished and to show that one thing comes after another. Beat The GMAT | http://www.beatthegmat.com V: SC: Credit Credit A with B: give responsibility for Thinking words (i.e., theory, belief, believe ) + that - Edison is credited with inventing the light bulb. - Thinking words are always followed by that Credit X to Y: give money or credit to - Lucy s belief that the Earth is flat is great. (Correct) - The bank credited $1 million to his account. - Lucy s belief of (Incorrect) Credit for (noun): money received for or in exchange for something - The customer received a $20 credit for the interruption of service. Beat The GMAT | http://www.beatthegmat.com V: SC: Might/May Beat The GMAT | http://www.beatthegmat.com V: SC: Number A number of always takes plural verbs. - A number of people have gone Might is the past tense of may. The number of always takes singular verbs. - The number of people has increased Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: Plural/Singular QUANTIFIER + of + NOUN + VERB The noun determines whether verb is singular or plural. - Most of the people are - Most of the water is Beat The GMAT | http://www.beatthegmat.com V: SC: Just as V: SC: Majority Majority should be used with count nouns only. - The majority of the talk (Incorrect) - The greater part of the talk (Correct) - The majority of the people (Correct) Beat The GMAT | http://www.beatthegmat.com V: SC: like vs. as Use like when you want to focus on two nouns. Just as can replace in the same way that. Use as when you want to focus on two nouns doing two actions. Beat The GMAT | http://www.beatthegmat.com V: SC: Strategy Beat The GMAT | http://www.beatthegmat.com V: SC: be-verb NOUN + BE-verb + NOUN/ADJECTIVE Whenever we have two options that are both grammatically correct, and the only difference is meaning, we MUST go with the original meaning. - The change was good for me. (Correct) - The change was when I came to the U.S. (Incorrect) - Use changed occurred instead. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: Pronoun V: SC: Idiom For = despite When you see a pronoun, especially it, immediately check the antecedent. Along with = in addition to Beat The GMAT | http://www.beatthegmat.com V: SC: Concern Beat The GMAT | http://www.beatthegmat.com V: SC: So, It Concerned for = worried, anxious So is used to replace a verb in a sentence. Concerned with = related to It is used to replace a noun. Beat The GMAT | http://www.beatthegmat.com V: SC: Each Beat The GMAT | http://www.beatthegmat.com V: SC: Whether, If Each is usually singular. But when each follows a plural subject, the verb and subsequent pronouns remain in the plural. Whether will almost always beat if. - Three cats each eat. (Correct) - Three cats, each of which eats (Correct) Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: Compare Compare to compares UNLIKE things, whereas compare with compares LIKE things. V: SC: So as to So + ADJECTIVE + as to + VERB - Her debts are so extreme as to threaten her company. (Correct) Compare to is used to stress resemblance. Compare with can be used to show either similarity or difference (usually difference). Beat The GMAT | http://www.beatthegmat.com V: SC: Due to - He exercises everyday so as to build his stamina. (Incorrect) Beat The GMAT | http://www.beatthegmat.com V: SC: Idiom Due to means caused by. Due to does not mean because of. - The game was postponed due to rain. (Incorrect) - The game was postponed because of rain. (Correct) Targeted at CORRECT Targeted to WRONG - The game s postponement was due to rain. (Correct) Beat The GMAT | http://www.beatthegmat.com V: SC: Rather than Use rather than to express a preference. - I want a cat rather than a dog. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: Not, But Use not/but to join linguistically equivalent things. - Pucci is not a dog but a cat. Beat The GMAT | http://www.beatthegmat.com V: SC: Guessing V: SC: Idiom In contrast to When in doubt, choose the most concise answer. Similar to Beat The GMAT | http://www.beatthegmat.com V: SC: Between and Beat The GMAT | http://www.beatthegmat.com V: SC: Whether/If Whether is correct when a sentence describes alternatives. and must always follow between - Whether to participate or not. - Between raising tuition and reducing staff If is correct when a sentence describes a hypothetical situation. - If he participated, he would Beat The GMAT | http://www.beatthegmat.com V: SC: Modifiers In order for a modifying phrase to be used correctly, it must be as close as possible to the thing or person it modifies. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: SC: END OF SC FLASHCARDS END OF SC FLASHCARDS Beat The GMAT | http://www.beatthegmat.com Critical Reasoning Flashcards 2008 Beat The GMAT | http://www.beatthegmat.com V: CR: Scope V: CR: Find the Conclusion The conclusion is usually found in the first or last sentence of the passage. Stay within scope of argument. - Look for signposts: therefore, hence, etc. - Premise words: because, since, in view of, given that, etc. Beat The GMAT | http://www.beatthegmat.com V: CR: Supply your own Conclusion In supply your own conclusion questions, the conclusion must be supported by ALL premises not just one. Beat The GMAT | http://www.beatthegmat.com V: CR: Assumption Assumptions are never stated in the passage. - Answer choice that comes from passage is INCORRECT. - Support conclusion, makes conclusion stronger. - Look out for gaps of logic. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: CR: Assumption Identify unstated premise of passage. - Causal assumption: take an effect and suggest a cause for it. Beat The GMAT | http://www.beatthegmat.com V: CR: Strengthen the Argument Find gap, fix it with additional information. - Connect evidence with conclusion. - Make conclusion stronger. - Strengthen with new information. Beat The GMAT | http://www.beatthegmat.com V: CR: Inference Inference questions are usually very basic, about one or more premises. PICK THE OBVIOUS ANSWER (even if it seems too obvious). Beat The GMAT | http://www.beatthegmat.com V: CR: Mimic the Reasoning Follow same line of reasoning from the passage in the answer. Simplify the terms - If it rains, I will stay at home today. V: CR: Resolve the Paradox Settle contradictory discrepancy. Beat The GMAT | http://www.beatthegmat.com V: CR: Strategy Read the critical reasoning QUESTION first before reading the passage. - If A, then B. Beat The GMAT | http://www.beatthegmat.com V: CR: Causal Assumption Ask whether there might be an alternative cause. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: CR: Analogy Assumptions Are the two situations analogous? Beat The GMAT | http://www.beatthegmat.com V: CR: Statistical Assumptions Are the statistics representative? Beat The GMAT | http://www.beatthegmat.com V: CR: 7 Principles of CR 1) Understand structure of argument (identify conclusion, evidence) look at structural signals. 2) Preview question before reading passage. 3) Paraphrase author s point. 4) Judge argument s persuasiveness read actively. 5) Answer question being asked. 6) Prephrase answer. 7) Keep SCOPE in mind. Moderate words, qualifiers usually correct. Beat The GMAT | http://www.beatthegmat.com V: CR: Strengthen/Weaken V: CR: Number of CR Questions There are about 12 CR questions on the GMAT. Beat The GMAT | http://www.beatthegmat.com V: CR: Assumption An assumption bridges the gap between argument s evidence and conclusion. - Use denial test. - Compare words in evidence against conclusion. - If you find an idea an important word in the conclusion but not in the evidence you found an assumption. Beat The GMAT | http://www.beatthegmat.com V: CR: Strengthen/Weaken Strengthen/Weaken questions are the most common CR question type on the GMAT. - Break down piece of evidence. - Attack validity of an assumption. Don t be careless! Wrong answer choices often have exactly opposite of desired effect. - Don t try to prove or disprove conclusion. - Tip the scales. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: CR: Inference V: CR: 4-Step Method Consider the evidence, draw a conclusion. 1) 2) Read stimulus. 3) Prephrase answer. 4) An inference is an extension of an argument, not a necessary part of it. Preview question stem. Choose an answer. Inferences need not have anything to do with conclusion. Beat The GMAT | http://www.beatthegmat.com V: CR, RC : Paraphrasing Actively translate passages into your own words. - Pretend you are explaining the information in a passage to a 10-year-old kid. Beat The GMAT | http://www.beatthegmat.com V: CR: Strategy Identify the conclusion and find the answer that addresses the conclusion. Most questions follow this guideline. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: CR: Weaken/Strengthen When you compare two items, you must be sure that the two items are indeed comparable. Beat The GMAT | http://www.beatthegmat.com V: CR: Assumption For assumption questions, find the conclusion and determine which answer choice needs to be true for a conclusion to be valid. Beat The GMAT | http://www.beatthegmat.com V: CR: Irrelevant Watch for irrelevant answer choices in CR. - Stay within SCOPE! Beat The GMAT | http://www.beatthegmat.com V: CR: Inference For inference questions, determine which answer choice must absolutely, positively be true based on what you ve read. - Pick the obvious answer choice. V: CR: Negate For assumption questions, negate CR answer choice to see if the conclusion can survive. Beat The GMAT | http://www.beatthegmat.com V: CR: Statistics When an argument is based on statistics, it is usually assumed that the people polled are representative of the whole. - Avoid extremes. Beat The GMAT | http://www.beatthegmat.com V: CR: Indicate Flaw Use the information that is present in the passage to answer Indicate the Flaw CR questions. - Not about new information like Weaken CR questions. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: CR: Prephrase Prephrase an answer before looking at the actual answer choices. Beat The GMAT | http://www.beatthegmat.com V: CR: Inferences Inferences pertain to one or more premises. V: CR: Scope Shifts Be wary of scope shifts. - Pick the obvious. Beat The GMAT | http://www.beatthegmat.com V: CR: Questions involving Surveys Beat The GMAT | http://www.beatthegmat.com V: CR: Evaluate the Argument Test relevance. Consider: Does the survey accurately represent the views of the whole group surveyed? Determine which a choice helps to determine whether a conclusion is valid. Beat The GMAT | http://www.beatthegmat.com V: CR: Explanation With explanation questions, reconcile the facts presented. - Stay within scope. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: CR: Weaken 2 most common ways to weaken an argument: - Break down central assumption. - Assert alternative possibilities relevant to the argument. Beat The GMAT | http://www.beatthegmat.com V: CR: Numbers, Percentages Watch for the distinction between NUMBERS and PERCENTAGES. V: CR: END OF CR FLASHCARDS END OF CR FLASHCARDS Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Reading Comprehension Flashcards 2008 Beat The GMAT | http://www.beatthegmat.com V: RC: Analyzing RC Passage V: RC: Types of Questions WHY is the author writing? Two types of RC questions: WHAT is being said? - General - Main idea, Structure HOW does the author accomplish his goal? Beat The GMAT | http://www.beatthegmat.com V: RC: Signposts - Specific Beat The GMAT | http://www.beatthegmat.com V: RC: Yin-Yang Yin words: Watch for trigger words. - however, but, etc. - Trigger words change tone, direction of a passage. - Generally, the old view, the widespread belief, most scientists think, on the other hand, etc. Yang words: - However, but, etc. Beat The GMAT | http://www.beatthegmat.com V: RC: Inference GMAT inferences go only a tiny bit further than what is said in the passage. - Eliminate exaggerations, offensive words, extreme words. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: RC: Indisputable Answers The answer choice that is high specific and unequivocal is usually wrong. - VAGUE AND GENERAL answers are best. - Words like perhaps and may. Beat The GMAT | http://www.beatthegmat.com V: RC: Indisputable Words V: RC: Respect Nice vague words - usually, sometimes, may, can, some, most ETS respects professionals, America. - Avoid disparaging answers. Too unequivocal BAD! - always, most, everybody, all, complete, never Beat The GMAT | http://www.beatthegmat.com V: RC: Strong emotions - Respectful answers about minorities always. - No prejudiced answers. Beat The GMAT | http://www.beatthegmat.com V: RC: Strategy Be mindful of: - Topic Avoid strong emotions. - Avoid words like: scornful, envious, overly enthusiastic, resolve, etc. - Scope narrowing of topic - Author s purpose - Structure - Author s voice fact from opinion Beat The GMAT | http://www.beatthegmat.com V: RC: Roadmap Make mental roadmap of passage. - Get a sense of the paragraph, argument structure. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: RC: Main Idea Thesis: personal interpretation bolstered by evidence. Beat The GMAT | http://www.beatthegmat.com V: RC: Global Questions Stay within topic and scope. Recognize author s overall intentions, idea, passage structure, purpose. Beat The GMAT | http://www.beatthegmat.com V: RC: Inference V: RC: Scope Scope is the entire passage. - Nouns and verbs must be consistent with tone/scope. Beat The GMAT | http://www.beatthegmat.com V: RC: Logic Why the author does something: Two types of inferences: - Cites a source - Regular inference. - Brings up detail - Agreement: Author/Character/Group would agree with Beat The GMAT | http://www.beatthegmat.com V: RC: Explicit Detail - Structure Beat The GMAT | http://www.beatthegmat.com V: RC: Strategy 1) Create a mental roadmap: label paragraphs, look for signal words. Synthesize. 4) Beat The GMAT | http://www.beatthegmat.com 2) 3) For explicit detail questions, the answer can be pinpointed in the text. Read actively and don t skim. Attack questions. Beat The GMAT | http://www.beatthegmat.com V: RC: Scope Scope is the aspect of the topic (subject matter) that the author discusses in the passage. Beat The GMAT | http://www.beatthegmat.com V: RC: Inference V: RC: Focus Focus on ideas, not facts. Beat The GMAT | http://www.beatthegmat.com V: RC: Anticipate Suggested by passage. Wrong answers: - Distort ideas - Superfluous Anticipate what s next by looking for key words. - Contradictory - Outside of scope With inference questions, be sure to see whether the attitude of passage is positive, negative, or neutral. Beat The GMAT | http://www.beatthegmat.com V: RC: Qualify Beat The GMAT | http://www.beatthegmat.com V: RC: Anticipation Supporting, Continuing Point Additional points: furthermore, in addition, also, to. To qualify a claim is to weaken or soften it. Additional examples: similarly, likewise, for example. Structure: secondly, thirdly. Conclusions: thus, therefore, in conclusion. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: RC: Contrary Words - although, though, even though V: RC: Strategy A strategy for RC: - but - Read for author s purpose and main idea. - despite, in spite of - Paraphrase the text. - except - Create an outline, roadmap of passage. - however, nevertheless - Don t over invest. - unless - while Beat The GMAT | http://www.beatthegmat.com V: RC: Main Idea - 4 min. on reading, 1 min. on question. - Read explanations. Beat The GMAT | http://www.beatthegmat.com V: RC: General Questions Decoy answers for general RC questions are: - Too specific Keep searching for the main idea of a passage! - Too broad - Too extreme - Not relevant Beat The GMAT | http://www.beatthegmat.com V: RC: Specific Questions Decoy answers for specific RC questions: Beat The GMAT | http://www.beatthegmat.com V: RC: Strengthen/Weaken Decoy answers for strengthen/weaken questions: - Refer to wrong part of passage - Out of scope - Make sense but are not mentioned in passage - Weaken instead of strengthen, vice versa - Refute passage directly - Logical answer but not mentioned or supported in passage - Stray away from passage Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: RC: How to Spot a Good Answer V: RC: Good Words for RC Answer Choices - some, many - often - sometimes, rarely usually A good answer: - Paraphrases text - can, could, may, might - Nice, respectful - some people - Not extreme - few people - more, less - likely, possibly - doubtful, unlikely Beat The GMAT | http://www.beatthegmat.com V: RC: Words to Avoid in RC Answer Choices - all - always - never - will - everyone, everybody - no one, nobody - most, least - absolutely - impossible Beat The GMAT | http://www.beatthegmat.com V: RC: Hard Details Note the location and purpose of intricate details, but do not attempt to memorize or even fully understand those details unless a question specifically asks about them. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com V: RC: Topic and Scope Always be mindful of TOPIC and SCOPE. - Topic and scope can often be determined in the first paragraph of a passage. Write them down as soon as you find them on your scrap paper. - Topic - General subject - Examples: stars, industrial safety - Scope - Narrowing of topic - Examples: logistics of space travel to Mars; analysis of industrial regulations in different historical eras Beat The GMAT | http://www.beatthegmat.com V: RC: Purpose, Main Idea Be mindful of author s PURPOSE and MAIN IDEA. Beat The GMAT | http://www.beatthegmat.com V: RC: Inference With inference questions, do not prephrase. - Go right to answer choices and make your judgment. Beat The GMAT | http://www.beatthegmat.com V: RC: Distinction Pay attention to a distinction in a passage that compares two or more people, theories or phenomena. Beat The GMAT | http://www.beatthegmat.com V: RC: END OF RC FLASHCARDS END OF RC FLASHCARDS Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Quantitative Flashcards 2008 Beat The GMAT | http://www.beatthegmat.com Q: Steps to Solve Q: PS: Backsolving Strategy Medium questions require 2 steps to solve. Difficult questions require at least 3 steps. Start with Choice (E) and work back to (A) when backsolving from the answer choices. The GMAT begins with a medium question. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Q: Multiple Q: Assuming Don t assume a number is an integer unless explicitly told so. Beat The GMAT | http://www.beatthegmat.com Q: How to check whether number is multiple of 3 Sum of digits is multiple of 3. Beat The GMAT | http://www.beatthegmat.com Multiples of 3: - 3, 6, 9 Beat The GMAT | http://www.beatthegmat.com Q: How to check whether number is multiple of 4 Last two digits is multiple of 4. Beat The GMAT | http://www.beatthegmat.com Q: How to check whether number is multiple of 6 Number is multiple of 3 and 2. Beat The GMAT | http://www.beatthegmat.com Q: How to check whether number is multiple of 12 Q: How to check whether number is multiple of 9 Sum of digits is multiple of 9. Beat The GMAT | http://www.beatthegmat.com Q: Common Factor Break down both numbers to their prime factors to see what factors they have in common. Multiply shared prime factors to find all common factors. Sum of digits is multiple of 3, last two digits multiple of 4. - What factors greater than 1 do 135 and 225 have in common? 135 = 3 x 3 x 3 x 5 225 = 3 x 3 x 5 x 5 Both share 3 x 3 x 5 in common find all combinations of these numbers: 3 x 3 = 9; 3 x 5 = 15; 3 x 3 x 5 = 45 Beat The GMAT | http://www.beatthegmat.com Q: Simple Probability (# of favorable outcomes) / (# of possible outcomes) Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Q: Gross Profit Gross profit = Selling Price - Cost Beat The GMAT | http://www.beatthegmat.com Q: Combined Events Q: Combinations If order of selection is not relevant and only k objects are able to be selected from a larger set of n objects: For events E and F: - not E = P(not E) = 1 P(E) - E or F = P(E or F) = P(E) + P(F) P(E and F) () n k = n! _____ k!(n-k)! - E and F = P(E and F) = P(E)P(F) () ( ) n k Beat The GMAT | http://www.beatthegmat.com Q: Permutations Counting the number of ways that a set of objects can be ordered: - n! Beat The GMAT | http://www.beatthegmat.com Q: Multiplication Principle If a first object may be chosen in m ways and a second object may be chosen in n ways, then there are mn ways of choosing both objects. Beat The GMAT | http://www.beatthegmat.com n = n-k Beat The GMAT | http://www.beatthegmat.com Q: Multiplication Principle The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event. Beat The GMAT | http://www.beatthegmat.com Q: 1st Rule of Probability Basic rule: The probability of event A occurring is the number of outcomes that result in A divided by the total number of possible outcomes. Beat The GMAT | http://www.beatthegmat.com Q: 2nd Rule of Probability Q: 3rd Rule of Probability Complementary Events: The probability of an event occurring plus the probability of the event not occurring = 1. - P(E) = 1 P(not E) Beat The GMAT | http://www.beatthegmat.com Conditional Probability: The probability of event A AND event B occurring is the probability of event A times the probability of event B, given that A has all ready occurred. Beat The GMAT | http://www.beatthegmat.com Q: 4th Rule of Probability Q: Dependent Events Two events are said to be dependent events if the outcome of one event affects the outcome of the other event. The probability of event A OR event B occurring is the probability of event A occurring plus the probability of event B occurring minus the probability of both events occurring. - P(A or B) = P(A) + P(B) P(A and B) Beat The GMAT | http://www.beatthegmat.com Q: Probability of Multiple Events Beat The GMAT | http://www.beatthegmat.com Q: Indistinguishable Events - A and B < A or B - A or B > Individual probabilities of A, B - P(A and B) = P(A) x P(B) less options - P(A or B) = P(A) + P(B) more options To find the number of distinct permutations of a set of items with indistinguishable items, divide the factorial of the items in the set by the product of the factorials of the number of indistinguishable elements. - How many ways can the letters in TRUST be arranged? 5! ___ = 60 2! Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Q: Circular Permutations The number of ways to arrange n distinct objects along a fixed circle is: (n 1)! Beat The GMAT | http://www.beatthegmat.com Q: Multiple Event Probability To determine multiple-event probability where each individual event must occur in a certain way: - Figure out the probability for each individual event. Q: Probability and Geometry If a point is chosen at random within a space with an area, volume, or length of Y and a space with a respective area, volume, or length of X lies within Y, the probability of choosing a random point within Y is the area, volume, or length of X divided by the area, volume, or length of Y. Beat The GMAT | http://www.beatthegmat.com Q: Trial Problems Look at the probability of NOT OCCURRING. - P(Event Not Occurring) = 1 P(Event Occurring) - Multiply the individual probabilities together. Beat The GMAT | http://www.beatthegmat.com Q: Combinations: Order doesn t matter n! _______ r!(n r)! Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Q: Permutations: Order matters Number of permutations of r objects from a set of n objects: n! _____ (n r)! Beat The GMAT | http://www.beatthegmat.com Q: Number Added or Deleted Q: Odd Factors Use mean to find number that was added or deleted. - Total = mean x (number of terms) Odd numbers have only odd factors. - Number deleted = (original total) (new total) - Number added = (new total) (original total) Beat The GMAT | http://www.beatthegmat.com Q: Purchase Price vs. Market Value Beat The GMAT | http://www.beatthegmat.com Q: Quadratic Formula To find roots of quadratic equation, ax^2 + bx + c = 0: Remember: purchase price is not the same as market value. x = [-b +- sq. root (b^2 4ac)] / 2a Beat The GMAT | http://www.beatthegmat.com Q: Exponents Beat The GMAT | http://www.beatthegmat.com Q: Highest Common Factor (HCF), Lowest Common Multiple (LCM) Prime Factorization 1. Start by writing each number as product of its prime factors. 2. Write so that each new prime factor begins in same place. (x^r)(y^r) = (xy)^r 3. Highest Common Factor is found by multiplying all factors appearing on BOTH lists. 60 = 2 x 2 x3 x5 72 = 2 x 2 x 2 x 3 x 3 (3^3)(4^3) = 12^3 = 1728 HCF = 2 x 2 x3 = 12 4. Lowest common multiple found by multiplying all factors in EITHER list. 60 = 2 x 2 x3 x5 72 = 2 x 2 x 2 x 3 x 3 LCM = 2 x 2 x 2 x 3 x 3 x 5 = 360 Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Q: Factor Out Q: rt = d For a fixed distance, the average speed is inversely related to the amount of time required to make the trip. 5^k 5^(k 1) - Since Mieko s average speed was of Chan s, her time was 4/3 as long. (1 (1/5))5^k 5^k (1/5)5^k (4/5)5^k - rt = d - (3/4)r(4/3)t = d Beat The GMAT | http://www.beatthegmat.com Q: Check for Prime Beat The GMAT | http://www.beatthegmat.com Q: Backsolving Strategy 1. Pick a number n. 2. Start with the least prime number, 2. See if 2 is a factor of your number. If it is, your number is not prime. 3. If 2 is not a factor, check to see if the next prime, 3, is a factor. If it is, your number is not prime. 4. Keep trying the next prime number until you reach one that is a factor (in which case n is not prime), or you reach a prime number that is equal to or greater than the square root of n. When answer choices have variables in them, start from the LAST choice and work back to the first. 5. If you have not found a number less than or equal to the square root of n, you can be sure that your number is prime. Beat The GMAT | http://www.beatthegmat.com Q: Squaring Fractions Beat The GMAT | http://www.beatthegmat.com Q: Inscribed Angle, Minor Arc Inscribed angle = 35 degrees When positive fractions between 0 and 1 are squared, they get smaller. Minor arc = 70 degrees - (1/4)^2 = (1/16) Radius Minor arc = 2 x (inscribed angle) Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Q: Evenly Divisible Problem Q: Set Problem Each of 25 people is enrolled in history, math, or both. If 20 are enrolled in history and 18 are enrolled in math, how many are enrolled in both? History Math To determine the number of integers less than 5000 that are evenly divisible by 15: 20 n - Divide 4999 by 15 => 333 integers n 18-n (20 n) + n + (18 n) = 25 => n = 13 Beat The GMAT | http://www.beatthegmat.com Q: Interest Problem If $10,000 is invested at 10% annual interest, compounded semi-annually, what is the balance after 1 year? Beat The GMAT | http://www.beatthegmat.com Q: Mixture Problem How many liters of a solution that is 15% salt must be added to 5 liters of a solution that is 8% salt so that the resulting mixture is 10% salt? 10,000 + (10,000)(0.05) = 10,500 10,500 + (10,500)(0.05) = $11,025 0.15n + 0.08(5) = 0.1(n + 5) 15n + 40 = 10n + 50 OR 10,000(1 + (0.10/2))^2 = $11,025 Beat The GMAT | http://www.beatthegmat.com Q: Area of a Trapezoid (sum of bases)(height) Beat The GMAT | http://www.beatthegmat.com 5n = 10 => n = 2 liters Beat The GMAT | http://www.beatthegmat.com Q: Rules of Exponents r xs = () 1 s x r = s xr Beat The GMAT | http://www.beatthegmat.com Q: Always Try to Factor! Q: Intersecting Sets x^3 2x^2 + x = -5(x 1)^2 x(x^2 2x + 1) = -5(x 1)^2 x(x 1)^2 + 5(x 1)^2 = 0 |A union B| = |A| + |B| - |A intersect B| (x + 5)(x 1)^2 = 0 x= -5, 1 Beat The GMAT | http://www.beatthegmat.com Q: Standard Deviation of n Numbers Beat The GMAT | http://www.beatthegmat.com Q: Consecutive Integers 1. Find arithmetic mean. 2. Find differences between mean and each of the n numbers. 3. Square each of the differences. Even: 2n, 2n + 2, 2n + 4 Odd: 2n + 1, 2n + 3, 2n + 5 4. Find average of squared differences. 5. Take non-negative square root of this average. Beat The GMAT | http://www.beatthegmat.com Q: Prime Number A prime number is a positive integer that has exactly two different positive divisors: 1 and itself. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Q: Zero is Even Zero is an even integer. Beat The GMAT | http://www.beatthegmat.com Q: Percent Increase vs. Percent of Q: Geometry: Similar Triangle Areas D A 8 4 4 2 B Be careful about percent increase vs. percent of. 3 C E 6 The ratio of the areas of two similar triangles is the square of the ratio of corresponding lengths. - Each side of triangle DEF is 2 times the length of corresponding triangle ABC - Triangle DEF must have 2^2, or 4, times the area of triangle ABC. Beat The GMAT | http://www.beatthegmat.com Q: Geometry: Triangles Beat The GMAT | http://www.beatthegmat.com Q: Gross vs. Net a d=a+b b c Gross is the total amount before any deductions are made. d Net is the amount after deductions are made. Exterior angle d is equal to the sum of the two remote interior angles a and b. Beat The GMAT | http://www.beatthegmat.com Q: Use FOIL Method with Quadratics with Roots n 4(sq. root n) + 4 => ((sq. root n) - 2)((sq. root n) - 2) Beat The GMAT | http://www.beatthegmat.com Q: Useful Percents to Know 1/8 = 12.5% 1/6 = 16.6% x^2 4x + 4 Beat The GMAT | http://www.beatthegmat.com F 5/6 = 83.3% Beat The GMAT | http://www.beatthegmat.com Q: Odd and Even Q: Simplify Base Odd + Odd = Even Odd x Odd = Odd Even + Even = Even Even x Even = Even Odd + Even = Odd Odd x Even = Even Always try to simplify the base. - If 27^n = 9^4, then n = Any addition involving an odd number creates an odd sum. (3^3)^n = (3^2)^4 => n = 8/3 Any multiplication involving an even number creates an even product. Beat The GMAT | http://www.beatthegmat.com Q: Powers and Roots To multiply one radical by another, multiply or divide the numbers outside the radical signs, then the numbers inside the radical signs. 6(sq.rt. 3) x 2(sq.rt. 5) = (6 x 2)((sq.rt. 3 x sq.rt. 5) = 12(sq.rt. 15) (12(sq.rt. 15))/(2(sq.rt. 5)) = (12/2)(sq.rt. 15/sq.rt. 5) = 6(sq.rt. 3) Beat The GMAT | http://www.beatthegmat.com Q: Averages Beat The GMAT | http://www.beatthegmat.com Q: Percentage To make a percentage, multiply by 100%: - 1/400 = % = 0.25% To drop a percent, divide by 100%: - % x 1/100 = 1/20,000 Beat The GMAT | http://www.beatthegmat.com Q: Divisors Think of averages as balancing. - The average of 3, 4, 5, and x is 5. What is x? 3 is 2 less than 5 You can find all the divisors of a number by finding all the prime factors. 4 is 1 less than 5 5 is the average. x=5+3=8 Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Q: Volume of a Sphere Q: Factor Out and Simplify Immediately try factoring/simplifying when possible. - Is (2x + 24)/6 an integer? (4/3) r^3 => 2x/6 + 24/6 => x/3 + 4 Beat The GMAT | http://www.beatthegmat.com Q: Sum of Angles in a Regular Polygon Beat The GMAT | http://www.beatthegmat.com Q: Multiple Event Probability 2 things to do: Sum of interior angles in a polygon with n sides: - Find the total number of possible outcomes. 180(n 2) - Find the number of desired outcomes. - Write them out if necessary. Beat The GMAT | http://www.beatthegmat.com Q: Group Problems Involving Either/Or Q: Group Problems Involving Both/Neither Some GMAT word problems involve groups with distinct either/or categories (male/female, blue collar/white collar, etc.). The key is to organize the information into a grid. Doctors Male Dentists Total 55 27 9 48 36 MIXED GROUP FORMULA: 82 130 Female Total Beat The GMAT | http://www.beatthegmat.com 48 Beat The GMAT | http://www.beatthegmat.com Group1 + Group2 + Neither Both = Total Beat The GMAT | http://www.beatthegmat.com Q: Balancing Method for Mixtures/Dilutions Q: Average Rate (percent/price difference between weaker solution and desired solution) x (amount of weaker solution) = (percent/price difference between the stronger solution and desired solution) x (amount of stronger solution) Average A per B = (Total A)/(Total B) Ex. How many liters of a solution that is 10% alcohol by volume must be added to 2 liters of a solution that is 50% alcohol by volume to create a solution that is 15% alcohol by volume? Average Speed = (Total Distance)/(Total Time) - n(15 10) = 2(50 15) 5x = 2(35) => n = 70/5 => 14 liters of 10% solution must be added. Beat The GMAT | http://www.beatthegmat.com Q: Added, Deleted Beat The GMAT | http://www.beatthegmat.com Q: A Common Digits Problem Number added: (new sum) (original sum) Number deleted: (original sum) (new sum) Ex. The average of 5 numbers is 2. After one number is deleted, the new average is 3. What number was deleted? AB + BA => CDC 47 + 74 or 121 83 + 38 121 Original sum: 5 x 2 = 10 New sum: 4 x (-3) = -12 Number deleted = 10 (-12) = 22 Beat The GMAT | http://www.beatthegmat.com Q: Compound Interest Beat The GMAT | http://www.beatthegmat.com Q: Compound Interest (final balance) = (principal) x (1 + (interest)/C)^[(time)(C)] C = the number of times compounded annually Usually you don t need to calculate compound interest. Try finding simple interest and looking for the answer that is a little bit larger. If $10,000 is invested at 8% annual interest, compounded semiannually, what is the balance after 1 year? - Final balance = (10,000)(1 + (0.08)/2)^[(1)(2)] = 10,000 x (1.04)^2 = $10,816 Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Q: Factorial of Zero Q: Simple Interest Simple interest = (principal)(interest rate)(time) decimal years 0! = 1 If $12,000 is invested at 6% simple annual interest, how much interest is earned after 9 months? - ($12,000)(0.06)(9/12) = $540 Beat The GMAT | http://www.beatthegmat.com Q: Sum of Consecutive Numbers Beat The GMAT | http://www.beatthegmat.com Q: Count Consecutive Numbers Number of integers from A to B inclusive = B A + 1 Sum = (average)(number of terms) Ex. How many consecutive integers are there from 73 through 419, inclusive? 419 73 + 1 = 347 Beat The GMAT | http://www.beatthegmat.com Q: Average of Consecutive Answers The average of a set of evenly spaced consecutive numbers is the average of the smallest and largest numbers in the set. - Ex. What is the average of all integers from 13 to 77? (13 + 77)/2 = 90/2 = 45 Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Q: Percent 15 is 3/5 percent of what number? 3/5 percent = 3/500 15 = (3/500) x whole whole = 2500 Beat The GMAT | http://www.beatthegmat.com Q: Work Problems Q: PS: Guessing Consider work done in one hour. Inverse of the time it takes everyone working together = Sum of the inverses of the times it would take each person working individually. Ex. You have worker A and worker B doing a job: 1 A 1 + B If you have to guess in a problem solving question, go with (D) or (E). - Especially with problems that force you to use or plug in the answer choices. 1 = T Beat The GMAT | http://www.beatthegmat.com Q: Prime Numbers Beat The GMAT | http://www.beatthegmat.com Q: Simple Compounding A = P(1 + r)^n 1 is not a prime number. A = amount accumulated The first eight prime numbers are: P = principal - 2, 3, 5, 7, 11, 13, 17, 19 r = annual rate of interest n = number of years Beat The GMAT | http://www.beatthegmat.com Q: Factors Beat The GMAT | http://www.beatthegmat.com Q: Slope Factors of 18: 1, 2, 3, 6, 9, 18 y = mx + b Factors of 6: 1, 2, 3, 6 m = slope = (difference in y coordinates) / (difference in x coordinates) Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Q: Triangles Q: Approximations 30-60-90 45-45-90 3-4-5 2x 5 x x(sq.rt.2) 3 x x(sq.rt 3) 4 Square root of 2 = 1.4 x 5-12-13 13 15 Square root of 3 = 1.7 9-12-15 12 5 12 9 Beat The GMAT | http://www.beatthegmat.com Q: Quadratics (x + y)^2 = x^2 + 2xy + y^2 (x + y)(x y) = x^2 y^2 Beat The GMAT | http://www.beatthegmat.com Q: Equation Rule You must have as many equations as you have variables for the data to be sufficient. Ex. What is the value of y? When you see an equation in factored form in a question, immediately UNFACTOR it; vice versa. Beat The GMAT | http://www.beatthegmat.com Q: DS: Insufficient Half the time statements (A) and (B) are both insufficient. Given: x + y = 1 => insufficient without another distinct equation Beat The GMAT | http://www.beatthegmat.com Q: DS: Rephrase A good data sufficiency strategy is to rephrase the information in a question: Ex. z + z < z? => z < 0? Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Q: DS: What is Being Asked? In Data Sufficiency questions, you are usually being asked 1 of 3 things: 1. A specific value. 2. A range of numbers Q: DS: Strategy Immediately write out the DS problem type (value, range, yes/no) on your scratch paper before you begin a DS problem. 3. Yes/No Beat The GMAT | http://www.beatthegmat.com Q: DS: Strategy 1. Focus on the question stem thinking about the information needed to answer the question. 2. Look at each stem separately. 3. Look at both statements in combination. Beat The GMAT | http://www.beatthegmat.com Q: DS: First DS Questions Calculate out the first DS questions to make sure they are correct. It is important to start out the section strong. - Half of the DS answers on the GMAT come down to step 3. Beat The GMAT | http://www.beatthegmat.com Q: DS: Hard Questions Beat The GMAT | http://www.beatthegmat.com Q: DS: Hard Questions On harder DS questions, answer choices tend to be more sufficient than they might appear. Skip statements that you do not understand. - Eliminate as much as possible. - DON T CHOOSE (E) if you have to guess. - Pick between (A) or (C), if you can eliminate (B). - Historically, (A) is slightly more common as the right answer. Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Q: DS: Yes/No About 1/3 of DS questions are YES/NO questions. Beat The GMAT | http://www.beatthegmat.com Q: DS: Common Trap Do NOT use the information in one statement as an assumption in the second statement. - Statements are not necessarily related. Q: DS: Looking at Both Statements Together Only about half the time do you have to look at both statements in combination. Beat The GMAT | http://www.beatthegmat.com Q: DS: Sufficiency in YES/NO Questions On YES/NO DS questions, if a statement answers the question conclusively in the affirmative or in the negative, then IT IS SUFFICIENT. - View separately! Beat The GMAT | http://www.beatthegmat.com Q: DS: Equations Beat The GMAT | http://www.beatthegmat.com Q: DS: Strategy AD or BCE To achieve sufficiency, there must be as many equations as there are variables. If you can determine that choice (A) is correct in your DS question, then you know that the ultimate answer must be either (A) or (D). If you can determine that choice (A) is not correct in your DS question, then you know that the ultimate answer must be (B), (C), or (E). Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Q: END OF QUANTITATIVE FLASHCARDS END OF QUANTITATIVE FLASHCARDS Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com Beat The GMAT | http://www.beatthegmat.com GMAT Flashcards 2008 Beat The GMAT | http://www.beatthegmat.com

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