Strategy

Question 1

Algebra vs. Arithmetic Strategy: Test Cases (TC)

Answer 1

DS: “Theory” problem. Use when the problem allows multiple possible values for the unknowns. Try at least two different cases to see whetehr you can get a different answers (Yes AND No; two DIFFERENT values)

PS: Use when the problem asks a “must be” or “could be” question. Test cases until only one answer choice remains

Question 2

Algebra vs. Arithmetic Strategy: Choose Smart Numbers (SN)

Answer 2

PS Only.

When you see variable expressions or relative values (sich as percents, fractions, ratios) in the answers, check the problem to see whether you can use smart numbers.

If the problem never gives you a real number for that variable or relative value, you can use smart numbers.

Question 3

Algebra vs. Arithmetic Strategy: Work Backwards (WB)

Answer 3

PS only.

Clues to work backwards:

1. Pretty answer choices
2. Questions asks for single value that you can plug in

B wrong + D wrong in opposite direction => C

B wrong + D wrong but getting better => E

Question 4

Sufficiency of a Statement for a Value DS Problem

Answer 4

Sufficient: Provides exactly one possible value

Insufficient: Provides more than one possible value

Question 5

Sufficiency of a Statement for a Yes/No DS Problem

Answer 5

Sufficient: Answer is Always Yes or Always No

Insufficient: Answer is Sometimes Yes, Sometimes No

Question 6

Exponents in Test Cases Problem

Answer 6

Start with 0 and 1

Consider negatives

Consider fractions between 0 and 1 (or maybe between 0 and -1)

Question 7

DS Guessing Strategies: “Identical Twins”

Answer 7

If both statements provide the exact same information, immediately cross off A, B, C

Question 8

DS Guessing Strategies: “The Cannibal”

Answer 8

If statement 1 gets cannibalized, cross of A and C.

If statement 2 gets cannibalized, cross of B and C.

Of the 3 remaining answers, the best guess is the one associated with the cannibal (A or B) since that statement provides at least two pieces of relevant information.

Question 9

DS Guessing Strategies: Suspecting a C Trap

Answer 9

If you suspect a C trap (i.e. it looks obvious that using the information together would be sufficient), then cross of C and E.

Then choose A or B depending on whether statement 1 or 2, respectively, look more complicated.

Question 10

Primary Purpose Cheat Sheet

Answer 10

1. Identify the question

Common language for Primary Purpose: primary purpose or function, author is primarily concerned with, author would be most likely to agree with

Common language for Paragraph: purpose of paragraph, relationship of paragraph to passage as a whole

2. Find the spuport using map or general understanding of passage
3. Predict an answer BEFORE looking at the answer choices
4. Eliminate answers based on common traps (direct contradiction, extremes, one word off, out of scope, true but not right i.e. doesn’t answer the question)

Question 11

Common Traps for Primary Purpos Questions

Answer 11

1. Direct contradiction: the passage says the opposite
2. Extremes: extreme language (“all” or “never”) without support in the passage
3. One word off: tempting but 1-2 words are wrong
4. Out of scope: goes beyond what the passage says
5. True but not right: passage says it but it doesn’t answer the question
6. Mix-up: uses words directly from the passage but the meaning is not what the passage says

Question 12

When to estimate & things to keep in mind

Answer 12

If possible, try to make your rounding errors cancel out (i.e. round one number slightly up and the other number slightly down)

Estimate when:

1. Problem explictely uses words like “approximate”
2. Answer choices are far apart (in relative terms) or they cover certain “divided” characteristics

Divided characteristics:

1. Positive vs. negative
2. Fraction Problem: >1 vs. <1
3. Probability Problem: >0.5 vs. <0.5

Question 13

Specific Question Cheat Sheet

Answer 13

1. Identify the question: detail (“according to the passage”); inference (“infer”, “imply”, “suggest”); specific purpose (“in order to”); EXCEPT
2. Find the support. Find the specific paragraph of sentences needed or try to work backwards from the answers
3. Predict an answer - formulate in your own words
4. Eliminate and pick the right answer

Question 14

More similar statements signify…

Answer 14

1. The answer is less likely to be C or D
2. The method to evaluate each statement will likely be the same

Question 15

Data Sufficiency Framework

Answer 15

Across the top: Facts, Question (REPHRASE!), Type (Value or Yes/No), Elimination Grid (AD/BCE or BD/ACE)

Question 16

Steps to solve a Sentence Correction question

Answer 16

0. Write out A-E
1. First Glance - scan for differences
2. Read the “original” - ready for meaning and structure (core) and with my clues in mind
3. Find an issue THAT I KNOW WHAT TO DO WITH
4. Eliminate everything I can

Steps 3 and 4 are iterative until an answer is found

Question 17

First step of a Problem Solving question

Answer 17

Look at the answers!

Question 18

When to avoid algebra

Answer 18

Algebra is ugly if you have a system of nonlinear equations. You will end up with a quadratic if two unknowns get multiplied.

Common use cases to look out for:

1. Area (base x height)
2. Price x quantity

Question 19

Reading Comprehension Process

Answer 19

4-Step Process:

1. ID Question Type

“WHAT?” = Specific detail, inference, strengthen/weaken

“WHY?” Primary purpose/main idea, “in order to” (these questions require you to look at context)

2. Find proof (except for Main Idea questions)
3. PREDICT AN ANSWER
4. Eliminate / find a match

Question 20

Wrong answer types for Reading Comprehension questions

Answer 20

For Main Idea Questions:

1. Wrong tone (too strong)
2. True but too limited
3. Too broad
4. Incorrect facts / inaccurate (“word salad” - uses words from passage)

For Detail Questions:

1. Incorrect facts / inaccurate (“word salad”) - every other choice is just WRONG

These are easy to predict. The answer normally comes from the first time a piece of evidence/word is mentioned, if it is mentioned multiple times.

Question 21

On TC, when I see absolute value (|x|), I’ll try…

Answer 21

Positive (+) and negative (-)

Question 22

On TC, when I see exponents (x²), I’ll try…

Answer 22

0, 1, fractions

Question 23

“Good” numbers when choosing smart numbers

Answer 23

• Don’t pick weird numbers - your numbers should lead directly to the correct answer
• Avoid 0 and 1
• Avoid numbers that already appear in the problem
• If you have to pick values for 2+ variables, choose different values for each variable
• If appropriate, pick numbers with different characteristics (e.g. even/odd)

Question 24

Building Blocks of an Argument: Premise

Answer 24

• Part of the core of teh argument; present in every argument
• Supports the author’s conclusion
• Can be a fact or an opinion; can be a description, historical information, data, or a comparison of things
• Often signaled by words or phrases such as because of, since, due to, or as a result of

Question 25

Building Blocks of an Argument: Conclusion

Answer 25

• Part of the core of an argument; present in most arguments
• Represents the author’s main opinion or claim; can be in the form of a prediction, a judgment of quality or merit, a statement of casuality, or the outcome of a plan
• Supported by at least one premise
• Often signaled by words such as therefore, thus, so, or consequently

Question 26

Building Blocks of an Argument: Background

Answer 26

• Not part of the core; not always present
• Provides context to help understand the core; similar to premises but less important to the argument itself
• Almost always fact-based; can be in almost any form

Question 27

Building Blocks of an Argument: Counterpoint or Counterpremise

Answer 27

• Not part of the core; only present occassionally
• Opposes or goes against the author’s conclusion in some way
• Introduces multiple opportunities for traps: believing that the conclusion is the opposite of what it is, mistakenly thinking that a counterpoint is a premise, etc.
• Often signaled by transition word such as although, though, however, yet, and but

Question 28

Building Blocks of an Argument: Assumption

Answer 28

• Not part of the core; not written down in the argument
• Something the author must believe is true in order to draw the given conclusion

Question 29

Common Argument Types and relevant issues/questions

Answer 29

Causation

Circumstances are presented. The conclustion proposes a particular cause for that set of circumstances.

Correct answer choices often realted to potetnial other causes for the observed result.

Plan

Proposes a course of action to achieve a sepcific goal. The conclusion is the goal of the plan. The words in order to or simply to frequently precede the goal of the plan.

A plan must work as expected to achieve its aim. A plan may fail if the steps of teh plan don’t work as anticipated or there are unexpected costs or hindrances not discussed in the original argument.

Prediction

Sometimes arguments conclude with a prediction of a future event.

In order for a prediction to come true, no other circumstances can intervene that might work against the prediction.

Profit

Conclusion often states profits will increase or decrease. Profit arguments are often a sub-categoy of predictions. Profit = Revenue - Cost.

Arguments will often discuss only one element of profit (either revenues or costs) whereas the answer choice will focus on the other component.

Question 30

Argument Structure Cheat Sheet

Answer 30

Question 31

Structure-Based Family of Critical Reasoning Questions

Answer 31

1. Describe the Role: Identify the roles (building blocks) of the boldface portions of the argument.
2. Describe the Argument: Describe how a certain piece of information affects the argument.

Question 32

Assumption-Based Family of Critical Reasoning Questions

Answer 32

WITHOUT THE ASSUMPTION, THE ARGUMENT FAILS.

1. Find the Assumption: Identify an unstated assumption.
2. Strengthen the Argument: Identify a new piece of information that strengthens the author’s argument.
3. Weaken the Argument: Identify a new piece of information that weakens the author’s argument.
4. Evaluate the Argument: Identify a new piece of information that would help to determine the soundness of the argument.
5. Identify something illogical in the argument.

Question 33

Evidence-Based Family of Critical Reasoning Questions

Answer 33

1. Inference: Identify soemthing that must be true based on the given information
2. Explain a Discrepancy: Identify a new piece of information that resolves some apparent paradox in the argument

Question 34

Critical Reasoning Methodology Cheat Sheet

Answer 34

1. Identify the Question
2. Deconstruct the Argument
3. State the Goal
4. Work from Wrong to Right

Question 35

Describe the Role Cheat Sheet

Answer 35

1. Identify Question: “Role”, boldface text in the argument
2. Deconstruct Argument: Find conclusion, premises, counterpremises if present

Label the boldface statement(s):

Primary Method: C, P, or X

Secondary Method: Fact/Opinion, For/Against Conclusion, Same/Opposite “Sides”

3. State Goal: Know desired labels before going to answers
4. Wrong to Right: Common trap answers are half right or one word off

Question 36

Describe the Argument Cheat Sheet

Answer 36

1. Identify Question: Often how one person responds or objects to something
2. Deconstruct Argument: Find conclusion, premises

Does the second person flat-out contradict what the first one says? Or just question whether the conclusion is relevant/accurate? Does the second person introduce new info?

3. State Goal: What was attacked and how?
4. Wrong to Right: Common trap answers are one word off, or don’t address what the person directly attacks

Question 37

Find the Assumption Cheat Sheet

Answer 37

1. Identify Question: Look for “assumption” most commonly, or less common, “assume”, “required”, “more reasonably drawn”
2. Deconstruct Argument: Find conclusion, premises; brainstorm assumptions, gaps in argument
3. State Goal: Something that must be true in order for the author to draw this conclusion
4. Work from Wrong to Right:

Right = Must be true to draw conclusion; if not true, argument will be severely weakened (if stuck, try Negation technique)

Wrong (Traps) = No Tie to Conclusion, Reverse Logic, Irrelevant Distinction or Comparison

Question 38

CR: Strengthen the Argument Cheat Sheet

Answer 38

1. Identify Question: most common = strengthen, support, if true; less common = if feasbile, best basis or best reason. For FitB, because or since before the blank.
2. Deconstruct Argument: Find conclusion/premises, brainstorm assumptions/gaps in argument.
3. State Goal: A new piece of info that makes the argument MORE LIKELY to be valid.
4. Work from Wrong to Right: RIGHT makes the argument stronger. WRONG = Reverse Logic (makes conclusion weaker) or No Tie to Argument.

Question 39

CR: Weaken the Argument Cheat Sheet

Answer 39

1. Identify Question: most common = weaken, undermine, if true; less common = if feasbile, doubt.
2. Deconstruct Argument: Find conclusion/premises, brainstorm assumptions/gaps in argument.
3. State Goal: A new piece of info that makes the argument LESS LIKELY to be valid.
4. Work from Wrong to Right: RIGHT makes the argument weaker. WRONG = Reverse Logic (makes argument stronger) or No Tie to Argument.

Question 40

Testing Cases Cues

Answer 40

All the Quant Chapter 27, Page

Question 41

Geometry Strategy: The 3 Principles

Answer 41

1. If they don’t tell you, don’t assume.
2. If they give you a piece of information, use it.
3. Know your rules and formulas.

Question 42

Evaluate the Argument Cheat Sheet

Answer 42

1. Identify Question: common = evaluate, determine, useful to know; less common = important to research or establish
2. Deconstruct Argument: find conclusion/premises; brainstorm assumptions/gaps in argument
3. State Goal” An issue or question that could either strengthen or weaken the argument, depending on which way it goes
4. Work from Wrong to Right: RIGHT = strengthens and weakens conclusion; WRONG = No Tie to Argument, Irrelevant Distinction or Comparison. Note: Don’t add assumptions! Right answers should work as is

Question 43

Find the Flaw Cheat Sheet

Answer 43

1. Identify Question: common = flaw, no “if true” language; less common = vulnerable to criticism
2. Deconstruct Argument: Find conclusion/premises, brainstrom assumptions/gaps in arguments
3. State Goal: something tied to an assumption that would undermine the concluion, not strengthen it
4. Work from Wrong to Right: RIGHT = points out a flaw, harms the conclusion; WRONG = Irrelevant Distinction/Comparison, No Tie to Argument, Reverse Logic (strengthens)

Question 44

Inference Cheat Sheet

Answer 44

1. Identify Question: common = conclude, infer; less common = assertion, hypothesis, must be true

Infer = Use argument to support answer. Strengthen = Use answer to support conclusion in argument.

2. Desconstruct Argument: Find premises (No conclusion! No assumptions!)
3. State Goal: Must be true based on info given in argument/ Does not need to use all argument info.
4. Work from Wrong to Right: RIGHT = Must be true given info in argument. WRONG = Real-World Distinction (logical in real world but not necessarily true based on argument), Reverse Direction (says X leads to Y, when really Y leads to X), Switch Terms (leads to different meaning: not the right group, object, or idea)

Question 45

Explain a Discrepancy Cheat Sheet

Answer 45

1. Identify Question: common = explain, resolve, if true; les common = accounts for the findings
2. Deconstruct Argument: Find premises (No conclusion! No assumptions!)
3. State Goal: Articulate the apparent contradiction or padardox. Find an answer that resolves the paradox - makes it go away.
4. Work from Wrong to Right: RIGHT = resolves apparent paradox. WRONG = Reverse Logic (answer highlights discrepancy rather than resolving it), Half Way (addresses one of the premises but not both)