Sum of exterior angles in a polygon with any number of sides: 360 degrees
Sum of internal angles in a polygon with "n" sides: (n - 2) x 180 degrees
Backup tip: On the GRE, if you feel that you are running very short of time on a Verbal section......you must mark one RC randomly and move on...
-- Use the saved time to perform very well on the remaining questions!
To find the remainder of a number with 11...
Divide the difference between the sum of odd-numbered digits and the sum of even-numbered digits by 11.
Example: 54321
Sum of odd-numbered digits = 1 + 3 + 5 = 9Sum of even-numbered digits = 2 + 4 = 6Difference = 9 – 6 = 3Remainder with 11 = 3 % 11 = 3Hence, the remainder of 12345 with 11 is 3
Parallelism...
Parallelism is about conveying similar meanings in a similar way.In such constructions, one part of the sentence requires a logical counterpart.
Scarcity is at the core of all economics: the more ______ a resource is, the less it is worth.
~ abundant
Use of present participle for conveying a cause-effect relationship
Present participle is “verb + ing”studyingeatingsleeping
Use of present participle on only one of the two sides of a comma generally suggests a cause-effect relationship.
- Scientists discovered a vaccine, putting an end to the epidemic.- Discovering a vaccine, scientists put an end to the epidemic.
Two successive discounts of 50% are equivalent to what percentage of discount?
100 --> 50 --> 25
75% discount.
Percentage change:
[(New Value-Old Value)/ Old Value] x 100
Please note: the denominator is "old value".
Some helpful roots...
in / un: no
- insomnia
hyper: more
- hypersomnia
hypo: less
- hyposomnia
Be cautious when you see "numbers" in CR questions.- Often, the key to solving the question lies in those numbers.
Be cautious when you see "numbers" in CR questions.- Often, the key to solving the question lies in those numbers.
Time management for AW response:
~2 Minutes: Read and understand the topic + instructions.
- Decide your stand.
~3 Minutes: Write the first and the last paragraphs.
- As per your template.
~4 Minutes: List-down, the “reason + example” sets.
- Rank them in order of importance.
~2 Minutes: List-down, points in favor of counter-argument.
~16 Minutes: Type middle 4 – 6 paragraphs.
Remember: size DOES matter!
~3 Minutes: Proofread carefully.
Percentage change:
[(New Value-Old Value)/ Old Value] x 100
Please note: the denominator is "old value".
172
The mind-map-approach (MMA) for RCs
1.Skim through the first byte.
2. Answer yourself: WHAT did the byte DO?
Keep it truly simple & brief.Avoid paraphrasing the details.
3. Skim through the next byte.
Answer yourself: WHAT did the byte DO?Link the WHAT of this byte with the WHAT of the earlier byte.
4. Keep repeating Step 3 for all the subsequent bytes.
Interesting roots coming together...
venter: belly
- ventral, ventricle
loqui: speak
- eloquent, loquacious, soliloquy
ventriloquist: one who speaks without moving lips (speaks from the belly)
1-week gap in prep hurts your progress by 3-weeks.
Monday-to-Friday: Concept-building + PracticeSaturday: Re-attempt incorrectly answered questions + ConsolidateSunday: A full-length test with proper analysis
Practice RCs, everyday!The skill will help you in all sections and question types!!
Don't leave mocks for the end - it's a common mistake.Take a mock every week.
RCs make or break your GRE.Practice RCs everyday!
Don't exhaust official material early - it's a common mistake.Save it for the last few weeks of prep.
Mocks are not just for testing "preparedness".They build stamina/temperament/strategy.They keep you in touch with all topics.TAKE MOCKS REGULARLY!
SE and TC concepts should be regularly revisited.Make Stage-1 videos and GRE Shots your good friends!
60% of all learning comes from analyzing mistakes!
On Verbal questions, don't "Select 1 choice."Rather, "Eliminate 4 choices."
You can score high despite getting a few questions incorrect.
On the test, don't get stuck on any one question!
Schedule your GRE (only) once you get your target score on 3 consecutive mocks!
While attempting AW, type the first and the last paragraphs first.
- This will ensure that your essay will look 'complete'. even if you run out of time.
- This will give you more time to think about the middle paragraphs.
On the GRE, ensure answering each question.-- Even if it means guessing on a few.
- Scoring-wise, "not attempted" is no better than "incorrectly attempted".
If it really comes down to "guessing" on the GRE...
- On RCs and CRs, go for the "longest" answer choices.
- On QC, go for "D".
Understanding the "intended meaning" is the key to solving SE & TC questions.
Do not chase "tricks/tips/shortcuts", chase "concepts"!
Do not chase "scores", chase "learning". Scores will follow.
Backup tip: On the GRE, if you get an RC that you just can't comprehend......you must mark randomly and move on...
- Don't let one RC decide the fate of your complete GRE score.
-- Rather, save time and get the remaining questions correct!
Backup tip: On the GRE, if you feel that you are running very short of time on a Verbal section......you must mark one RC randomly and move on...
-- Use the saved time to perform very well on the remaining questions!
Crucial Exam Tip...
On the GRE, don't get stuck on any one question for too long...
Easier questions shall be waiting for you. :)
Approach for attempting SE questions...
1. Read the COMPLETE sentence and get the CORE meaning.
2. Set a BROAD EXPECTATION from the correct answer choices.
3. Eliminate!
4. Cross-check.
Incorrect answer choices on SE questions...
- Irrelevant to our “broad expectation” from the correct answer choice.
-- Most common.
- Opposite to our “broad expectation” from the correct answer choice.
~40% SE questions feature an antonym-pair!
- Logically complete the sentence but are alone.
-- Don’t have a partner answer choice!-- ~20% SE questions feature such a logical-but-lone choice!BIG TRAPS!
Correct answer choices on SE questions...
- Match our broad expectation from the correct answer choice.
- Each correct choice leads to a complete and coherent sentence.
- Logically conveying the intended meaning.
- Lead to two sentences with equivalent meaning.
-- Similar meaning.-- Not strictly the “same”; that's rare.
The most common mistake on TC/SE questions...
Directly plugging-in the answer choices
-- The answer choices are there to confuse you!
-- When you start directly plugging-in, you fall into the trap!!-- And you will often take longer!
Common mistake on SE questions...
Directly Looking for Two Synonyms
When you start directly looking for a synonym-pair, you may end up…
- Selecting a wrong pair!- Losing focus from reasoning.- Taking longer!
SE questions hinge on meaning.
High-difficulty ones, all the more!
Common mistake on SE questions...
Directly Looking for Two Synonyms
GRE SE often tests you with multiple synonym-pairs.
- A trap for candidates who directly start looking for synonym pairs.
--Without processing the complete meaning.-- ~25% SE questions feature 2 pairs of synonyms.-- ~5% SE questions feature 3 pairs!
Common mistake on SE questions...
Not going by elimination
- The correct approach is NOT to SELECT 2 answer choices.
-- But to ELIMINATE 4 answer choices!
- When you don't go by elimination, you may end up…
-- Selecting an inferior pair of answer choices.-- Overlooking a better pair of answer choices.-- Selecting “intuitive” but “incorrect” answer choices.-- Taking much longer to solve!
Common mistake on TC questions...
Not going by elimination
- The correct approach is NOT to SELECT correct answer choice.
-- But to ELIMINATE incorrect answer choices!
- When you don't go by elimination, you may end up…
-- Getting confused.-- Selecting “intuitive” but “incorrect” answer choices.-- Depending more-than-required on vocabulary.--Taking much longer to solve!
Some words mean something very different from what they sound like.
It’s about getting two sentences with EQUIVALENT meaning
Not the “exactly same” meaning, as such“Exactly same” is anyways difficultAs “exact synonyms” are rareEach word has its own character
Look for 2 choices that lead to...
Complete, coherent sentencesEQUIVALENT in meaning
Sometimes on SE, words that are NOT “clear synonyms” may lead to equivalent sentences...
The overworked manager purchased a set of paints, hoping to rekindle his love of art, but it sat largely ______ for years.
Correct pair of answers:unusedignored
Big Trap: SE questions with logical-but-lone answer choices
Often, an answer choice that leads to a complete, coherent sentence is still incorrect..
- Because it doesn’t have a partner answer choice.
Remember, on SE, you need a PAIR of correct answer choices.
Hence, please don’t commit early to an answer choice!
Wait for a pair that leads to equivalent sentences.
A common trap on SE questions...
Superficial synonyms
Examples:
ancient & obsolete
mingling & cooperating
wise & educated
Common mistake on SE/TC questions...
Not spotting contrast or shift in meaning
Please be careful to spot the “contrast triggers”
Examples:
- but, however, though, although, yet, even though, despite of, in spite of, still…- no (and all its derivatives – not, neither, nor etc.)
Common mistake on SE/TC questions...
Not reading closely enough
When you don't read closely enough, you may end up…
- Having an incomplete idea of the intended meaning.
- Missing the clues for filling in the blank.- Missing the intended contrast/shift in the sentence.
C-R-C technique for navigating unknown words...
Context: the setting in which a word has been used
Root: the etymology of the word
Connotation: the sound of the word
Some helpful roots...
phil: love
- philanthrope
miso: hate
- misanthrope
mal: bad
- malafide
bene: good
- benefactor
phobia: fear
- hydrophobic
Interesting roots coming together...
xeno: unknown/foreigner
phobia: fear- xenophobia
regus: king/royal
cide: kill- regicide
aster: star
logy: study- astrology
Interesting roots coming together...
tele: far
phone: sound- telephone
centi: 100
meter: measure- centimeter
uno: one
animus: life/mind- unanimous
Interesting roots coming together...
tri: 3
dec: 10- tridecaphobia: fear of 13 :)
regus: king/royal
cide: kill- regicide
aster: star
logy: study- astrology
Interesting roots coming together...
somnus: sleep
- insomnia, hypersomnia, hyposomnia
+
ambulare: walk
- ambulance, ambulate
= somnambulance: sleepwalking
Some helpful roots...
ego: self
- egocentric
auto: self
- automatic
psych: soul/mind
- psychology...
anima: living
- animal, animated...
anthrop: human
- philanthropic, anthropology...
Some helpful roots...
aud: hear
- audio, audience, auditorium, audible...
dict: say
- dictate, predict, dictionary, contradict...
cap: head
- decapitate, capsize, capitol, captain...
Some helpful roots...
in / un: no
- insomnia
hyper: more
- hypersomnia
hypo: less
- hyposomnia
Some helpful roots...
bio: life
- biology
geo: earth
- geology
astro: star
- astrology
aqu: water
- aquarium
Some helpful roots...
chron: time
- chronology
photo: light
- photograph
lum: light
- luminous
phon: sound
- telephone
chrome: color
- monochromatic
Some helpful roots...
cred: trust
- credence
homo: same
- homeopathy
hetero: different
- heterogeneous
itis: inflammation
- dermatitis
Some helpful roots...
uno: one
- uniform
bi: two
- bipedal
tri: three
- tricycle, trident
tetra: four
- tetragon
pent: five
- pentagon
hex: six
- hexagon
The original Roman calendar had just 10 months...
oct: 8
- octagon, october
dec: 10
- decade, december
cent: 100
- century, percent
Some helpful roots...
pre: before
- precede, predate, preamble, prescient
post: later
- postpone, posthumous, posterior
syn / con: together
- synchronous, concurrent
Some helpful roots...
crypt: hide
- encrypt
graph: write
- graphology
meter: measure
- sonometer
Interesting roots coming together...
meta: change
- metabolic
morph: shape
- morphed, polymorph
metamorphosis: change of shape
Some helpful roots...
jur: law
- jury, jurisdiction
scientia: knowledge
- science, prescience
medeor: heal
- medical, medicine
Some helpful roots...
magni: big
micro: small
mono: one
multi: many
omni: all
pan: all
Some helpful roots...
fin: end
- finish, final, finale, finite
pre: before
- predate, prejudice
post: after
- postdate, postmortem
tele: far
- television
Some helpful roots...
arch: ancient
- archeology
circ: around
- circumference, circumspect
norm: typical
- normal, abnormal, normalize
sen: old
- senior, senator, senate
derma: skin
- dermatologist, dermatitis, epiderm, pachyderm
Some helpful roots...
sect: cut
- sector, bisect, dissect
cise: cut
- decision (to cut on options), circumcision
ectomy: surgical removal
- tonsillectomy
Some helpful roots...
fac: to do
- factory, facilitate
vor: eat
- herbivore, omnivore, voracious
ambul: walk
- ambulance, ambulate, preamble, somnambulance
Some helpful roots...
ortho: straight
- orthopaedic, orthodontist
scientia: knowledge
- science, prescience
medeor: heal
- medical, medicine
Interesting roots coming together...
venter: belly
- ventral, ventricle
loqui: speak
- eloquent, loquacious, soliloquy
ventriloquist: one who speaks without moving lips (speaks from the belly)
Some helpful roots...
equi: equal
- equivocal, equivalent, equator
equus: horse
- equestrian, equine
Some helpful roots...
equus: horse
- equestrian, equine
canis: dog
- canine
felis: cat
- feline
avis: bird
- avian, aviation
Some helpful roots...
pater: father
mater: mother
frater: brother
dem: people
pedo: child
andro: male
gyn: female
Some helpful roots...
endo: inner
exo: outer
ortho: straight
Tips for reading faster...
Skip complex-looking proper nouns
Run-through the text between commas
Run-through names, facts, figures
Run-through prepositional phrases (beginning with "of", "to" etc)
Some counter-intuitive words...
"fastidious" has nothing to do with "fast"
- it means a "stickler" (strict)
"enervate" doesn't mean "energetic"
- It means "exhausted"
"restive" doesn't mean "restful"
- It means "restless" :)
Some counter-intuitive words...
"precocious" has nothing to do with "precaution"
- it means "advanced and intelligent" (bright)
"prodigal" has nothing to do with "prodigy"
- it means "wasteful" (extravagant)
"spendthrift" doesn't mean "thrifty"
- It means just the opposite: "extravagant"
Some misunderstood words...
"disinterested" doesn't necessarily mean "lack of interest"
- it means "impartial"
"surprise" isn't necessarily positive
"shock" isn't necessarily negative
Some words can have a very broad application...
Examples:
PROFOUND
- means intelligent/scholarly- can also mean deep/thoughtful/philosophical- can also mean thorough/comprehensive
HOMELY
- means home-like/comforting- can also mean unhandsome/lacking in physical beauty
Homographs are words which have the same spelling but different meanings
Examples:
bark & bark
mean & mean
Homophones are words which have the same pronunciation but different meanings
Examples:
accept & exceptair & heir
Homographs are words which have the same spelling but different meaningsExample: bark & bark
Homophones are words which have the same pronunciation but different meanings
Example: air & heir
Together, homographs and homophones are called "homonyms"
"Contrast" suggests a “shift” in meaning
~50% TC/SE questions involve contrast!
Common contrast/shift triggers:
But, yet, however
Though, although, even though, despite, in spite of…Strangely, shockingly, unexpectedly…Opposed to, contrary to, in contrast with, by contrast, counterintuitively…Rarely, barely, hardly, scarcely, scantly…
No (and its variations)
“anything but” means “not at all”Or simply, “not”
The following two sentences have similar meanings...
Laura is confident.
Laura is anything but timid.
Don’t confuse "negative words" with "contrasting words"
Don’t confuse "negative thoughts" with "contrasting thoughts"
Focus on WHETHER there is a SHIFT in the meaning.
Henry didn’t study well; he didn’t score well.She stumbled; she hurt herself
No contrastBecause there is no “shift” in meanings.
Don’t confuse negative words/thoughts with contrast
A negative action or circumstance leading to a negative outcome- No contrast
A negative action or circumstance leading to a positive outcome- No contrast
A positive action or circumstance leading to a negative outcome- No contrast
A positive action or circumstance leading to a positive outcome- No contrast
"Contrast over time" suggests “shift” over time
Once considered impossible, organ transplants are now ______, if still risky, procedures.- routine
Henry was ______ to learn that 2 million years ago, the now arid Sahara was a vast ocean.- bemused
"Contrast in perception" suggests “shift” in perception or attitude about something
Often accused of being overly ______, Chris’s writing is, in fact, quite straightforward.- fancy
Chinua’s father was ______ towards him but rather lenient with his younger sister.- strict
"Contrast from usual" suggests “shift” from the norm
Normally a ______ individual, Norman grows quite irate, if he is accused falsely.- calm
Mongooses are not usually aggressive, but will relentlessly ______ any snake they come across.- fight
Sometimes, the word in the blank may be a "contrast trigger"
Not nearly as excitable as her peers, Yara was an ______ calm 13-year-old.- uncharacteristically
The construction has, ______, been forced to halt: the builders have been sincere in adhering to safety codes.- unnecessarily
Beware of superficial contrast
Contrast triggers do not necessarily induce contrast, every time.
Though often with substantial local variations, the cuisine has ______ prominence in the culinary world map.(a) forfeited(b) acquired
Correct answer: acquired
Double contrast...
Contrast suggests a “shift” in meaning
“Double contrast” suggests two such shifts!
Although Rose did not study much for the test, she performed ______.~ well
Although Rose did not study much for the test, she did not perform ______.~ poorly
Multiple contrasts...
Contrast suggests a “shift” in meaning
“Multiple contrasts” suggests multiple shifts!
Although Rose did not study much for the test, she performed ______.~ well
Although Rose did not study much for the test, she did not perform ______.~ poorly
An SE example with multiple contrasts...
Although Jack did not perform well in the league stage of the tournament, he did not ______ in the knockout stage.
(a) impress(b) perform(c) fail to impress(d) disappoint(e) misconstrue(f) enervate
Correct answers: c and d
A TC example with multiple contrasts...
Ibrahim’s acting was consistently lackluster throughout rehearsals, but he did not _________ the audience on the opening night.
(a) enthuse(b) fail to excite(c) surprise(d) care to impress(e) posture
Correct answers: b
Double negatives...
Usage of a negative word leads to a negative shiftUsage of two negative words negates the negative shift
Though Sarah is not lactose intolerant, as she is not fond of their taste, she rarely _________ milk products.
(a) consumes(b) avoids
Correct answers: a
Similarity triggers...
as, just as, like…similar to, similarly…just as…so too…
Just as cardiovascular exercise is a great way to burn calories, strength training is a great way to _____ muscles.~ gain
Sweltering one day and frigid the next, the weather in this city is as _______ as it is extreme.
erratic
Parallelism...
Parallelism is about conveying similar meanings in a similar way.In such constructions, one part of the sentence requires a logical counterpart.
Scarcity is at the core of all economics: the more ______ a resource is, the less it is worth.
~ abundant
Appositives...
A noun or noun phrase that provides additional information about another noun or noun phrase in a sentence.
In such a construction, two words or phrases with similar meaning, follow each other, conveying similar meaning.
Henry is a suave, refined orator.
The article was so abstract, even unintelligible, that no reader found it interesting.
The mansion is so expensive, to an extent ______, that it is likely to stay unsold.
~ unaffordable
Cause-effect triggers...
because, as, since, so, for…thus, therefore, thereby, hence…as a result, resultantly, consequently…
Because Jack rehearsed it several times, his speech was ______.~ flawless
Use of present participle for conveying a cause-effect relationship
Present participle is “verb + ing”studyingeatingsleeping
Use of present participle on only one of the two sides of a comma generally suggests a cause-effect relationship.
- Scientists discovered a vaccine, putting an end to the epidemic.- Discovering a vaccine, scientists put an end to the epidemic.
Read beyond the blank...
Always read the COMPLETE sentence and…understand the intended meaning.- Key to solving GRE TC/SE questions
Text beyond the blank is equally important.Sometimes, MORE important!
Text beyond the blank generally contains…- Information crucial to the complete meaning- Clues for the blank- Shift in meaning-- Contrast
Be cautious when you see "numbers" in CR questions.- Often, the key to solving the question lies in those numbers.
Be cautious when you see extreme tonality on a CR question or answer choices.Example: must, most, highest, lowest, worst, best, will, etc.
- Often, the key to elimination/selection of an answer choice lies in such extreme terms.
Key difference between "Assumption statements" and "Strengthening statements" on CR:
Assumption statements are a subset of Strengthening statements.
- A strengthening statement fills the missing link.- An assumption statement fills the missing link and must be true for the argument to hold ground.
"Inference statements" on CR...
- A statement that can be derived from the information presented in the passage.-- Without the need for any assumption or extrapolation or exaggeration.
Difference between "Inference" and "Main Point" on CR
- Inference is any statement that can be derived from the passage, without any assumption/extrapolation/exaggeration.
- Main point is the reason why the passage was written.-- Often, the conclusion.
- "Main Point" is a subset of "Inferences".-- The "main inference".
Key to solving "para-completion" questions on CR:
- Prepare a mind-map.
- Follow the logical chain-of-thought.- Eliminate four choices to reach a choice that best complete the complete chain of thoughts.
-- Beware: Consider the complete of chain of thought.
--- Not just the "last sentence".
Approach for highlighted text questions on CR:
Step 1: Identify the conclusion.
Step 2: Link the highlighted part(s) with the conclusion.
Step 3: Know what to expect from the correct answer choice.
Step 4: Eliminate four choices.
Confusing-cause-with-effect
A fallacy tested on the GRE.
Example: When I dream, I sleep.
-- It's actually the other way around. :)
Confusing-correlation-with-causation
A fallacy tested on the GRE.
Example: Grandma sneezed, so a tornado hit Nebraska.
Generalization- The fallacy of making a claim on evidence that is too small.
A fallacy tested on the GRE.
Example: At 90, Mr McGill drinks sweetened soda every day and yet, maintains good health. The elderly can, therefore, have sweetened soda every day and, yet, maintain good health.
Circular Reasoning- The fallacy of assuming a conclusion to be true, in reaching the conclusion.
A fallacy tested on the GRE.
Example: Jack cannot lie because Jack always tells the truth.
Example: A is true because B is true; B is true because A is true.
Incorrect Analogy- The fallacy of drawing comparison between dissimilar entities.Or, without establishing similarity.
A fallacy tested on the GRE.
Example: Country X increased import tariffs and achieved good results; country Y must increase import tariffs.
Assuming that bases are same- The fallacy when post-event difference in results is attributed to the event.-- Without establishing that the pre-event results were similar.
A fallacy tested on the GRE.
Example: Group A was given tonic Xinca. Group B was given a placebo. Post experiment, on the same IQ test, Group A performed significantly better than Group B.
Comparing percentage with absolute numbers- The fallacy when percentage/proportion is compared with absolute data.
A fallacy tested on the GRE.
Example: Jack improved his score by 200%.
Inference: Jack performed well. - Incorrect
Comparing one with oneself- The fallacy of drawing a conclusion based on one entity’s comparison with oneself
-A fallacy tested on the GRE.
Example: Jack improved his score by 200%.
Inference: Jack performed well. - Incorrect
For AW response, keep your raw template ready.Must-watch: "Approach for attempting AW" video under our AW section
In your AW response, also have a paragraph for what someone with counter-view would argue.
- Give your essay, the treatment of a dialogue!
-- That's a mature approach!!
In your AW response, have a new paragraph for each "reason + example" set.
Broad structure of your AW essay...
Introduction paragraph
- Paraphrase the issue (topic) + clearly state your stand.
First reason + example
Second reason + example
Third reason + example
Fourth reason + example
Optional: Fifth reason + example
Important: A rich paragraph on what someone with counterview would argue.
Conclusion paragraph
- That the argument in favor of your stand……outweighs the counter-argument.
Time management for AW response:
~2 Minutes: Read and understand the topic + instructions.
- Decide your stand.
~3 Minutes: Write the first and the last paragraphs.
- As per your template.
~4 Minutes: List-down, the “reason + example” sets.
- Rank them in order of importance.
~2 Minutes: List-down, points in favor of counter-argument.
~16 Minutes: Type middle 4 – 6 paragraphs.
Remember: size DOES matter!
~3 Minutes: Proofread carefully.
Save last ~3 minutes on AW section for proofreading, carefully.
Typos, grammatical errors can undo the hardwork!
The mind-map-approach (MMA) for RCs
1.Skim through the first byte.
2. Answer yourself: WHAT did the byte DO?
Keep it truly simple & brief.Avoid paraphrasing the details.
3. Skim through the next byte.
Answer yourself: WHAT did the byte DO?Link the WHAT of this byte with the WHAT of the earlier byte.
4. Keep repeating Step 3 for all the subsequent bytes.
On the verbal section, be cautious when you see an answer choice with "extreme" emotion.
Answer choices with "moderate" tonality have a higher probability of being correct.
While solving an RC, please think from the "author's point of view".- Don't let your own opinion or general knowledge affect your thought process.
Answering "purpose of the passage" questions...
"Purpose of the passage" refers to the central idea of the passage.
The reason why the passage was written.
It captures the gist of all parts of the passage.
Not just any one, prominent part.
Answering "purpose of a sentence" questions...
Purpose of a sentence is the role that the sentence plays in the passage.Key: It is not just about the content of the sentence.But the role that the content plays!
Big Traps:
Answer choices that delve into details within the sentence.- Content of such answer choice is correct.- But the question is about the purpose of the sentence.
Answering "purpose of a term" questions...
Purpose of a term is the role that the term plays in the passage.
Key: It is NOT just about the meaning of the term.But the role that the meaning plays!
Traps:
Answer choices that delve into the meaning of the term.The question is about the purpose of the term.
Approach for QC questions...
Aim for Choice D.
- Try to get contradictory answers.- When you are not able to get contradictory answers.- You have a unique answer.
0 is even.0 is not prime.
2 is the only even number that is prime.
1 is not a prime number.A prime number must have exactly two factors."1" has only one factor.
For “Must be true” questions…Try to get a “No”.A “No” is sufficient to eliminate an answer choice.If you cannot get a “No”, you must select the answer choice!
For “Can be true” questions…
Try to get a “Yes”.A “Yes” is sufficient to select an answer choice.If you cannot get a “Yes”, you must eliminate the answer choice!
To check whether an integer 'x' is prime…
We need to check for divisibility ONLY by…
All prime numbers less than √x
Example:
To check whether 79 is prime, we need to check for divisibility by prime numbers that are smaller than 8.
Beware of exceptions.
X is an integer such that |X| = X
Quantity A: X
Quantity B: 0.5
The answer is not A.
The answer is D.
Because of the exception "X = 0" case, the relationship between A and B cannot be determined.
In QC, when you are able to solve "too easily", you are probably missing a trap.
Q. P, Q, R, and S are positive integers and P = 27, Q = 49.
Quantity A: The highest common factor of P, Q, R, and S.
Quantity B: 3
The answer is not D.
The answer is B.
No matter what "R" and "S" are, if HCF of "P" and "Q" is 1, the HCF of P, Q, R, S is "1".
Irrational: Can’t be presented in p/q form, where p and q are integers. Ex: √3, Pi
Rational: Can be presented in p/q form, where p and q are integers. Ex: 2, -6, 0.45, 3/7, etc.
Even x Even = EvenEven x Odd = EvenOdd x Odd = Odd
Even + Even = Even
Even + Odd = OddOdd + Odd = Even
Even^Even = Even
Even^Odd = EvenOdd^Even = OddOdd^Odd = Odd
To find the "units digit" of a huge multiplication, simply multiple all the units digits.
324 x 533 x 4356
4 x 3 x 672
The answer is "2".
Factors of a number are integers which can ‘divide’ the given number.Multiples of a number are integers which are ‘divisible’ by the given number.
Example: 20
Factors: 1, 2, 4, 5, 10, 20Multiples: 20, 40, 60…
"What is the remainder when (100! + 17) is divided by 7? 100! is a multiple of 7. So, it leaves remainder 0. 17 leaves remainder 3 with 7. So, the answer is 0 + 3 = 3."
"A fraction will terminate if its denominator has no prime factor other than 2 or 5. 17/160 Prime factors of ""160"" are ""2"" and ""5"". So, this fraction WILL terminate. 13/480 One of the prime factors of ""480"" is ""3"". So, this will NOT terminate."
"In a group of 100, 80 take tea, and 60 take coffee. How many take both? Answer: Cannot be determined. Because we don't know how many take ""neither""."
Percentage change:
[(New Value-Old Value)/ Old Value] x 100
Please note: the denominator is "old value".
Two successive discounts of 50% are equivalent to what percentage of discount?
100 --> 50 --> 25
75% discount.
Profit = Selling Price – Cost Price
Profit Percentage = (Profit / Cost Price) x 100
Profit Margin = (Profit / Selling Price) x 100
Simple Interest = (P x r x T) / 100
P: Principal invested.
r: Rate of simple interest.T: Time.
Compound Interest = P[(1 + r/100)^n – 1]
P: Principal invested.
r: Rate of compound interest.n: Period.
MedianThe middle value that separates the greater and lesser halves of a set.
To find the median, first arrange the terms in a set in increasing (or decreasing) order.
If the number of terms in the set is odd, the median is [(n + 1)/2]th term.If the number of terms in the set is even, the median is the mean of (n/2)th term and (n/2 + 1)th term.
Range:The difference between the greatest and smallest elements in a set.
When two bodies move in same direction: difference of their speeds.When two bodies move in opposite direction: sum of their speeds.
Sum of exterior angles in a polygon with any number of sides: 360 degrees
Sum of internal angles in a polygon with "n" sides: (n - 2) x 180 degrees
Angle from a chord at the centre is twice that at the circumference.
Angle from a chord at any point on the circumference is the same.
Angle between a tangent and a radius is 90 degrees.
From any point on a plane, only two tangents can be drawn on a circle.
Lengths of the two tangents are the same.
Cyclic Quadrilateral
All its four vertices lie on a circle.
Sum of the diagonally opposite angles is 180 degrees.
GRE's favorite triangles
30-60-90
Sides in ratio 1 : √3 : 2
45-45-90
Sides in ratio 1 : 1 : √2
Similar Triangles
All angles are equal.
Hence, shape is the same. Size may differ.All corresponding sides, medians, and angle bisectors are in the same ratio; say "k".Areas are in ratio "k^2".
Congruent Triangles
All sides and all angles are equal.
Hence, shape as well as size is the same.All corresponding angle bisectors, altitudes, and medians are equal.Areas are equal.
A circle is a polygon with infinite sides.
Pi doesn't define circumference. It's the other way around.
Ratio of circumference and diameter of any circle is a constant value. This constant value is "Pi".
Rhombus is a quadrilateral with all sides equal.Area: 1/2 x diagonal 1 x diagonal 2
If angles of a rhombus become equal, the rhombus becomes a square.
- And the diagonals become equal.
Trapezium is a quadrilateral with one pair of opposite sides parallel.Area: ½(sum of parallel sides) x height
If a trapezium's other two sides are also parallel, it becomes a parallelogram.
Area becomes: base x height
Prisms:Solids with congruent base and topExamples: cube, cylinder, cuboid
Pyramids:
Solids with a pointed topExample: cone
Curved surface area of Prisms:Perimeter of base x height
Curved surface area of Pyramids:
1/2 x Perimeter of base x slant height
Total surface area of Prisms:(Perimeter of base x height) + 2 x area of base
Total surface area of Pyramids:
(1/2 x Perimeter of base x slant height) + Area of base
Volume of Prisms:Area of base x height
Volume of Pyramids:
1/3 x Area of base x height
When a solid is melted / reshaped to form another solid(s)…
- The volume remains the same.
- The area changes
-- If a big solid is broken into smaller solids, the area increases.-- If smaller solids are combined to form a bigger solid, the area decreases.
Permutation is used when ‘order’ matters.Example: Arranging children in a row.
Combination is used when ‘order’ doesn't matter.
Example: Selecting teams.
Circular arrangements:
"N" entities can be arranged on a circle in (N-1)! ways.
Areal probability
When you need to find probability of a specific area to be selected out of the total area.
P(E) = Desired Area / Total Area
Sum of first n positive integers: n x (n + 1)/2
Sum of first n positive even integers: n x (n + 1)
Sum of first n positive odd integers: n^2
To find remainder of a number with 2, 5, 10...
Simply divide the last digit of the number by 2, 5, or 10, respectively.
Example: 876345
With 2, the remainder is 5 % 2 = 1With 5, the remainder is 5 % 5 = 0With 10, the remainder is 5 % 10 = 5
To find the remainder of a number with 4, 20, 25, 50, 100...
Divide the last 2 digits by 4, 20, 25, 50, or 100, respectively.
Example: 9887963450
With 4, the remainder is 50 % 4 = 2With 20, the remainder is 50 % 20 = 10With 25, the remainder is 50 % 25 = 0With 50, the remainder is 50 % 50 = 0With 100, the remainder is 50 % 100 = 50
To find the remainder of a number with 2^n or 5^n...
Divide the last n digits by 2^n or 5^n, respectively.
Example: 8377334346380
With 8, the remainder is 380 % 8 = 4With 125, the remainder is 380 % 125 = 5With 16, the remainder is 6380 % 16 = 12
To find the remainder of a number with 3 or 9...
Divide the sum of the digits of the number by 3 or 9, respectively.
Example: 43457
Sum of digits = 4 + 3 + 4 + 5 + 7 = 23With 3, the remainder is 23 % 3 = 2With 9, the remainder is 23 % 9 = 5
To find the remainder of a number with 11...
Divide the difference between the sum of odd-numbered digits and the sum of even-numbered digits by 11.
Example: 54321
Sum of odd-numbered digits = 1 + 3 + 5 = 9Sum of even-numbered digits = 2 + 4 = 6Difference = 9 – 6 = 3Remainder with 11 = 3 % 11 = 3Hence, the remainder of 12345 with 11 is 3
Interquartile range...
The middle 50% of a set of scores.
i.e.
Q3 - Q1
The equation of a circle with center at (h, k) and radius r is…(x – h)^22 + (y – k)^22 = r^2
Parabola...
A U-shaped curve that is mirror-symmetric.
Along the line of symmetry.
Not “directly” tested on GRE.
Indirect application may be tested.You just need a broad understanding.
Vertex
Point where the parabola makes its sharpest turn.
x-intercept(s)
point(s) where the curve meet the x-axis.y = 0
y-intercept(s)
point(s) where the curve meet the y-axis.x = 0
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