If x^2 > y^2, does that imply x > y?

NO! Example: Let x = -5 and y = 2. Then x^2 = 25 > y^2 = 4, but x = -5 < y = 2. Taking square roots without considering signs is a classic QC trap.

What is the Geometric Diagram Trap in Quantitative Comparison?

Diagrams are NOT drawn to scale unless explicitly stated! You cannot assume relative lengths, angle sizes, or perpendicularity based on visual appearance. A triangle that looks equilateral may be scalene.

How do Opprobrium and Acclaim contrast?

• Opprobrium: Harsh criticism, public condemnation, or disgrace arising from shameful conduct. • Acclaim: Enthusiastic, public praise and approval.

How do Munificent and Parsimonious contrast?

• Munificent: Extremely generous, lavish, and open-handed in giving. • Parsimonious: Excessively stingy, frugal, tightfisted, and unwilling to spend.

What are the four standard answer choices for Quantitative Comparison (QC) questions on the GRE?

• (A) Quantity A is greater. • (B) Quantity B is greater. • (C) The two quantities are equal. • (D) The relationship cannot be determined from the information given.

How do Vituperate and Eulogize contrast?

• Vituperate: To blame, berate, or insult in violent, abusive language. • Eulogize: To praise highly and formally in speech or writing.

What are Calumny and Obloquy in advanced GRE vocabulary?

• Calumny: The making of false and defamatory statements to damage someone's reputation; slander. • Obloquy: Strong public criticism, verbal abuse, or public disgrace resulting from shameful conduct.

How do Desultory and Perfunctory differ in nuance?

• Desultory: Lacking a plan, purpose, or enthusiasm; unfocused, erratic (e.g., desultory reading). • Perfunctory: Carried out with minimum effort, routine duty, or reflection; mechanical (e.g., a perfunctory nod).

How do Bellicose and Truculent contrast in advanced GRE vocabulary?

• Bellicose: Demonstrating aggression and a willingness to fight; warlike, hawkish. • Truculent: Eagerly quick to argue or fight; aggressively defiant, hostile, and ferocious.

How do Salubrious and Pernicious contrast?

• Salubrious: Health-giving, wholesome, beneficial to well-being. • Pernicious: Having a harmful, destructive effect, especially in a gradual, subtle manner.

How do fractions between 0 and 1 behave under exponentiation compared to numbers > 1?

• For x > 1: x^3 > x^2 > x > sqrt(x). • For 0 x > x^2 > x^3 (powers decrease value, roots increase value!). Example: (1/2)^2 = 1/4 1/4.

How do Inchoate and Consummate contrast?

• Inchoate: Just begun and so not fully formed or developed; rudimentary, nascent. • Consummate: Showing complete perfection, supreme mastery, and skill; complete.

How do Gainsay and Asseverate contrast?

• Gainsay: To deny, dispute, contradict, or speak against (often used with negative: 'there is no gainsaying his brilliance'). • Asseverate: To state, declare, or affirm positively, earnestly, and solemnly.

How do Excoriate and Extol contrast?

• Excoriate: To criticize, censure, or berate with extreme severity. • Extol: To praise enthusiastically and lavishly.

When should you choose choice (D) in Quantitative Comparison?

Choose (D) the instant you find TWO valid test cases that yield DIFFERENT relationships (e.g., Case 1 gives Quantity A > Quantity B, but Case 2 gives Quantity A = Quantity B). Once D is established, stop testing.

What is the Integer Assumption Trap in Quantitative Comparison?

Assuming variables represent integers when the problem only states 'x is a real number' or 'x > 0'. Always test fractions between 0 and 1 (e.g., x = 0.5).

What is the trap with Quantitative Comparison questions involving roots: sqrt(x + 9) vs sqrt(x) + 3 (for x > 0)?

Squaring both quantities (both are positive): • (Quantity A)^2 = x + 9 • (Quantity B)^2 = (sqrt(x) + 3)^2 = x + 6*sqrt(x) + 9. Since x > 0, 6*sqrt(x) > 0, so Quantity B is STRICTLY GREATER (Answer B).

How do negative numbers behave under exponentiation?

• If x x (e.g., -1/8 > -1/2).

What operations are allowed when simplifying both sides of a Quantitative Comparison?

• Allowed: Adding or subtracting the same quantity from both sides. • Allowed: Multiplying or dividing both sides by a KNOWN POSITIVE number. • FORBIDDEN: Multiplying or dividing by an unknown variable x whose sign is not strictly positive!

How do Lachrymose and Jovial contrast?

• Lachrymose: Tearful, given to weeping, or mournful. • Jovial: Cheerful, friendly, full of good humor.

How do Hubris and Humility contrast?

• Hubris: Excessive pride, dangerous overconfidence, or arrogance, often leading to downfall. • Humility: The quality of having a modest or low view of one's own importance.

What is the trap when comparing arithmetic mean vs median in Quantitative Comparison without knowing distribution symmetry?

Unless the set is explicitly stated to be evenly spaced or symmetric, the relationship between mean and median cannot be determined (Answer D). A single extreme outlier can pull the mean far above or below the median.

How do Turbid and Limpid contrast?

• Turbid: Cloudy, opaque, or thick with suspended sediment; obscure, muddled. • Limpid: Completely clear, transparent, pellucid, effortlessly comprehensible.

What is the Positive Number Assumption Trap in Quantitative Comparison?

Assuming variables are positive when the problem only states 'x != 0'. You must test negative numbers, which often reverse inequalities when raised to odd powers or inverted.

How do Fractious and Factious differ in GRE vocabulary?

• Fractious: Irritable, quarrelsome, peevish, difficult to control. • Factious: Relating to or inclined to form dissident factions within a larger group; sectarian.

How do Pusillanimous and Intrepid contrast?

• Pusillanimous: Showing a contemptible lack of courage; timid, cowardly. • Intrepid: Fearless, adventurous, bold, and undaunted.

What is the 'ZONE F' number-testing strategy for Quantitative Comparison?

Test extreme and boundary values systematically: • Z: Zero (0) • O: One (1) • N: Negative numbers (-1, -2) • E: Extreme large/small values (100, -100) • F: Fractions between 0 and 1 (1/2, 1/4).

What is the absolute value inequality trap: Comparing |x + y| with |x| + |y|?

By the Triangle Inequality: |x + y| <= |x| + |y|. • Quantity B is greater than Quantity A whenever x and y have OPPOSITE signs. • Quantity A EQUALS Quantity B whenever x and y have the SAME sign (or at least one is 0). Without sign constraints, the answer is (D)!

What happens when comparing a Circle's area and circumference without radius information?

Comparing numerical values: Area = pi * r^2 and Circumference = 2 * pi * r. If r = 2, both equal 4*pi (equal). If r > 2, Area > Circumference numerically; if 0 < r < 2, Area < Circumference numerically. Answer is (D) unless r is restricted.

How do Nadir and Zenith contrast?

• Nadir: The lowest point in the fortunes or success of an individual or institution. • Zenith: The time at which something is most powerful, flourishing, or successful; peak, apex.

What is an Epigone in academic and artistic critique?

A second-rate imitator, follower, or disciple of a great artist, philosopher, or writer. Synonyms: Derivative follower, imitator.

What is the trap when given a system of equations that is dependent: 2x + 4y = 10 and x + 2y = 5?

The two equations are scalar multiples of each other! They represent the exact same line, having infinitely many (x, y) solutions. Individual values of x and y cannot be uniquely determined, yielding answer (D).

Advanced Vocabulary & Quantitative Comparison Traps

Archaic/esoteric vocabulary nuance, Quantitative Comparison 'Information not sufficient' testing strategies, non-integer/negative boundary value traps, and geometric drawing traps.

Level: advanced
Languages: en → en
Cards: 32
Markdown: Advanced Vocabulary & Quantitative Comparison Traps (.md)

Flashcards (32)

#	Front (Term / Question)	Back (Definition / Answer)
1	If x^2 > y^2, does that imply x > y?	NO! Example: Let x = -5 and y = 2. Then x^2 = 25 > y^2 = 4, but x = -5 < y = 2. Taking square roots without considering signs is a classic QC trap.
2	What is the Geometric Diagram Trap in Quantitative Comparison?	Diagrams are NOT drawn to scale unless explicitly stated! You cannot assume relative lengths, angle sizes, or perpendicularity based on visual appearance. A triangle that looks equilateral may be scalene.
3	How do Opprobrium and Acclaim contrast?	• Opprobrium: Harsh criticism, public condemnation, or disgrace arising from shameful conduct. • Acclaim: Enthusiastic, public praise and approval.
4	How do Munificent and Parsimonious contrast?	• Munificent: Extremely generous, lavish, and open-handed in giving. • Parsimonious: Excessively stingy, frugal, tightfisted, and unwilling to spend.
5	What are the four standard answer choices for Quantitative Comparison (QC) questions on the GRE?	• (A) Quantity A is greater. • (B) Quantity B is greater. • (C) The two quantities are equal. • (D) The relationship cannot be determined from the information given.
6	How do Vituperate and Eulogize contrast?	• Vituperate: To blame, berate, or insult in violent, abusive language. • Eulogize: To praise highly and formally in speech or writing.
7	What are Calumny and Obloquy in advanced GRE vocabulary?	• Calumny: The making of false and defamatory statements to damage someone's reputation; slander. • Obloquy: Strong public criticism, verbal abuse, or public disgrace resulting from shameful conduct.
8	How do Desultory and Perfunctory differ in nuance?	• Desultory: Lacking a plan, purpose, or enthusiasm; unfocused, erratic (e.g., desultory reading). • Perfunctory: Carried out with minimum effort, routine duty, or reflection; mechanical (e.g., a perfunctory nod).
9	How do Bellicose and Truculent contrast in advanced GRE vocabulary?	• Bellicose: Demonstrating aggression and a willingness to fight; warlike, hawkish. • Truculent: Eagerly quick to argue or fight; aggressively defiant, hostile, and ferocious.
10	How do Salubrious and Pernicious contrast?	• Salubrious: Health-giving, wholesome, beneficial to well-being. • Pernicious: Having a harmful, destructive effect, especially in a gradual, subtle manner.
11	How do fractions between 0 and 1 behave under exponentiation compared to numbers > 1?	• For x > 1: x^3 > x^2 > x > sqrt(x). • For 0 < x < 1: sqrt(x) > x > x^2 > x^3 (powers decrease value, roots increase value!). Example: (1/2)^2 = 1/4 < 1/2; sqrt(1/4) = 1/2 > 1/4.
12	How do Inchoate and Consummate contrast?	• Inchoate: Just begun and so not fully formed or developed; rudimentary, nascent. • Consummate: Showing complete perfection, supreme mastery, and skill; complete.
13	How do Gainsay and Asseverate contrast?	• Gainsay: To deny, dispute, contradict, or speak against (often used with negative: 'there is no gainsaying his brilliance'). • Asseverate: To state, declare, or affirm positively, earnestly, and solemnly.
14	How do Excoriate and Extol contrast?	• Excoriate: To criticize, censure, or berate with extreme severity. • Extol: To praise enthusiastically and lavishly.
15	When should you choose choice (D) in Quantitative Comparison?	Choose (D) the instant you find TWO valid test cases that yield DIFFERENT relationships (e.g., Case 1 gives Quantity A > Quantity B, but Case 2 gives Quantity A = Quantity B). Once D is established, stop testing.
16	What is the Integer Assumption Trap in Quantitative Comparison?	Assuming variables represent integers when the problem only states 'x is a real number' or 'x > 0'. Always test fractions between 0 and 1 (e.g., x = 0.5).
17	What is the trap with Quantitative Comparison questions involving roots: sqrt(x + 9) vs sqrt(x) + 3 (for x > 0)?	Squaring both quantities (both are positive): • (Quantity A)^2 = x + 9 • (Quantity B)^2 = (sqrt(x) + 3)^2 = x + 6sqrt(x) + 9. Since x > 0, 6sqrt(x) > 0, so Quantity B is STRICTLY GREATER (Answer B).
18	How do negative numbers behave under exponentiation?	• If x < 0 and n is EVEN: x^n is strictly POSITIVE. • If x < 0 and n is ODD: x^n is strictly NEGATIVE. • For -1 < x < 0: x^3 > x (e.g., -1/8 > -1/2).
19	What operations are allowed when simplifying both sides of a Quantitative Comparison?	• Allowed: Adding or subtracting the same quantity from both sides. • Allowed: Multiplying or dividing both sides by a KNOWN POSITIVE number. • FORBIDDEN: Multiplying or dividing by an unknown variable x whose sign is not strictly positive!
20	How do Lachrymose and Jovial contrast?	• Lachrymose: Tearful, given to weeping, or mournful. • Jovial: Cheerful, friendly, full of good humor.
21	How do Hubris and Humility contrast?	• Hubris: Excessive pride, dangerous overconfidence, or arrogance, often leading to downfall. • Humility: The quality of having a modest or low view of one's own importance.
22	What is the trap when comparing arithmetic mean vs median in Quantitative Comparison without knowing distribution symmetry?	Unless the set is explicitly stated to be evenly spaced or symmetric, the relationship between mean and median cannot be determined (Answer D). A single extreme outlier can pull the mean far above or below the median.
23	How do Turbid and Limpid contrast?	• Turbid: Cloudy, opaque, or thick with suspended sediment; obscure, muddled. • Limpid: Completely clear, transparent, pellucid, effortlessly comprehensible.
24	What is the Positive Number Assumption Trap in Quantitative Comparison?	Assuming variables are positive when the problem only states 'x != 0'. You must test negative numbers, which often reverse inequalities when raised to odd powers or inverted.
25	How do Fractious and Factious differ in GRE vocabulary?	• Fractious: Irritable, quarrelsome, peevish, difficult to control. • Factious: Relating to or inclined to form dissident factions within a larger group; sectarian.
26	How do Pusillanimous and Intrepid contrast?	• Pusillanimous: Showing a contemptible lack of courage; timid, cowardly. • Intrepid: Fearless, adventurous, bold, and undaunted.
27	What is the 'ZONE F' number-testing strategy for Quantitative Comparison?	Test extreme and boundary values systematically: • Z: Zero (0) • O: One (1) • N: Negative numbers (-1, -2) • E: Extreme large/small values (100, -100) • F: Fractions between 0 and 1 (1/2, 1/4).
28	What is the absolute value inequality trap: Comparing \|x + y\| with \|x\| + \|y\|?	By the Triangle Inequality: \|x + y\| <= \|x\| + \|y\|. • Quantity B is greater than Quantity A whenever x and y have OPPOSITE signs. • Quantity A EQUALS Quantity B whenever x and y have the SAME sign (or at least one is 0). Without sign constraints, the answer is (D)!
29	What happens when comparing a Circle's area and circumference without radius information?	Comparing numerical values: Area = pi * r^2 and Circumference = 2 * pi * r. If r = 2, both equal 4*pi (equal). If r > 2, Area > Circumference numerically; if 0 < r < 2, Area < Circumference numerically. Answer is (D) unless r is restricted.
30	How do Nadir and Zenith contrast?	• Nadir: The lowest point in the fortunes or success of an individual or institution. • Zenith: The time at which something is most powerful, flourishing, or successful; peak, apex.
31	What is an Epigone in academic and artistic critique?	A second-rate imitator, follower, or disciple of a great artist, philosopher, or writer. Synonyms: Derivative follower, imitator.
32	What is the trap when given a system of equations that is dependent: 2x + 4y = 10 and x + 2y = 5?	The two equations are scalar multiples of each other! They represent the exact same line, having infinitely many (x, y) solutions. Individual values of x and y cannot be uniquely determined, yielding answer (D).