What is the fundamental Distance-Rate-Time relationship and the formula for Average Speed?

Distance = Rate * Time. Crucial rule: Average Speed = (Total Distance) / (Total Time). It is NEVER the simple arithmetic mean of the two speeds unless the time spent at each speed is identical!

How do you handle rate problems involving simultaneous inlet and outlet pipes?

Net Rate = (Inlet Rate) - (Outlet Rate) = (1/T_in) - (1/T_out). If Net Rate > 0, the pool/tank fills in Time = 1 / (Net Rate).

What are the common wrong-answer traps in GMAT RC Detail questions?

1. Verbatim trap: Uses exact phrasing from the text but alters the context or logical relationship. 2. Too broad / Too narrow. 3. Out of scope: True in the real world, but absent from the passage.

How do you calculate catch-up time in head-start motion problems?

Catch-up Time = (Head-start Distance) / (Relative Speed difference). Example: If Runner B is 10 miles ahead and Runner A is 2 mph faster, Time = 10 / 2 = 5 hours.

What remains constant during a solvent-evaporation mixture problem?

The mass (or molar amount) of dissolved non-volatile solute remains constant while solvent evaporates. As total solution volume or mass decreases, the solute concentration increases accordingly: C1 * V1 = C2 * V2.

How does percent profit on cost (markup) differ from profit margin on revenue?

Where Profit = Revenue - Cost: • Percent Profit on Cost (Markup %) = (Profit / Cost) * 100%. • Profit Margin (Gross/Net Margin on Revenue) = (Profit / Revenue) * 100%. Always check whether a word problem defines percentage profit relative to cost price or selling price (revenue).

In GMAT RC, what does 'According to the passage' signal in the question stem?

It indicates a direct retrieval question. The correct answer will be a paraphrase of an explicit statement in the passage. No deep inference is required.

What is the markup and discount trap in profit calculations?

Markup is calculated on Cost Price; Discount is calculated on Marked (Selling) Price. A markup of 25% on $100 yields $125; a subsequent 20% discount on $125 brings the price back to $100.

What is the rule when dilution is performed using pure water?

The solute concentration of pure water is 0%. In C1*V1 + C2*V2 = C_final*(V1 + V2), set C2 = 0, so C1*V1 = C_final*(V1 + V2).

What is the core strategy of GMAT Reading Comprehension 'Passage Mapping'?

Note three elements per paragraph: (1) Main idea / paragraph function; (2) Author's thesis or stance; (3) Major shifts (e.g., 'However', 'A second explanation'). Do NOT memorize granular facts.

How do water current or wind speed affect travel rates?

• Downstream (with wind): Effective Speed = Boat Speed + Current Speed • Upstream (against wind): Effective Speed = Boat Speed - Current Speed

In GMAT RC, how do you recognize a Primary Purpose question?

Question stems ask: 'The primary purpose of the passage is...', 'The author is primarily concerned with...'. Look for active verbs like 'reconcile', 'critique', 'trace', or 'evaluate'.

What is the difference between Simple Interest and Compound Interest formulas?

• Simple: Interest = P * r * t; Total = P(1 + rt) • Compound: Total = P * (1 + r/n)^(nt), where n is compounding periods per year.

How does the Alligation Cross Method work for two-component mixtures?

The ratio of volumes V1 / V2 is equal to the inverse ratio of their distances from the target concentration: V1 / V2 = |C2 - C_target| / |C1 - C_target|.

How do successive percentage changes combine mathematically?

An increase of a% followed by a decrease of b% results in a multiplier of (1 + a/100) * (1 - b/100). Example: +20% then -20% = 1.20 * 0.80 = 0.96 (a net 4% decrease, NOT 0% change!).

What is the formula for the distance traveled by a train crossing a stationary platform of length L_p?

Total Distance = (Length of Train) + (Length of Platform). The train has crossed only when its caboose completely exits the far end of the platform.

What is the formula for the concentration of a mixture created by combining two solutions?

C_final = (C1*V1 + C2*V2) / (V1 + V2), where C is percentage concentration and V is volume. Amount of pure solute = C * V.

What is the combined work formula for two workers working simultaneously?

Combined Rate = (1/T1) + (1/T2). The combined time to complete 1 job is T = (T1 * T2) / (T1 + T2).

How does an author qualify a thesis in academic writing?

By introducing boundary conditions or concessions using words like 'to be sure', 'admittedly', 'granted', followed by a defense of the central claim.

How do you tackle Comparative / Multi-perspective RC passages?

Track exactly where Author 1 and Author 2 agree and where they explicitly disagree. Questions will test whether Scholar B would endorse or refute a specific assertion of Scholar A.

How do you calculate percent decrease when an item drops from A to B?

Percent Decrease = [(A - B) / A] * 100%. Dividing by B instead of A is a common error.

How do you calculate relative speed for objects moving toward each other vs moving in the same direction?

• Moving toward each other (converging): Relative Speed = R1 + R2 (closing rate). • Moving in same direction (chasing/overtaking): Relative Speed = R1 - R2 (where R1 > R2).

In RC, what is an 'Application / Parallel Reasoning' question?

A question asking which new situation is most analogous to a situation described in the passage. You must abstract the core causal relationship and match it to a new domain.

How do you distinguish an author's tone in GMAT RC?

Pay close attention to adjectives and adverbs. GMAT academic tone is rarely extreme (never 'scornful' or 'rapturous'); it is typically 'measured', 'guardedly optimistic', 'critical', or 'objective'.

What is the Work-Rate-Time relationship and the rate of an individual working alone?

Work = Rate * Time. If worker A completes a whole job in T hours, worker A's rate is 1/T jobs per hour.

What is the replacement mixture formula when y liters of solution are repeatedly removed and replaced with pure solvent?

Final Solute = Initial Solute * (1 - y/V)^n, where V is total vessel capacity and n is the number of successive replacement cycles.

What is the Double-Matrix Method for overlapping categorical word problems?

Create a 2x2 grid for binary traits (e.g., Men vs Women; Employed vs Unemployed). Fill in row and column totals; every row and column must sum correctly, allowing rapid subtraction.

What is the golden rule for GMAT RC Inference questions?

The correct answer MUST BE TRUE based strictly on facts directly stated in the passage. It is not an imaginative prediction or plausible guess; it is an unstated logical consequence.

How do you solve rate-work problems where workers work on alternating hours?

Calculate the work completed in one full cycle (e.g., 2 hours). Determine how many full cycles fit into the total job, then calculate the fraction of an hour the remaining worker requires.

What is the formula for average speed when equal distances are traveled at speed v1 and speed v2?

Harmonic Mean: Average Speed = (2 * v1 * v2) / (v1 + v2). Example: Driving 60 mph out and 40 mph back over the same distance yields (2 * 60 * 40)/(60 + 40) = 48 mph, NOT 50 mph.

Why is extreme language ('always', 'never', 'completely') almost always wrong in GMAT RC?

Academic passages include nuance and caveats. Answers using universal absolute words are almost impossible to support from measured scholarly texts unless the passage author explicitly uses them.

What is the formula for percentage increase or decrease?

Percent Change = [(New Value - Old Value) / (Old Value)] * 100%. The denominator is ALWAYS the original/initial value.

GMAT Focus Verbal Reading Comprehension & Quantitative Word Problems

32 GMAT Focus review cards combining Quantitative word problems (distance–rate–time, relative speed, work rates, mixtures, percent change, markup, profit margin, and interest) with Verbal Reading Comprehension passage mapping and question strategies.

Level: intermediate
Languages: en → en
Cards: 32
Markdown: GMAT Focus Verbal Reading Comprehension & Quantitative Word Problems (.md)

Flashcards (32)

#	Front (Term / Question)	Back (Definition / Answer)
1	What is the fundamental Distance-Rate-Time relationship and the formula for Average Speed?	Distance = Rate * Time. Crucial rule: Average Speed = (Total Distance) / (Total Time). It is NEVER the simple arithmetic mean of the two speeds unless the time spent at each speed is identical!
2	How do you handle rate problems involving simultaneous inlet and outlet pipes?	Net Rate = (Inlet Rate) - (Outlet Rate) = (1/T_in) - (1/T_out). If Net Rate > 0, the pool/tank fills in Time = 1 / (Net Rate).
3	What are the common wrong-answer traps in GMAT RC Detail questions?	1. Verbatim trap: Uses exact phrasing from the text but alters the context or logical relationship. 2. Too broad / Too narrow. 3. Out of scope: True in the real world, but absent from the passage.
4	How do you calculate catch-up time in head-start motion problems?	Catch-up Time = (Head-start Distance) / (Relative Speed difference). Example: If Runner B is 10 miles ahead and Runner A is 2 mph faster, Time = 10 / 2 = 5 hours.
5	What remains constant during a solvent-evaporation mixture problem?	The mass (or molar amount) of dissolved non-volatile solute remains constant while solvent evaporates. As total solution volume or mass decreases, the solute concentration increases accordingly: C1 * V1 = C2 * V2.
6	How does percent profit on cost (markup) differ from profit margin on revenue?	Where Profit = Revenue - Cost: • Percent Profit on Cost (Markup %) = (Profit / Cost) * 100%. • Profit Margin (Gross/Net Margin on Revenue) = (Profit / Revenue) * 100%. Always check whether a word problem defines percentage profit relative to cost price or selling price (revenue).
7	In GMAT RC, what does 'According to the passage' signal in the question stem?	It indicates a direct retrieval question. The correct answer will be a paraphrase of an explicit statement in the passage. No deep inference is required.
8	What is the markup and discount trap in profit calculations?	Markup is calculated on Cost Price; Discount is calculated on Marked (Selling) Price. A markup of 25% on $100 yields $125; a subsequent 20% discount on $125 brings the price back to $100.
9	What is the rule when dilution is performed using pure water?	The solute concentration of pure water is 0%. In C1V1 + C2V2 = C_final(V1 + V2), set C2 = 0, so C1V1 = C_final*(V1 + V2).
10	What is the core strategy of GMAT Reading Comprehension 'Passage Mapping'?	Note three elements per paragraph: (1) Main idea / paragraph function; (2) Author's thesis or stance; (3) Major shifts (e.g., 'However', 'A second explanation'). Do NOT memorize granular facts.
11	How do water current or wind speed affect travel rates?	• Downstream (with wind): Effective Speed = Boat Speed + Current Speed • Upstream (against wind): Effective Speed = Boat Speed - Current Speed
12	In GMAT RC, how do you recognize a Primary Purpose question?	Question stems ask: 'The primary purpose of the passage is...', 'The author is primarily concerned with...'. Look for active verbs like 'reconcile', 'critique', 'trace', or 'evaluate'.
13	What is the difference between Simple Interest and Compound Interest formulas?	• Simple: Interest = P * r * t; Total = P(1 + rt) • Compound: Total = P * (1 + r/n)^(nt), where n is compounding periods per year.
14	How does the Alligation Cross Method work for two-component mixtures?	The ratio of volumes V1 / V2 is equal to the inverse ratio of their distances from the target concentration: V1 / V2 = \|C2 - C_target\| / \|C1 - C_target\|.
15	How do successive percentage changes combine mathematically?	An increase of a% followed by a decrease of b% results in a multiplier of (1 + a/100) * (1 - b/100). Example: +20% then -20% = 1.20 * 0.80 = 0.96 (a net 4% decrease, NOT 0% change!).
16	What is the formula for the distance traveled by a train crossing a stationary platform of length L_p?	Total Distance = (Length of Train) + (Length of Platform). The train has crossed only when its caboose completely exits the far end of the platform.
17	What is the formula for the concentration of a mixture created by combining two solutions?	C_final = (C1V1 + C2V2) / (V1 + V2), where C is percentage concentration and V is volume. Amount of pure solute = C * V.
18	What is the combined work formula for two workers working simultaneously?	Combined Rate = (1/T1) + (1/T2). The combined time to complete 1 job is T = (T1 * T2) / (T1 + T2).
19	How does an author qualify a thesis in academic writing?	By introducing boundary conditions or concessions using words like 'to be sure', 'admittedly', 'granted', followed by a defense of the central claim.
20	How do you tackle Comparative / Multi-perspective RC passages?	Track exactly where Author 1 and Author 2 agree and where they explicitly disagree. Questions will test whether Scholar B would endorse or refute a specific assertion of Scholar A.
21	How do you calculate percent decrease when an item drops from A to B?	Percent Decrease = [(A - B) / A] * 100%. Dividing by B instead of A is a common error.
22	How do you calculate relative speed for objects moving toward each other vs moving in the same direction?	• Moving toward each other (converging): Relative Speed = R1 + R2 (closing rate). • Moving in same direction (chasing/overtaking): Relative Speed = R1 - R2 (where R1 > R2).
23	In RC, what is an 'Application / Parallel Reasoning' question?	A question asking which new situation is most analogous to a situation described in the passage. You must abstract the core causal relationship and match it to a new domain.
24	How do you distinguish an author's tone in GMAT RC?	Pay close attention to adjectives and adverbs. GMAT academic tone is rarely extreme (never 'scornful' or 'rapturous'); it is typically 'measured', 'guardedly optimistic', 'critical', or 'objective'.
25	What is the Work-Rate-Time relationship and the rate of an individual working alone?	Work = Rate * Time. If worker A completes a whole job in T hours, worker A's rate is 1/T jobs per hour.
26	What is the replacement mixture formula when y liters of solution are repeatedly removed and replaced with pure solvent?	Final Solute = Initial Solute * (1 - y/V)^n, where V is total vessel capacity and n is the number of successive replacement cycles.
27	What is the Double-Matrix Method for overlapping categorical word problems?	Create a 2x2 grid for binary traits (e.g., Men vs Women; Employed vs Unemployed). Fill in row and column totals; every row and column must sum correctly, allowing rapid subtraction.
28	What is the golden rule for GMAT RC Inference questions?	The correct answer MUST BE TRUE based strictly on facts directly stated in the passage. It is not an imaginative prediction or plausible guess; it is an unstated logical consequence.
29	How do you solve rate-work problems where workers work on alternating hours?	Calculate the work completed in one full cycle (e.g., 2 hours). Determine how many full cycles fit into the total job, then calculate the fraction of an hour the remaining worker requires.
30	What is the formula for average speed when equal distances are traveled at speed v1 and speed v2?	Harmonic Mean: Average Speed = (2 * v1 * v2) / (v1 + v2). Example: Driving 60 mph out and 40 mph back over the same distance yields (2 * 60 * 40)/(60 + 40) = 48 mph, NOT 50 mph.
31	Why is extreme language ('always', 'never', 'completely') almost always wrong in GMAT RC?	Academic passages include nuance and caveats. Answers using universal absolute words are almost impossible to support from measured scholarly texts unless the passage author explicitly uses them.
32	What is the formula for percentage increase or decrease?	Percent Change = [(New Value - Old Value) / (Old Value)] * 100%. The denominator is ALWAYS the original/initial value.