GMAT (Graduate Management Admission Test) Quantitative Reasoning: Word Problems, Statistics & Combinatorics Syllabus

Quantitative Reasoning: Word Problems, Statistics & Combinatorics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Reasoning: Word Problems, Statistics & Combinatorics in GMAT (Graduate Management Admission Test), not a summary of it.

1. 1

   Applied Word Problems

   6 topics

   • Rate, time, and distance
     • Average speed
     • Two travelers (meeting and overtaking)
   • Work and combined-rate problems
   • Mixtures and weighted blends
   • Interest problems
     • Simple interest
     • Compound interest
   • Profit, revenue, cost, and discount
   • Age and consecutive-quantity problems
2. 2

   Descriptive Statistics

   5 topics

   • Mean, median, and mode
   • Range and interquartile spread
   • Standard deviation (conceptual and comparative)
   • Weighted averages
   • Effect of adding/removing data points on measures of center
3. 3

   Counting Methods & Combinatorics

   4 topics

   • Fundamental counting principle
   • Permutations
     • Ordering with and without repetition
     • Circular and restricted arrangements
   • Combinations
   • Distinguishing permutation vs combination scenarios
4. 4

   Probability

   5 topics

   • Basic probability of single events
   • Independent and dependent events
   • Mutually exclusive vs overlapping events
   • Complementary probability (1 minus P)
   • Sequential and conditional probability
5. 5

   Sets, Overlapping Groups & Logic

   4 topics

   • Venn diagrams for two and three sets
   • The double-matrix (two-variable) method
   • Union, intersection, and inclusion-exclusion
   • Neither / both categories in group problems

Quantitative Reasoning: Word Problems, Statistics & Combinatorics flashcards for GMAT (Graduate Management Admission Test)

23 of 50 cards from the Quantitative Reasoning: Word Problems, Statistics & Combinatorics deck — real questions with worked answers.

1. What is the fundamental rate-time-distance formula, and how do you rearrange it for time and rate?

   Distance = Rate x Time (D = RT). Therefore Time = Distance / Rate, and Rate = Distance / Time.

2. How do you compute average speed for a trip with multiple legs?

   Average speed = total distance / total time. Never average the speeds directly (unless the times are equal).

3. Two objects move toward each other. How do their rates combine, and how do they combine when moving apart or in the same direction?

   Toward each other (or apart): add the rates (closing/separating speed = r1 + r2). Same direction (one chasing): subtract the rates (gap closes at r1 - r2).

4. In work-rate problems, how do you find the combined rate of two workers, and the time to finish together?

   Add individual rates: combined rate = 1/a + 1/b (jobs per unit time). Time together = 1 / (1/a + 1/b) = ab/(a+b).

5. A person does a job in 'a' hours, another in 'b' hours. What is the shortcut for the time to complete it together?

   Time together = ab / (a + b) hours.

6. How do you handle a work problem where one agent fills and another drains (opposing rates)?

   Subtract the draining rate from the filling rate: net rate = 1/fill - 1/drain. The net rate determines the time to complete.

7. In a mixture problem, how do you set up the equation for combining two solutions of different concentrations?

   (concentration1 x amount1) + (concentration2 x amount2) = (final concentration) x (total amount). Track the pure substance amounts.

8. What does the weighted-average (allegation) approach tell you about where a blend's value falls between two components?

   The blend value lies between the two component values, closer to the component present in greater quantity; the distances from the blend to each component are inversely proportional to their amounts.

9. What is the simple interest formula?

   Interest = Principal x Rate x Time (I = PRT); total amount A = P(1 + RT). Rate and time must use matching periods.

10. What is the compound interest formula?

    A = P(1 + r/n)^(nt), where P = principal, r = annual rate, n = compounding periods per year, t = years. Interest earned = A - P.

11. How does the number of compounding periods affect the final amount at a fixed annual rate?

    More frequent compounding yields a larger final amount; compound interest always exceeds simple interest over more than one period at the same nominal rate.

12. How are profit, revenue, and cost related?

    Profit = Revenue - Cost. Revenue = price per unit x quantity sold; Cost = fixed costs + (variable cost per unit x quantity).

13. How do you compute a selling price after a percent discount, and the discount amount?

    Sale price = original x (1 - discount%). Discount amount = original x discount%. Successive discounts multiply: (1 - d1)(1 - d2).

14. How is percent markup (or percent profit) on cost calculated?

    Percent markup = (Selling price - Cost) / Cost x 100. Profit margin on revenue = (Revenue - Cost) / Revenue x 100.

15. How do you set up a typical age problem involving the relationship now and in the future/past?

    Assign a variable to a current age; add/subtract the same number of years to all people for past or future times, then translate the stated relationship into an equation.

16. For n consecutive integers, how do you represent them and what is their sum?

    Represent as n, n+1, n+2, .... Sum of consecutive integers = (number of terms) x (average), where average = (first + last)/2.

17. How do you represent consecutive even or consecutive odd integers?

    Both use a step of 2: x, x+2, x+4, .... Consecutive even start from an even x; consecutive odd start from an odd x.

18. Define mean, median, and mode.

    Mean = sum of values / number of values (average). Median = the middle value when ordered (average of the two middle values if the count is even). Mode = the most frequently occurring value.

19. For a data set with an even number of values, how is the median found?

    Order the values and take the average of the two middle values.

20. In a symmetric distribution versus a skewed distribution, how do mean and median compare?

    Symmetric: mean = median. Right-skewed (long high tail): mean > median. Left-skewed (long low tail): mean < median.

21. How do you compute the range of a data set?

    Range = maximum value - minimum value.

22. What are the quartiles and how is the interquartile range (IQR) defined?

    Q1 = median of the lower half, Q3 = median of the upper half. IQR = Q3 - Q1, measuring the spread of the middle 50% of the data.

23. What does standard deviation measure conceptually?

    It measures how spread out values are around the mean; a larger standard deviation means values are more dispersed, a smaller one means they cluster near the mean.

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