Graduate Management Admission Test (GMAT) Quantitative Reasoning Flashcards

24 sample cards from the Quantitative Reasoning deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. What is a function, and what do domain and range mean?

   A function assigns each input exactly one output. The domain is the set of allowed inputs; the range is the set of resulting outputs.

2. Give the formulas for the $n$th term and the sum of an arithmetic sequence.

   $n$th term: $a_n = a_1 + (n-1)d$. Sum: $$S_n = \frac{n}{2}\left(a_1 + a_n\right) = \frac{n}{2}\left[2a_1+(n-1)d\right]$$

3. Give the formulas for the $n$th term and the sum of a geometric sequence.

   $n$th term: $a_n = a_1 r^{\,n-1}$. Sum of $n$ terms: $$S_n = a_1\frac{r^{n}-1}{r-1}\quad (r\neq 1)$$

4. When translating word problems, how are 'is', 'of', 'percent', and 'more than' rendered in math?

   'is' $\to =$; 'of' $\to \times$; 'percent' $\to \div 100$; '$x$ more than $y$' $\to y + x$; '$x$ less than $y$' $\to y - x$.

5. State the fundamental rate equation relating distance, speed, and time.

   $$\text{distance} = \text{speed}\times \text{time},\qquad \text{speed}=\frac{\text{distance}}{\text{time}},\qquad \text{time}=\frac{\text{distance}}{\text{speed}}$$

6. How do you compute average speed for a round trip with two different speeds over equal distances?

   Use total distance over total time, not the simple average of speeds. For equal distances at speeds $v_1,v_2$: $$\bar v = \frac{2v_1 v_2}{v_1+v_2}$$ (the harmonic mean).

7. How do relative speeds combine when two objects move toward each other versus in the same direction?

   Toward each other (or closing): add speeds, $v_1+v_2$. Same direction (overtaking): subtract speeds, $|v_1-v_2|$.

8. If one worker finishes a job in $a$ hours and another in $b$ hours, how long do they take together?

   Add their rates: combined rate $=\frac{1}{a}+\frac{1}{b}$, so time together is $$T = \frac{ab}{a+b}$$

9. What is the basic work equation, and how do rates add?

   $\text{Work} = \text{Rate}\times\text{Time}$. Rates of workers acting together add: $R_{\text{total}} = R_1 + R_2 + \cdots$. Each individual rate is $\frac{1 \text{ job}}{\text{time}}$.

10. For a mixture, how do you find the amount of a component given concentration?

    Amount of component $=$ concentration $\times$ total amount. When mixing, the component amounts add: $$c_1 V_1 + c_2 V_2 = c_{\text{final}}(V_1+V_2)$$

11. What is the weighted average formula, and when is it used in mixture problems?

    $$\bar x = \frac{w_1 x_1 + w_2 x_2 + \cdots}{w_1 + w_2 + \cdots}$$ Used when combining groups of different sizes or concentrations; the result lies between the extremes, closer to the larger weight.

12. State the simple interest formula.

    $$I = P\,r\,t$$ where $P$ is principal, $r$ the rate per period (as a decimal), and $t$ the number of periods. The total amount is $A = P(1+rt)$.

13. State the compound interest formula.

    $$A = P\left(1+\frac{r}{n}\right)^{nt}$$ where $r$ is the annual rate, $n$ the compoundings per year, and $t$ the number of years.

14. What is the formula for the union of two overlapping sets?

    $$|A\cup B| = |A| + |B| - |A\cap B|$$

15. For two groups with a 'neither' category, how do you account for all members of a total set?

    $$\text{Total} = |A| + |B| - |A\cap B| + \text{Neither}$$ Subtract the overlap once because it was counted in both $|A|$ and $|B|$.

16. Define mean, median, and mode.

    Mean: sum of values divided by count. Median: the middle value when ordered (average of the two middle values if the count is even). Mode: the most frequently occurring value.

17. What is the range of a data set, and how does it differ from standard deviation?

    Range $=$ maximum $-$ minimum, measuring total spread from extremes. Standard deviation measures how far values typically lie from the mean; larger standard deviation means more dispersion.

18. What is the fundamental counting principle?

    If one choice can be made in $m$ ways and an independent second choice in $n$ ways, the two together can be made in $m\times n$ ways. Extend by multiplying across all independent stages.

19. Give the formulas for permutations and combinations of $n$ items taken $r$ at a time.

    $$P(n,r)=\frac{n!}{(n-r)!},\qquad C(n,r)=\frac{n!}{r!\,(n-r)!}$$ Permutations count ordered selections; combinations count unordered selections.

20. What is the basic probability formula for equally likely outcomes?

    $$P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$$ with $0 \leq P \leq 1$.

21. How do you find the probability of A or B, and of the complement of an event?

    $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. For independent events, $P(A\cap B)=P(A)\,P(B)$. Complement: $P(\text{not }A)=1-P(A)$.

22. What is a good estimation strategy when answer choices are spread far apart?

    Round numbers to convenient values, compute the approximate result, and select the closest choice. Track whether rounding pushed the estimate up or down to avoid picking a near-miss trap answer.

23. What is back-solving (plugging in the answer choices), and which choice should you test first?

    Substitute the numeric answer choices into the problem's conditions until one works. Start with the middle value (often choice C); if it is too large or too small, you can eliminate that direction's choices.

24. On the GMAT Quant section, roughly how much time should you budget per question, and what should you do when stuck?

    The section gives about $2$ minutes per question on average. If a question runs well past that with no clear path, make an educated guess, mark it mentally, and move on—pacing protects your score more than any single hard question.

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