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GMAT Arithmetic Progression — practice questions

Explore 87 free Arithmetic Progression questions in GMAT Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Arithmetic Progression questions and exercises with answers

Showing questions 1–30 of 87.

A fair six-sided die is rolled once. What is the probability of getting an even number?Read the answer and worked solution →A **random variable** is best defined as:Read the answer and worked solution →A **discrete** random variable is one whose possible values:Read the answer and worked solution →For a continuous random variable $X$, the probability that $X$ equals any specific value is:Read the answer and worked solution →The **cumulative distribution function (c.d.f.)** $F(x)$ of a discrete random variable is:Read the answer and worked solution →When two fair dice are rolled and $X$ denotes the sum of the upper faces, the range of $X$ is:Read the answer and worked solution →If a fair coin is tossed twice and $X$ = number of heads, then $P[X = 1]$ equals:Read the answer and worked solution →If two cards are drawn with replacement from a deck of 52, $P[X = 2]$ where $X$ = number of aces equals:Read the answer and worked solution →A fair die is thrown. Let $X$ = number of factors of the number on the upper face. $P[X = 2]$ equals:Read the answer and worked solution →$f(x) = 3x^2$ for $0 < x < 1$ is the p.d.f. of $X$. The probability $P[1/2 < X < 1]$ is:Read the answer and worked solution →If $f(x) = kx^2(1 - x)$ for $0 < x < 1$ is the p.d.f. of $X$, the value of $k$ is:Read the answer and worked solution →For p.d.f. $f(x) = x/8$, $0 < x < 4$, the probability $P[x < 1.5]$ is:Read the answer and worked solution →Find $k$ if $f(x) = kx$ for $0 < x < 2$ and 0 otherwise is a valid p.d.f.Read the answer and worked solution →The c.d.f. $F(x)$ of the p.d.f. $f(x) = 3x^2$ for $0 < x < 1$ is:Read the answer and worked solution →Two cards are drawn with replacement. $X$ = number of aces. The probability $P[X \geq 1]$ equals:Read the answer and worked solution →For p.d.f. $f(x) = x^2/3$ for $-1 < x < 2$, the probability $P[0 < X \leq 1]$ equals:Read the answer and worked solution →For p.d.f. $f(x) = k(4 - x^2)$ for $-2 \leq x \leq 2$ (and 0 elsewhere), the value of $k$ is:Read the answer and worked solution →For the c.d.f. $F(x) = 3x - 2x^3$ (from p.d.f. $f(x) = 3(1 - 2x^2)$ on $[0, 1]$), $F(0.5)$ equals:Read the answer and worked solution →If a fair coin is tossed $n$ times, the probability of any exact pattern (like all heads) is:Read the answer and worked solution →If a die is thrown and 'getting an odd number' is success, then $p$ and $q$ are:Read the answer and worked solution →A bag has balls marked 0–9. Four balls drawn with replacement. Probability that **none** is marked '0' is:Read the answer and worked solution →Probability of bomb hitting target = 0.8. Out of 10 bombs dropped, probability that **exactly 2 miss** equals (with $p = 0.2$ miss):Read the answer and worked solution →The distance between two points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is:Read the answer and worked solution →The distance of the point $P(x,y)$ from the origin is:Read the answer and worked solution →The midpoint of the segment joining $(x_1,y_1)$ and $(x_2,y_2)$ is:Read the answer and worked solution →The distance between the origin and the point $(3,4)$ is:Read the answer and worked solution →The midpoint of the segment joining $(2,3)$ and $(4,7)$ is:Read the answer and worked solution →The distance between the points $(1,2)$ and $(1,5)$ is:Read the answer and worked solution →The y-coordinate of any point lying on the x-axis is:Read the answer and worked solution →The x-coordinate of any point lying on the y-axis is:Read the answer and worked solution →

Worked practice questions

A fair six-sided die is rolled once. What is the probability of getting an even number?

  1. $\dfrac{1}{6}$
  2. $\dfrac{1}{2}$
  3. $\dfrac{1}{3}$
  4. $\dfrac{2}{3}$
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Correct answer: B. $\dfrac{1}{2}$

The even outcomes are {2, 4, 6}, so the number of favourable outcomes is 3. The total sample space has 6 outcomes. $P(\text{even}) = \dfrac{3}{6} = \dfrac{1}{2}$.

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A **random variable** is best defined as:

  1. The probability of an event
  2. A real number chosen by random guess
  3. A real-valued function defined on the sample space of a random experiment
  4. A variable with arbitrary letter name
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Correct answer: C. A real-valued function defined on the sample space of a random experiment

**A random variable X is a function X :** S → ℝ from the sample space to real numbers. It assigns a numerical value to every outcome of the random experiment. Conventionally denoted by capital letters (X, Y, Z).

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A **discrete** random variable is one whose possible values:

  1. Are finite or countably infinite
  2. Form an interval of real numbers (uncountably infinite)
  3. Are always negative
  4. Are obtained only by measurement
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Correct answer: A. Are finite or countably infinite

**Discrete RV:** finite or countably infinite values (typically non-negative integers — number of heads, defective items, etc.). Continuous RV has uncountably infinite values forming an interval.

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More Mathematics topics

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