GRE Quantitative Reasoning — practice questions
120 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice GRE Quantitative Reasoning in the app →Which of the following is a complete list of the positive factors of 60?Which statement about even and odd integers is **false**?When the integer $-32$ is divided by $3$, the quotient $q$ and remainder $r$ (with $0 \le r < 3$) satisfy:The prime factorization of $1{,}155$ is:What is the **least common multiple** (LCM) of $30$ and $75$?A positive integer $n$ has the property that $n^2$ has exactly $9$ positive divisors. If $n$ is a prime power,Expand and simplify $(x + 2)(3x - 7)$.If $2^{3c + 1} = 2^{10}$, what is the value of $c$?For all values of $x$ for which the expression is defined, simplify $\dfrac{7x^{2} + 14x}{2x + 4}$.What is the degree of the polynomial $2x^{2} - 7xy^{3} - 5$?Which of the following is **always** true for all real numbers $x$ and $y$?For all $x \ne 3$, the expression $\dfrac{x^{2} - 9}{4x - 12}$ simplifies to:Which of the following sets of three lengths could be the side lengths of a triangle?What is the measure of each interior angle of a **regular octagon**?A right triangle has a hypotenuse of length $8$ and one leg of length $5$. What is the length of the other legIn a $30^{\circ}$-$60^{\circ}$-$90^{\circ}$ right triangle, the lengths of the sides opposite the $30^{\circ}$
In triangle $ABC$ shown above, the measures of ang
In the figure above, lines $k$ and $m$ are paralleA survey was taken to find the number of children in each of 25 families. The relative frequency distribution Thirty students took a history test. The grouped frequency distribution of their scores is shown below.
| ScoThe table shows annual per capita income in a certain state.
| Year | Annual Per Capita Income |
|---|---|
| The table shows the closest and farthest distances of the eight planets from the Sun, in millions of kilometer
The bar graph above (Data Analysis Figure 1) shows
The circle graph above shows U.S. production of phA computer password consists of four characters: the first is one of the 10 digits 0–9, and each of the next tIf a fair coin is tossed $8$ times, how many distinct outcome sequences (ordered head/tail outcomes) are possiHow many distinct 5-digit positive integers can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ if **no digitIn how many ways can a $3$-person committee be selected from a group of $9$ students? (The order of selection A fair $12$-sided die, with faces numbered $1$ through $12$, is rolled once. Each outcome is equally likely. WAn experiment has three events $A$, $B$, and $C$ with $P(A) = 0.23$, $P(B) = 0.40$, and $P(C) = 0.85$. Events What is the **arithmetic mean** of the five numbers $6$, $4$, $7$, $10$, and $4$?The list of $11$ numbers is $1$, $2$, $3$, $3$, $3$, $5$, $7$, $10$, $10$, $10$, $20$. Which of the following Consider the list of five numbers $4$, $4$, $6$, $7$, $10$. If the value $10$ is replaced by $24$ (so the new For the list of $16$ numbers $2$, $4$, $4$, $5$, $7$, $7$, $7$, $7$, $7$, $8$, $8$, $9$, $9$, $9$, $9$, $9$ (aWhat is the (population) **standard deviation** of the five numbers $0$, $7$, $8$, $10$, and $10$, rounded to A group of $600$ job applicants is rated on a scale of $1$ to $50$. The ratings have **mean** $32.5$ and **staIn the $xy$-plane, what is the distance between the points $Q(-2, -3)$ and $R(4, 1.5)$?What is the slope of the line passing through the points $Q(-2, -3)$ and $R(4, 1.5)$?A line $\ell$ has equation $y = 2x + 5$. Which of the following lines is **perpendicular** to $\ell$?A line has slope $0.75$ and passes through the point $(-2, -3)$. What is the equation of the line in slope-int
The graph above shows the two linear equations
$The point $P(5, -2)$ is reflected about the line $y = x$ to obtain point $P'$. What are the coordinates of $P'Pilar bought a purse on sale for $\$18$, which was one-half of the original price. What was the original priceThe **difference** of a number and $6$ is $13$. What is the number?Ginny's study group has three more than twice as many girls as boys. There are $11$ girls in the group. How maOne number is **five more than** another number. The sum of the two numbers is $21$. What are the two numbers?One number is **ten more than twice** another number. Their sum is $1$. What is the **second** (larger) numberFind three **consecutive integers** whose sum is $-42$. What is the **smallest** of the three?What are the **real solutions** of the equation $2x^{2} - x - 6 = 0$?How many **real solutions** does the equation $x^{2} + 4x + 4 = 0$ have, and what are they?How many **real solutions** does the equation $x^{2} + x + 5 = 0$ have?What are the real solutions of $5x^{2} + 3x - 2 = 0$?Solve the inequality $-3x + 5 \le 17$ for $x$.What is the **domain** of the real-valued function $g(x) = x^{3} + qrt{x + 2} - 10$?If $\dfrac{x}{49} = \dfrac{3}{21}$, what is the value of $x$?$13$ is what percent of $20$?$15$ is $60\%$ of what number?What is $30\%$ of $350$?An investment in a mutual fund increases by $12\%$ in a single day. If the value before the increase was $\$1{A quantity increases from $600$ to $750$. What is the **percent increase**?A rectangular solid has length $8.5$, width $5$, and height $10$. What is its volume?A cube has edge length $4$. What is its volume?A rectangular solid has length $8.5$, width $5$, and height $10$. What is its total **surface area**?A right circular cylinder has a base of radius $3$ and height $6.5$. What is its volume?
The right circular cylinder above (Geometry Figure 3A right circular cylinder has radius $3$ and height $6.5$. What is its total surface area (including both circAdalberto has $\$2.25$ in dimes and nickels in his pocket. He has nine more nickels than dimes. How many of eaMaria has $\$2.43$ in quarters and pennies in her wallet. She has twice as many pennies as quarters. How many At a school concert, the total value of tickets sold was $\$1{,}506$. Student tickets sold for $\$6$ each, andMichaela has $\$2.05$ in dimes and nickels. She has **seven more dimes than nickels**. How many nickels does sDanny has $\$2.14$ in pennies and nickels in his piggy bank. The number of nickels is **two more than ten timeMarco has $\$8{,}000$ to invest. He puts part of it in an account earning $3\%$ interest and the rest in an acAn arithmetic sequence has first term $a_{1} = 3$ and common difference $d = 6$. What is the $15$th term?Which of the following is the common ratio of the geometric sequence $27, 9, 3, 1, \dfrac{1}{3}, \dfrac{1}{9},What is the sum of the first $30$ terms of the arithmetic sequence $8, 13, 18, 23, 28, \ldots$?A geometric sequence has first term $a_{1} = 64$ and common ratio $r = \dfrac{1}{2}$. What is the $14$th term?What is the sum of the first $20$ terms of the geometric sequence $7, 14, 28, 56, 112, 224, \ldots$?What is the sum of the **infinite** geometric series $54 + 18 + 6 + 2 + \dfrac{2}{3} + \dfrac{2}{9} + \ldots$?A car travels at a constant speed of $70$ miles per hour for $3$ hours. What distance does it cover?An express train and a local train leave Pittsburgh for Washington, D.C. on the same route. The express takes Christopher and his parents live $115$ miles apart. They drive toward each other and meet at a restaurant. ChrWayne and Dennis ride the same bike path from a park to the beach. Dennis is $7$ mph faster than Wayne. It takTwo trucks leave the same rest area at the same time, one heading east and the other west. The westbound truckAshley and her parents both drive for $2$ hours to meet at a restaurant on the road between her college and hePress #1 can print the magazine in $6$ hours alone, and Press #2 can do the same job in $12$ hours alone. If bMike, an experienced bricklayer, can build a wall in $3$ hours; his son, who is learning, can do the same job Corey can finish a job in $4$ hours alone. When Corey and Casey work together, they finish the same job in $2$Pete can paint a room in $10$ hours alone, and Alicia can paint the same room in $8$ hours alone. Working togeTwo hoses, opened simultaneously, can fill a swimming pool in $10$ hours. If hose A working alone would take $Working together, Cara and Cindy can rake the yard in $4$ hours. Working alone, Cindy takes $6$ hours. How lonSimplify the expression $\dfrac{\pi}{2} + \dfrac{\pi}{3}$.What is the value of $(-3)^{5}$?Which of the following statements is **true**?What is the value of $5^{-2}$?Which of the following correctly evaluates $ qrt{100}$ in the real number system?Simplify $\dfrac{\dfrac{1}{ qrt{2}}}{\dfrac{3}{ qrt{5}}}$.Which of the following expressions is equivalent to $(a + b)^{3}$ for all real $a, b$?Simplify the expression $\left(2x^{3}\right)^{4}$.Solve the equation $3(x - 2) + 5 = 2x + 7$.Simplify $\dfrac{x^{8}}{x^{3}}$ for $x \ne 0$.Solve the equation $\dfrac{2x + 1}{3} = \dfrac{x - 4}{2}$.Expand $(2x - 3)^{2}$.What is the sum of the measures of the interior angles of a **decagon** (a $10$-sided polygon)?If the polygon in the previous problem is a **regular** decagon, what is the measure of each interior angle?The lengths of two sides of an isosceles triangle are $15$ and $22$. Which of the following are the **possibleTriangles $PQR$ and $XYZ$ are **similar**, with the vertices in corresponding order. If $PQ = 6$, $PR = 4$, anIn a $30^{\circ}$-$60^{\circ}$-$90^{\circ}$ right triangle, the side opposite the $60^{\circ}$ angle has lengtTwo triangles are congruent if their corresponding sides and angles are equal. Which of the following statemenWhat is the **common difference** of the arithmetic sequence $-7, -2, 3, 8, 13, \ldots$?What is the $20$th term of the arithmetic sequence with first term $a_{1} = 4$ and common difference $d = -3$?Find the sum of the **first $50$ positive odd integers**: $1, 3, 5, 7, \ldots, 99$.What is the $7$th term of the geometric sequence $2, -6, 18, -54, \ldots$?What is the sum of the **infinite** geometric series $1 + \dfrac{1}{2} + \dfrac{1}{4} + \dfrac{1}{8} + \dfrac{A geometric sequence has $a_{2} = 12$ and $a_{5} = 324$. What is the common ratio?Which point is the reflection of $(3, -5)$ across the **x-axis**?What is the slope of a line parallel to the line with equation $y = -2x + 7$?The line passing through the points $(2, 5)$ and $(6, 13)$ has what slope?The line with equation $y = \tfrac{1}{3}x + 2$ crosses the $x$-axis at what $x$-value?Find the **midpoint** of the segment connecting $A(-4, 6)$ and $B(8, -2)$.In the $xy$-plane, line $\ell$ passes through the origin and is perpendicular to the line $4x + 3y = 12$. What