GRE Math Questions
the radius of a circle is 6 meters. what is the circumference of the circle
12πm or 37.86m
a square has a diagonal of length 5. what is the length of a side of the square
(5_/2)/2
the product of 4 less than x and 6 more than x is 20
(x-4)(x+6) = 20
factor the expression x^2 - 10x + 25
(x-5)(x-5)
what is the maximum value for the function g(x) = -2x^2 - 1
-1
what is the domain of this function: {(-3,4), (-2, 5) (-1, 6), (0, 7), (1, 8)}
-3, -2, -1, 0, 1
6w^2 - w - 15 = 0
-3/2, 5/3
what is the minimum value for the function f(x) = -x^2 + x + 4 where -6 < x < 6
-38
3x = -12
-4
what is the minimum value for the function f(x) = x^2 - 5
-5
what is the value of x if the average of -6, 4, 10, and x is 2
0
x(x-2) = 0
0, 2
y^2 - 7y = 0
0, 7
convert to a percent: 0.0003
0.03%
if P(A) = 0.3, P (A n B) = 0.12, and the events A and B are independent, then find P(B)
0.2
a cylinder has a surface area of 22π. if the cylinder has a height of 10, what is its radius
1
each of 48 employees has entered for a chance to win 3 prizes. if the probability of drawing any given employee is the same, and if winning a prize makes the employee ineligible for the remaining prizes, what is the probability of any given employee winning a prize
1/16
if 9500 is invested at 4.5% annual interest, compounded quarterly, what is the balance after 2 years?
10 389.20$
what is the median, mode, range: 4, 7, 8, 8, 9, 11, 12, 21, 36, 45
10, 8, 41 (4-45)
what is the sum of the five consecutive even numbers whose average is 20
100
a quiz has 10 true/false questions. if each question is answered with "true" or "false" and none are left blank, in how many ways can the quiz be answered?
1024
a brick with dimensions 3, 4, 9, has three holes bored completely through it. each hole has a diameter of 2. what is the volume of the brick?
108-9π
if a = -2 abd c=4, what is the value of 4-2a+c
12
t + 14 = 16
12
what is the greatest integer that will divide evenly into both 48 and 60
12
what is the perimeter of a right triangle with legs of length 3 and 4
12
in how many different ways can the letters in the word DANCE be ordered?
120
in how many distinct ways can the letters of the word METHODS be rearranged such that M and S occupy the first and last position
120
in a certain year, california produced 7/10 and south carolina produced 1/10 of all fresh peach crops in the US. If all the other states combined produced 242 million pounds that year, how many million pounds did south carolina produce?
121
what is the smallest positive integer divisible by both 18 and 7
126
find the surface area of a cube with an edge of 1.5
13.5
a 5 by 12 rectangle is inscribed in a circle. what is the circumference of the circle
13π
twelve people (3 men and 9 women) want to attend a conference. if 4 people are chosen at random from this group, what is the probability that no men will attend the conference
14/55
what is the greatest number that is less than 153 and is also divisible by 3 and 7
147
a cube with an edge of 4 has the same volume as a rectangular solid with a length and width of 2. what is the height of the rectangular solid
16
the arc of a quarter circle with endpoints at the vertices of a square has the area 4π. what is the area of the square
16
find the surface area of a rectangular solid with dimensions 1/2, 6, 12 (2)
162
a circular image is to be enlarged. the new radius will be 25% larger than the original. what is the ratio of the area of the current image to the area of the new image
16:25
(2a) ^ 4
16a ^4
point x lies on a line segment rs. the length of segment rx is 2 more than half of the length of segment xs. if the length of xs is 10, what is the length of segment rs?
17
if the ratio of boys to girls in a class is 4:3 and there are 24 boys, how many girls are in the class?
18
the distance around a circular fountain is 38π meters. what is the radius of the fountain
19
what is 28% of 70
19.6
what is the ratio of the areas of two congruent triangles (9)
1:1
what is the slope of the line that contains the points (4, 8) and (-1, -2)
2
what is the range of the function f(x) = 6 + x if the domain is [-4, 0, 4]
2, 6, 10
the average weight of 10 packages increases by 2 ounces when the weight of a book is added to one of them. if the average weight of the packages, after including the weight of the book, is 34 ounces, what is the weight of the book in ounces
20
after spending 1/4 of her paycheck, rachelle has $150 left. how much was rachelle's paycheck?
200
julia is picking 4 books randomly from a bookshelf. if she has 18 science fiction books, 6 drama books, and 8 how to books, what is the probability that she will pick 3 science fiction books and then 1 how to book?
204/4495
jake went to a football game with 4 of his friends. there are 120 different ways in which they can sit together in a row of 5 seats, with one person per seat. In how many of those ways is jake sitting in the middle seat?
24
a cube of ice has edges of length 10. what is the volume of the largest cylinder that can be carved from the cube?
250π
nine coins are tossed simultaneously. in how many of the outcomes will the fourth coin tossed show heads
256
(5a/2b) ^ 2
25a^2/4b^2
a rectangle inscribed in a circle has a length of 8 and a width of 6. what is the area of the circle in terms of π?
25π
the radius of a circle is 5 inches. what is the area of the circle
25πinches or 78.5inches
the dimensions of a rectangular solid (3, 4, 5) are tripled. by what factor is the volume of the rectangular solid increased
27
two numbers have a sum of 51. one number is 3 more than the other. what is the greater number?
27
if 8 schools are all in the same conference, how many soccer games are played during the season if the teams all play each other exactly once
28
if the average of 5 consecutive intergers is 14, what is the sum of the least and greatest of the 5 integers
28
how many 3-digit positive integers are even and do not contain the digit 4
288
for two similar triangles, the ratio of their corresponding sides is 2:3. what is the ratio of their perimeters?
2:3
fifteen percent of 40% of 50 is what number?
3
the length of a rectangle is 2x-1 and the width is 3x + 5 and the perimeter is 38. what is x
3
the sides of a triangle are of length 5, 8, and c. what is the range of the possible values of c?
3 < c < 13
if there are 8 people (3 women and 5 men) under consideration for 2 positions on the city council, what is the probability of both positions being filled by women if the people to fill the positions are randomly chosen
3/28
find the probability of tossing at least 1 tail with 2 tosses of a fair coin
3/4
if a fair coin is tossed 3 times, what is the probability that the coin will land heads up exactly 2 times?
3/8
there are 6 doors leading into a library. how many different ways could a student enter the room by one door and then leave it using a different door
30
2^3 x 2^2
32
(3 x 2) ^ 2
36
find the volume of a rectangular solid with dimensions 10, 4, 9 (1)
360
if an angle is twice as large as its complement, what is the measure of the larger angle
360
the diameter of a circle is 12 feet. what is the area of the circle
36π ft
what is the sum of the five consecutive odd numbers whose average is 75
375
the dimensions of a cube are each doubled, from 2 to 4. by what factor is the surface area of the cube increased
4
the height of a cylinder is twice its radius. if the volume of the cylinder is 128π, what is the radius?
4
where do graphs f(x) = 3x and g(x) = 2x + 4 intersect?
4
find the probability of randomly selecting 2 blue socks, one at a time without replacement, from a drawer with 14 white and 8 blue socks
4/33
what is the area of a triangle with a height of 8 and a base of 10
40
of 25 students in a class, 15 completed their tests. what percent of the students in the class did not complete the test
40%
find the volume of a cylinder with a radius of 10 and a height of 4
400π
what is the average of 5, 10, 50, 100
41.25
a company places a 6-symbol code on each product. the code consists of the letter T, followed by 3 numerical digits, and then 2 consonants. how many different codes are possible? (Y is a consonant)
441000
jeff sold $650,000 in software in the fourth quarter. if this was a 40% increase over his third quarter sales, what were his third quarter sales?
464, 286
what is the area of a parallelogram with a height of 6 and a base of 8
48
regular pentagon ABCDE has a side length of 28. regular pentagon FGHIJ has a perimeter of 60 and an area of 248. what is the ratio of the area of ABCDE to the area of FGHIJ
49:9
in similar hexagons, the ratio of the areas is 16:25. what is the ratio of their corresponding sides
4:5
for similar triangles, the ratio of their corresponding sides is 2:3. what is the ratio of their areas?
4:9
what is the side length of an equilateral triangle with an altitude of 6
4_/3
the square inscribed in the circle has side lengths of 4. what is the circumference of the circle?
4π
2r = 10
5
the product of 5 and one-half of n
5 (1/2n)
4n^2 + 5 = 9n
5/4, 1
five bakeries sell an average of 300 muffins per bakery per day. if two of the bakeries stop making muffins, but the total number of muffins sold stays the same, what is the average number of muffins sold per bakery among the remaining bakeries?
500
the square inscribed in the circle has side lengths of 10. what is the area of the circle?
50π
find the volume of a cube with an edge of 8
512
if angle x has a measure of 36 degrees, what is the measure of its complement
54
what is the area of a regular hexagon with sides of length 6
54_/3
a sportswear store ordered an equal number of blue and white jerseys. the jersey company delivered 22 extra blue jerseys, making the ratio of blue jerseys to white jerseys 7:5. how many jerseys of each colour did the store originally order?
55
what percent of 40 is 22
55%
which of the following numbers is divisible by 7: 43, 51, 56, 58
56
what is the area of a right triangle with legs of lengths 12 and 16
6
what is the value of x if the average of 3, 7, 8, and x is 6
6
for what values should the domain be restricted for this function? f(n) = n - 6/n^2 - 6n
6 and 0
how many times can a cube-shaped container with an edge of 2 be emptied into a rectangular prism container with dimensions 4, 8, and 15
60
if you toss a fair coin 6 times, what is the number of total possible outcomes
64
the measure of an angle is 48 more than the measure of its complement. what is the measure of the angle?
69
if the point (2, y) lies on the fraph of f(x) = x^2 + 3, what is y
7
the average of 6 numbers is 8. if 2 is subtracted from 3 of the numbers, what is the new average
7
the length of a rectangle is 3 less than twice its width. if the perimeter is 36, what are the dimensions of the rectangle?
7 and 11
a fair coin is tossed 3 times. what is the probability of NOT getting zero tails across all the three tosses
7/8
the angles of a triangle are 50, 60, and x. what is the value of x
70
what is the measure of an exterior angle of a regular pentagon
72
find all numbers between 70 and 90 that are evenly divisible by 8
72, 88, 80
gloria has 7 shirts to display on 7 mannequins. if she has already placed the first shirt on mannequin 1, how many different ways can she display the rest of the shirts
720
what is the number of degrees that the hour hand of a clock moves between noon and 2:30 in the afternoon of the same day
75
what is the ratio of the surface area of a cube with an edge of 10 to the surface area of a rectangular solid with dimensions 2, 4, and 6
75:11
from a box of 12 candles, you are to remove 5. how many different sets of 5 candles could you remove
792
the sum of the cube of 7 and the value of 1
7^3 + 1
what is the length of the diagonal in a rectangular solid if the height is 5, width is 3, and length is 8
7_/2
what is the slop of the line represented by the equation y = 8x + 3
8
8 more than k is the same as 2
8 + k = 2
m^2 - 10m + 16 = 0
8, 2
the length and width of a rectangular solid are reduced by 10%. the new volume is what percent of the original volume?
81%
selena collects football, baseball, and basketball cards. if the ratio of football to baseball cards is 4:2 and the ratio of baseball cards to basketball cards is 4:1, what is the ratio of football to basketball cards?
8:1
9 is at least 2 1/2 less than x
9 > x -2 1/2
if angle x has a measure of 90 degrees, what is the measure of its supplement?
90
the four angles around a point measure y, 2y, 35, 55. what is the value of y
90
what is the sum of the interior angles of a heptagon
900
find the surface area of a cylinder with a diameter of 12 and a height of 3
90π
ashley's scores on five math tests are 84, 100, 88, 95, 92. what does she need to score on the next test for her final average on all the tests to be at least 92
93
the ratio of the ages of anna and emma is 3:5 and the ratio of the ages of emma and nicholas is 3:5. wha tis the ratio of anna's age to nicholas's age?
9:25
the area of a rectangle is 588 square feet and its length is three times its width. what are the measures of the length and the width?
W = 14 L = 42
-8 < -2x
X < 4
5(x - 3) + 7 < 2x + 7
X < 5
the quotient of a number divided by -15 is less than 4. what could the number b?
X > -60
9 < x/5
X > 45
2x - 3(x - 4) > 4 - 2(x - 7)
X > 6
angle a and b are supplementary. the measure of angle a is (3x + 50) and the measure of angle b is 7x + 90. what are the measures of angle a and b
a = 62, b = 118
(ab ^2) ^3
a^3b^6
the quotient of h divided by -11
h/-11
javier is 2 years older than three times his sister's age, s. how old is javier
j = 2 + 3s
will the value be odd or even: the difference between an even number and an odd number, squared
odd
the number of hours spent on schoolwork is 6, 6, 7, 8, 10. what is the range, first quartile, and third quartile?
range = 4 Q1 = 6 Q3 = 9
describe the relationship between the graphs of f(x) = 3x^2 and g(x) = 3(x - 1)^2
the graph of g(x) is a translation (shift) of the graph f(x) one unit to the right
describe the relationship between the graphs of f(x) = x^2 and g(x) = 1/2x^2
the graph of g(x) is the graph of f(x) compressed vertically toward the x-axis by a factor of 1/2
if n is an integer, 2n + 2 will always be even
true
the product of three consecutive integers is always even
true
which line is steeper? y = 3x + 4 or 4x - 3y = 9
y = -3x + 4
which expression is greater: |(-6) + (-3)| or (-3)(-3)(-1)
|(-6) + (-3)|
which is greater |-6| or -6
|-6|
(-3/4st)^3
-27/64s^3t^3
if 10,800$ is invested at a simple interest rate of 4%, what is the value of the investment after 18 months
11 448
a punch recipe calls for 3 pints of ginger ale for every 2 quarts of juice. how many pints of ginger ale will be needed to mix with 10 quarts of juice?
15
bella's grade is determined by 5 quizzes and 1 exam. if the exam counts twice as much as each of the quizzes, what fraction of the final grade is determined by the exam?
15
if the ratio of the number of men to the number of women on a committee of 25 members is 2:3, how many members of the committee are women
15
two airplanes leave the same airport at the same time in opposite directions. their average speeds differ by 10 miles per hour. after 1.5 hours, they are 520 miles apart. what is the approximate average speed of each plane over the 1.5 hours
168.3mph and 178.3 mph
what is the x-intercept of the line represented by y = 4x - 8
2
the ratio of the age of a woman to that of her husband was 5:7 when they were first married. after 20 years of marriage, this ratio will be 5:6. what were the ages of the husband and the wife at the time they were first married?
20w:28h
sixty people attend a concert. children's tickets sold for 8$ and adult tickets sold for 12$. if 624$ was collected in ticket money, how many children and adults attended the concert
24 children and 36 adults
the ryder family traveled at an average rate of 60 miles per hour and it took 10 hours to complete their trip. if they traveled for 4 of their 10 hours at a constant speed of 70 miles per hour, at what average speed did they travel for the remaining 6 hours to obtain the 60 mph for the entire trip?
53 1/3 mph
what is the sum of the five consecutive even numbers whose average is 12
60
the price of a car accessory that originally costs $80 is discounted by 25%. what is the discounted price of the car accessory
60$
at a football game with 5400 fans, 2/3 of the fans are rooting for the home team. if 800 of the home-team fans are students, what fraction of the home-team fans are not students?
7/9
b is at most the sum of 2 and -1
b < 2 + (-1)
2c = 14 + 4g and 3g = 2 - c
c = 5, g = -1
will the value be odd or even: the product of an even number and an odd number
even
will the value be odd or even: the product of two even numbers multiplied by one odd number
even
will the value be odd or even: the sum of four odd numbers
even
will the value be odd or even: the sum of two odd numbers
even
will the value be odd or even: the sum of two odd numbers plus the product of an even number times an odd number
even
write the equation y = 2x + 7 using function notation
f(x) = 2x + 7
what is the slope of a line that is perpendicular to y = 1/3x - 7
m = -4/3
what is the slope of a line perpendicular to a line that contains the points (5, -1) and (-2, -1)
undefined
6w - 4 - 3w = 8 - 12 - 4w
w = 0
3x/-2 > -6
x < 4
if f(x) = 1/2x + 8, what value of x makes f(x) = 0
x = -16
3x = 9 and 2x + 4y = 22
x = 3 and y = 4
3(x+2) = 5x + 1
x = 5/2
2x-3x < 6
x > -6
x - 3 > 7
x > 10
