Problem 31 - GMAT Powers & Roots

Problem 30 - GMAT Combinatorics

In how many different arrangements can six trees be planted on the circumference of a circular garden if two arrangements are considered different when the positions of the trees are different relative to those of the others?

A) 720
B) 180
C) 160
D) 120
E) 60

Problem 29 - GMAT Geometry

How many diagonals does a polygon of nine sides have?

(A) 72
(B) 54
(C) 36
(D) 27
(E) 24

Problem 28 - GMAT Coordinate Geometry

In the coordinate system above, line segments BC and AC are parallel to the x and y axes, respectively. If line segment AB has length 30 and is on a line that has slope 4/3, what is the length of BC?

(A) 28
(B) 24
(C) 21
(D) 18
(E) 15

Problem 27 - GMAT Coordinate Geomery

In a coordinate system, points A and B have xy-coordinates (5, 2c) and (6, c^2), respectively. If points A and B lie on line k, which has slope 8, then c could equal

(A) -4
(B) -3
(C) 1
(D) 2
(E) 4

Problem 26 - GMAT Coordinate Geometry

In a coordinate system, line l is parallel to line k, does line l intersect the x-axis?

(1) Line k has slope zero.

(2) Point (0, 4) is on line k.

Problem 25 - GMAT Coordinate Geometry

In a rectangular coordinate system, if a and b are positive integers, is point (a, b) above line y = x?

(1) a = 4

(2) b = a + 2

Problem 24 - GMAT Powers & Roots

A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 1,000 and at the same time n is a perfect square and a perfect cube?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Problem 23 - GMAT Powers & Roots

Problem 22 - GMAT Geometry

An equilateral triangle of side 12 is inscribed in a circle, what is the area of the circle?

Problem 21 - GMAT Powers & Roots

(A) 5

(B) 4

(C) 3

(D) 2

(E) 1

Problem 20 - GMAT Number Properties

If (p - q) is not equal to zero, what is the value of p/(p - q)?

1) 13p - 11q = 0

2) 13 - p = 11 + q

Problem 19 - GMAT Number Properties

Which is the smallest positive integer y such that 120y is the square of an integer?

(A) 10
(B) 15
(C) 30
(D) 60
(E) 90

Problem 18 - GMAT Number Properties

If positive integer x is divided by 5, the result is p and the remainder 3. If x is divided by 11, the remainder is 3 again, what is the remainder when p is divided by 11?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

Problem 17 - GMAT Powers & Roots

What is the value of x if x is the units digit of 3^23 - 3?

A) 0
B) 2
C) 4
D) 6
E) 8

Problem 16 - GMAT Number Properties

If 34 books are picked from a box and distributed among a group of students, which of the following is NOT a possible number of students in the group if after giving each student the same number of books the number of books put back in the box is two less than the number of students?

(A) 6
(B) 9
(C) 10
(D) 12
(E) 18

Problem 15 - GMAT Overlapping Sets

If 20% of the people at a college party were men who were wearing red t-shirts, and 60% of the men at the party were not wearing redt t-shirts, what percent of the people at the party were men?

(A) 80 %
(B) 60 %
(C) 50 %
(D) 40 %
(E) 33 1/3 %

Problem 14 - GMAT Algebra

Mike can do a maximum of 4000 push-ups a week. His "fitness" index is given by the equation F = (2/5) (3000 - p)(p - 60), where F is his fitness index and p is the number of push-ups Mike does during one week. Which of the following represents the number of weekly push-ups that will maximize his fitness index?

(A) 1530
(B) 1580
(C) 3000
(D) 3100
(E) 3200

Problem 13 - GMAT Mixtures

Jamal and Mary read a total of 100 books and no book was read by both of them. If Jamal found 40% of the books he read boring and Mary found 50% of the books she read boring, and together they found 44% of the 100 books boring, what percent of the 100 books was read by Mary?

(A) 66 2/3 %
(B) 60 %
(C) 58 %
(D) 48 %
(E) 40 %

Problem 12 - GMAT Speed

Yolanda walks from her home to school at 4 miles per hour; she then rides her bike back home by the same route at c miles per hour. What is Yolanda’s average speed for the round trip?

1) The distance from Yolanda’s home to her school is 6 miles.

2) c = 10

Problem 11 - GMAT Geometry

What is the largest possible area of a rectangle that has sides of integer length and perimeter 28?

(A) 50
(B) 49
(C) 48
(D) 45
(E) 40

Problem 10 - GMAT Number Properties

Is positive integer x even?

(1) The greatest prime component of x is 13.

(2) The least prime component of x is 7.

Problem 9 - GMAT Work Problem

If Tom and Huckleberry working at their respective rates can each whitewash 600 square feet of fence in x and y hours, respectively, how long will it take both of them working together at their own rates to whitewash 600 square feet of fence?

(1) x - y = 1

(2) (xy)/(x + y) = 6/5

Problem 8 - GMAT Number Properties

Problem 7 - GMAT Speed

Juan drives all the way from his office to his girlfriend’s house at an average speed of 20 miles per hour, he drives back to his office by the same route. If he wants to average 24 miles per hour for the round trip, at what average speed should he drive home?

(A) 25
(B) 26
(C) 28
(D) 29
(E) 30

Problem 6 - GMAT Work

It takes Peter 4 hours to complete one half of a certain job working alone. It takes Peter and Mike, working together at their respective rates, 3 hours to do one half of the same job. How long does it take Mike, working alone at his rate, to complete the same job?

(A) 24
(B) 20
(C) 16
(D) 12
(E) 8

Problem 5 - GMAT Overlapping Sets

At a college party, 70% of the women are wearing red t-shirts. If 60% of the people at the party are wearing red t-shirts, what is the ratio of women to men at the party?

1) Forty percent of the men at the party are wearing red t-shirts.

2) There are 120 people at the party.

Problem 4 - GMAT Number Properties

How many different factors does 120 have, excluding 1 and 120?

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

Problem 3 - GMAT Combinatorics

To form a six-people case competition team, a business school professor is to choose 3 female and 3 male students from a group of male and female students. If there are 7 male students in the group and 140 different six-student teams are possible, how many female students are there in the group?

A) 4
B) 7
C) 10
D) 14
E) 20

Problem 2 - GMAT Powers & Roots

10^180 - 10^30 =

Which of the following best approximates the value of the expression above?

(A) 10^180

(B) 10^179

(C) 10^170

(D) 10^160

(E) 10^150