If x is an integer with n distinct prime factors, is n greater than or equal to 3?
(1) x is divisible by 6
(2) x is divisible by 10
If x3 < x, is x > x2?
(1) x > -5
(2) x < -2
Is |15 - m| + |m - 15| > 15?
(1) m > 6
(2) m < 7
What is the value of x?
(1) x2 - 9 = 16
(2) 3x(x - 5) = 0
Is y2 < 1?
(1) y > -1
(2) y < 1
If a coffee shop sold 600 cups of coffee, some of which were large cups and the remainder of which were small cups, what was the revenue that the coffee shop earned from the sale of coffee?
(1) The price of large cups sold was 3/5 the total number of small cups sold.
(2) The price of a small cup of coffee was $1.50
If y > 0, is x less than 0?
(1) xy = 16
(2) x - y = 6
If x + y = 2 and x2 - xy - 10 - 2y2 = 0, what does x - 2y equal?
If x and y are prime numbers, is y(x - 3) odd?
(1) x > 10
(2) y < 3
A certain company produces exactly three products: X, Y, and Z. In 1990, what was the total income for the company from the sale of its products?
(1) In 1990, the company sold 8,000 units of product X, 10,000 units of product Y, and 16,000 units of product Z.
(2) In 1990, the company charged $28 per unit for product X and twice as much for product Z.
If 2b - a2 = 18, what is the value of b?
(1) a2 = 1,156
(2) a > 0
Team X won 40 basketball games. What percent of its basketball games did Team X win?
(1) Team X played the same number of games as Team Y.
(2) Team Y won 45 games, representing 2.5 percent of the total games it played.
If x > 0, what is the value of x?
(1) x > 5
(2) 40 - x2 = 4
If the perimeter of a rectangular property is 46 meters, and the area of the property is 76 meters, what is the length of each of the shorter sides?
A basketball team plays games only against the other five teams in its league and always in the following order: Croton, Darby, Englewood, Fiennes, and Garvin. If the team's final game of the season is against Fiennes, which of the following could be the number of games in the team's schedule?
A drought decreased the amount of water in city X's reservoirs from 118 million gallons to 96 million gallons. If the reservoirs were at 79 percent of total capacity before the drought began, approximately how many million gallons were the reservoirs below total capacity after the drought?
George's draper has 10 loose black socks, 15 loose blue socks, and 8 loose white socks. If George takes socks out of the drawer at random, how many would he need to take out to be sure that the removed socks include at least one matching pair?
Youssef lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bicycle to work. If it takes him exactly 10 minutes more to walk to work than to ride his bicycle, then x equals
A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $867.50. If each member of the club paid at least $42, then what is the greatest possible number of members in the club?
A machine manufactures notebooks in a series of 5 colors: red, blue, black, white, and yellow. After producing a notebook of one color from that series, it produces a notebook of the next color. Once five are produced, the machine repeats the pattern. If the machine began a day producing a red notebook and completed the day by producing a black notebook, how many notebooks could have been produced that day?
At a certain diner, Joe ordered 3 doughnuts and a cup of coffee and was charged $2.25. Stella ordered 2 doughnuts and a cup of coffee and was charged $1.70. What is the price of 2 doughnuts?
What is the product of all the possible values of x if x2(x + 2) + 7x(x + 2) + 6 (x + 2) = 0?
If 4x + y = 8 and y - 3x = 7, then what is the value of x + 2y?
In a certain town, there are four times as many people who were born in the town's state as there are people who were born in another state or country. The ratio of those residents born in the town's state to the town's total population is:
(a) 1 to 4
(b) 1 to 3
(c) 1 to 2
(d) 3 to 4
(e) 4 to 5
A team won 50 percent of its first 60 games in a particular season, and 80 percent of its remaining games. If the team won a total of 60 percent of its games that season, what was the total number of games that the team played?
A local restaurant recently renovated its dining space, purchasing new tables and chairs to use in addition to the original tables and chairs. The new tables each seat 6 customers, while the original tables each seat 4 customers. Altogether, the restaurant now has 40 tables and is capable of seating 220 customers. How many more new tables than original tables does the restaurant have?
Susan weighs m pounds more than Anna does, and together they weigh a total of n pounds. Which of the following represents Anna's weight in pounds?
(c) (n/2) - n
(d) 2n - m
(e) n - 2m
Peter read P books last year, and Nikki read N books last year. If Peter read 35 more books than Nikki last year, which of the following reflects this relationship?
(a) P > 35N
(b) P < N - 35
(c) P > N + 35
(d) P = N - 35
(e) P = N + 35
The youngest of 4 children has siblings who are 3, 5, and 8 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 21, what is the age of the youngest sibling?
7b + 7b + 7b + 7b + 7b + 7b + 7b =
(b) 7b + 1
Carol spends 1/4 of her savings on a stereo and 1/3 less than she spent on the stereo for a television. What fraction of her savings did she spend on the stereo and television?
If w > x > y > z on the number line, y is halfway between x and z, and x is halfway between w and z, then (y-x)/(y-w) =
Company Z spent 1/4 of its revenues last year on marketing and 1/7 of the remainder on maintenance of its facilities. What fraction of last year's original revenues did company Z have left after its marketing and maintenance expenditures?
During a sale, a store sells 20 percent of its remaining stock every day, without replenishment. After four days, what fraction of its original stock has it sold?
Jacob is now 12 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?
Hallie has only nickels, dimes, and quarters in her pocket. If she has at least 1 of each kind of coin and has a total of $2.75 in change, how many nickels does she have?
(1) She has a total of 21 coins, with twice as many dimes as nickels.
(2) She has $1.50 in quarters.
A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?
What is the value of x - y?
(1) 3x + 3y = 31
(2) 3x - 3y = 13
If the average (arithmetic mean) of a and b is 45 and the average of b and c is 70, what is the value of c - a?
(e) It cannot be determined
What is the value of p?
(1) 2p - m = 5p + 2m
(2) 2(p - m) = 8 - 2m
What is the value of x?
(1) 3x + 2y = 6
(2) 4y = 12 - 6x
If (a - 3)2 = 5 - 10a, then which of the following is the value of a?
Is n negative?
(1) n2 + n - 6 = 0
(2) n2 + 6n + 9 = 0
Which of the following expressions CANNOT be equal to 0 when x2 - 2x = 3?
(a) x2 - 6x + 9
(b) x2 - 4x + 3
(c) x2 - x - 2
(d) x2 - 7x + 6
(e) x2 - 9
If x2 - 2x - 15 = (x + r)(x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of r - s?
If x + y = 5y - 13 and x - y = 5, then x =
If the function f is defined for all x by f(x) = ax2 + bx - 43, where a and b are constants, what is the value of f(3)?
(1) f(4) = 41
(2) 3a + b = 17
What is the value of g?
(1) f + g = 9
(2) 3f - 27 = -3g
Each of the 600 elements of Set X is a distinct integer. How many of the integers in Set X are positive odd integers?
(1) Set X contains 150 even integers
(2) 70% of the odd integers in Set X are positive
Is z an integer?
(1) 2z is an even integer
(2) 4z is an even integer
Is z an integer?
(1) z/3 is an integer
(2) z/2 is NOT an integer
The set S contains n integers. Is the sum of all the elements of set S odd?
(1) All the elements of S are prime numbers
(2) n = 2
If negative integers k and p are NOT both even, which of the following must be odd?
(b) 4(k + p)
(c) k - p
(d) k + 1 - p
(e) 2(k + p) - 1
Is x - 2y + z greater than x + y - z?
(1) y is positive
(2) z is negative
Is x > y?
(1) 9x = 4y
(2) x > -y
How many positive integers less than 50 are multiples of 4 but NOT multiples of 6?
If a certain number is divisible by 12 and 10, it is NOT necessarily divisible by which of the following?
What is the greatest positive integer x such that 3x is a factor of 910?
If a and b are prime numbers, which of the following CANNOT be the value of ab?
If n is a positive integer greater than 16, is n a prime number?
(1) n is odd
(2) The remainder when n is divided by 3 is 1, and the remainder when n is divided by 7 is 1.
If 2 is the remainder when m is divided by 5, what is the remainder when 3m is divided by 5?
If a = 105 and a3 = 21 x 25 x 45 x b, what is the value of b?
In an increasing sequence of 8 consecutive even integers, the sum of the first 4 integers is 268. What is the sum of all the integers in the sequence?
In the infinite sequence S, each term Sn after S2 is equal to the sum of the two terms Sn-1 and Sn-2. If S1 is 4, what is the value of S2?
(1) S3 = 7
(2) S4 = 10
If x is an integer and 2.134 x 10x is less than 210,000, what is the greatest possible value for x?
If 42x+2 = 163x-1, what is the value of x?
If a is a positive integer, then 2a + 2a+1 =
What positive number, when squared, is equal to the cube of the positive square root of 16?
How many possible integer values are there for x, if |4x - 3| < 6?
Which of the following could be the value of x, if |4x - 2| = 10?
What is the value of p?
(1) -|p| = -2
(2) p2 - 4 = 0
If x > 4 and 3x - 2y = 0, then which of the following must be true?
(a) y < -6
(b) y < -4
(c) y = 6
(d) y < 6
(e) y > 6
How many integer values are there for x such that 1 < 3x + 5 < 17?
If a and b are positive integers, is 3a2b divisible by 60?
(1) a is divisible by 10
(2) b is divisible by 18
A baseball team won 45 percent of the first 80 games it played. How many of the remaining 82 games will the team have to win in order to have won exactly 50 percent of all the games it played?
(a) 36 (b) 45 (c) 50 (d) 55 (e) 81
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