655-705 (Hard)
If b = a + 4 , for which of the following values of x is the expression (x − a) 2 + (x − b) 2 the smallest?
Sub 505 (Easy)
Today Rebecca, who is 34 years old, and her daughter, who is 8 years old, celebrate their birthdays. How many years will pass before Rebecca’s age is twice her daughter’s age?
Sub 505 (Easy)
1 3 + 1 2 − 5 6 + 1 5 + 1 4 − 9 20 = 1 3 + 1 2 − 5 6 + 1 5 + 1 4 − 9 20 =
Sub 505 (Easy)
− 2 (3 − x [ 5 + y − 2 x ] − 7 + 2 ⋅ 3 2) =
Sub 505 (Easy)
A rectangular floor that measures 8 meters by 10 meters is to be covered with carpet squares that each measure 2 meters by 2 meters. If the carpet squares cost $12 apiece, what is the total cost for the number of carpet squares needed to cover the floor?
Sub 505 (Easy)
John has 10 pairs of matched socks. If he loses 7 individual socks, what is the greatest number of pairs of matched socks he can have left?
505-555 (Easy)
Raffle tickets numbered consecutively from 101 through 350 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ?
Sub 505 (Easy)
A student's average (arithmetic mean) test score on 4 tests is 78. What must be the student's score on a 5th test for the student's average score on the 5 tests to be 80?
555-605 (Medium)
A certain fruit stand sold apples for 0.70eachandbananasfor0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase?
Sub 505 (Easy)
A case contains
c
cartons. Each carton contains
b
boxes, and each box contains 100 paper clips. How many paper clips are contained in 2 cases?
Sub 505 (Easy)
In the Johnsons' monthly budget, the dollar amounts allocated to household expenses, food, and miscellaneous items are in the ratio 5:2:1, respectively. If the total amount allocated to these three categories is $1,800, what is the amount allocated to food?
505-555 (Easy)
At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can be estimated by the formula N = 20 L d 600 + s 2 where L is the number of lanes in the same direction, d is the length of the portion of the highway, in feet, and s is the average speed of the cars, in miles per hour. Based on the formula, what is the estimated number of cars traveling on a 1/2-mile portion of the highway if the highway has 2 lanes in the same direction and the average speed of the cars is 40 miles per hour?
555-605 (Medium)
If y is an integer, then the least possible value of |23 - 5y| is
Sub 505 (Easy)
At least 2/3 of the 40 members of a committee must vote in favor of a resolution for it to pass. What is the greatest number of members who could vote against the resolution and still have it pass?
505-555 (Easy)
A glass was filled with 10 ounces of water, and 0.01 ounce of the water evaporated each day during a 20-day period. What percent of the original amount of water evaporated during this period?
Sub 505 (Easy)
When Leo imported a certain item, he paid a 7 percent import tax on the portion of the total value of the item in excess of 1,000.IftheamountoftheimporttaxthatLeopaidwas87.50, what was the total value of the item?
Sub 505 (Easy)
1 + 1 3 − 1 + 1 2
555-605 (Medium)
(0.0036) (2.8) (0.04) (0.1) (0.003) =
Sub 505 (Easy)
The sum 7 8 + 1 9 is between
Sub 505 (Easy)
A gym class can be divided into 8 teams with an equal number of players on each team or into 12 teams with an equal number of players on each team. What is the lowest possible number of students in the class?