If x and y are positive integers with x + y < 40, what is the largest possible product xy?

If n > 1, what is the smallest positive integer n such that the expression \(\sqrt{1+2+3+...+n}\) simplifies to an integer?

Triangle ABC has three different integer side lengths. Side AC is the longest side, and side AB is the shortest side. If the perimeter of ABC is 384 units, what is the greatest possible difference AC − AB?

Let the function R ¤ S be defined as R ¤ S = 2R + S2 . For instance, 2 ¤ 3 would have a value of (2 × 2 + 32 ), which yields a value of 13. What is the value of 4 ¤ −1? 

Henry walked on a flat field 9 meters due north from a tree. He then turned due east and walked 24 feet. He then turned due south and walked 9 meters plus 32 feet. How many feet away from his original starting point is Henry?

A legal-sized piece of paper measures 8.5 inches by 14 inches. A one-inch border of paper is cut off from each of the four sides. How many square inches have been cut off?

The numerical value of a particular square’s area is equal to the numerical value of its perimeter. What is the length of a side of the square? 

A standard six-sided die with its faces numbered 1 to 6 is rolled once, and a dime is tossed once. What is the probability of rolling a number less than 3 and tossing a tail? Express your answer as a common fraction.

The ratio of the length of a rectangular room to its width is 5:3. The perimeter of the room is 48 feet. What is the area of the room?

  Peter Pedals rode his bike a total of 500 miles in five days. Each day he rode 10 more miles than he had ridden on the previous day. How many miles did Peter ride on just the fifth day?

Ben and Dan are two of the members on the school’s chess team. In a tournament against their rival team, Ben played exactly 1 out of every 4 games. Dan, who played more games, played 14 games. What is the largest number of games the team could have played?

Among all three-digit integers from 100 to 400, how many have exactly one digit that is an 8?

Two integers have a difference of −18 and a sum of 2. What is the product of the two integers?

How many factors of 1000 can be divided by 20 without a remainder?

Susan reads at a rate of 240 words per minute. How many hours will it take her to read a 480-page book that averages 600 words per page?  

Given that a + b = 29 and ab = 204, what is the value of a² + b²?

Given that 2a + b = 19, 2c + d = 37 and b + d = 24, what is the value of a + b + c + d?

What is the 2011th term of the arithmetic sequence −4, −1, 2, 5, . . . , where each term after the first is 3 more than the preceding term? 

If Sara makes 80% of the free throws she attempts, what is the probability that she misses exactly two of her next three free throws? Express your answer as a common fraction.

Three stoplights on different streets each operate on their own independent schedules, as follows: the first stoplight is red 1 minute out of every 2 minutes (1 minute red, then 1 minute green), the second is red 2 minutes out of every 3 minutes (2 minutes red, then 1 minute green) and the third is red 3 minutes out of every 5 minutes (3 minutes red, then 2 minutes green.) At 9:00 am each stoplight turns red. The lights are either red or green (don’t worry about yellow). What time is it when the next 1-minute segment of time in which all three stoplights are red begins?