Number Theory!
What is the greatest number of consecutive integers that sum to 55?
110
Max is building a fence around his garden. He has 48 feet of fence available to fence three sides. The last side is backed up against the wall. In order to maximize the area of his garden, what is the legnth of the longest side of the garden?
24 feet
Oranges come in sets of 4, and bananas come in sets of 7. If you are going to buy 8 sets of fruit total and want 41 pieces of fruit, how many sets of bananas must you buy?
3 sets
I'm going to a donut shop. There are three different varieties (chocolate, powdered, and glazed), and I have enough money for 5 donuts. If I want at least one chocolate and one powdered donuts, how many different orders can I place?
10 orders
How many zeroes are at the end of 102! (102! = 1x2x3..102)
24 zeroes
A point is reflected across the line y=x and then across the x-axis, giving the point (-5,12). What is the original point?
(-12,-5)
A cat is sleeping when he sees a mouse whiz past him. From that moment, it takes the cat two seconds to react and abruptly runs to chase after the mouse, at a constant speed of 7 m/s. The mouse maintains its speed of 4 m/s. How far away should the mouse's home be from the where the cat was sleeping so that he just barely makes it to safety before the cat can catch him? Express your answer as a common fraction.
56/3 meter
Max is going to pick three real numbers a,b, and c in between 0-2 (inclusive). What is the probability that his selection of a,b, and c satisfies that c is greater than or equal to 1 and a and b are no more than 0.5 apart? Express your answer as a common fraction.
7/32
At an event, Kaitlyn is organizing the chairs into rows. If she organizes them into rows of 5, she has 3 chairs left over. If organizes them into rows of 7, she has 5 left over. If she organizes them into rows of 3, she has 1 left over. If she organizes them into two rows, there are none left over. What is the minimum number of chairs used at the event?
208 chairs
Given the point (3,4) in a standard coordinate system, what is its distance to the line y=-0.75x + 12.5?
5
If a + b = 20 and ab = -20, what is the value of 1/a + 1/b?
-1
A coin is weighted, meaning the probability of landing heads is not the same as rolling tails. If the probability of rolling 2 heads and 3 tails is 80/243 and the probability of rolling 3 heads and 2 tails is 40/243, what is the probability of rolling 5 heads in a row?
1/243
Evaluate 13(52 - 34) - 12 in base 6. Give your answer in base 6.
214 (base 6)
Two circles overlap so that the center of each circle lies on the outer edge of the other. The radius of both circles if 4. The distance between the two intersection points is what? Express your answer as a(sqrt(b)) where b is not divisible by the square of any integer.
4sqrt(3)
For what range of x does x4 + 3x3 - 3x2 - 7x + 6 have a negative value?
(-3,-2)
-3 < x < -2
Given a cloudy forecast, the probability that it will rain is 3/5. The probability that it will rain with a sunny forecast is 1/8. The probability of having a cloudy forecast is 5/8. What is the probability that, if it rains, it is sunny?
1/9