Number Theory!
What is the greatest common divisor of 78 and 169?
13
What is the side legnth of a square whose area equals its perimeter?
4 units
Kenna has a certain number of pencils. Her sister has 5 less than three times the number of pencils Kenna has. Max has 4 times the number of pencils that Kenna has. He has 16 pencils. How many pencils does Kenna have?
9 pencils
There are 10 red balls in Arya's basket, which has 15 balls total. If he is 5 times more likely to pick a red ball than Nina, who has 4 red balls in her basket. How many total balls does Nina have in her basket?
30 balls
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 meters
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