1
A furniture store set the sticker price of a table 40 percent higher than the wholesale price that the store paid for the table. During a special sale, the table sold for 35 percent less than this sticker price. Find the percent the final sale price was of the original wholesale price of the table.
91
A building contractor needs to pay his 108 workers $200 each. He is carrying 122 one hundred dollar bills and 188 fifty dollar bills. Only 45 workers get paid with two $100 bills. Find the number of workers who get paid with four $50 bills.
31
Find the number of perfect squares that divide 2020.
231
A rectangular wooden block has a square top and bottom, its volume is 576, and the surface area of its vertical sides is 384. Find the sum of the lengths of all twelve of the edges of the block.
112
There were three times as many red candies as blue candies on a table. After Darrel took the same number of red candies and blue candies, there were four times as many red candies as blue candies left on the table. Then after Cloe took 12 red candies and 12 blue candies, there were five times as many red candies as blue candies left on the table. Find the total number of candies that Darrel took.
48
Camilla drove 20 miles in the city at a constant speed and 40 miles in the country at a constant speed that was 20 miles per hour greater than her speed in the city. Her entire trip took one hour. Find the number of minutes that Camilla drove in the country rounded to the nearest minute
35
Let m > n be positive integers such that 3(3mn − 2)^2 − 2(3m − 3n)^2 = 2019. Find 3m + n.
46
Find the sum of all values of x such that the set {107, 122, 127, 137, 152, x} has a mean that is equal to its median.
381
The side lengths of a scalene triangle are the roots of the polynomial
x^3 − 20x^2 + 131x − 281.3
Find the square of the area of the triangle.
287
Find the number of permutations of the letters AAAABBBCC where no letter is next to another letter of the same type. For example, count ABCABCABA and ABABCABCA but not ABCCBABAA.
79
A deck of eight cards has cards numbered 1, 2, 3, 4, 5, 6, 7, 8, in that order, and a deck of five cards has cards numbered 1, 2, 3, 4, 5, in that order. The two decks are riffle-shuffled together to form a deck with 13 cards with the cards from each deck in the same order as they were originally. Thus, numbers on the cards might end up in the order 1122334455678 or 1234512345678 but not 1223144553678. Find the number of possible sequences of the 13 numbers.
572
Let p, q, and r be prime numbers such that 2pqr + p + q + r = 2020. Find pq + qr + rp.
585