Arnau

ABCD is a rectangle with AC=20 and AB=2BC. What is the area of rectangle ABCD?

How many ordered pairs of integers (x,y) are there that satisfy |x|+|y| ≤ 10?

Two runners have a race. The first runner decides to run with his full speed v₁=9 m/s over the 250 meters of the race and then slows to v₂=7 m/s for the rest, since he's tired. The second runner wants to save energy, so he runs with v₃=8 m/s for the whole...

The ratio of three positive integers is 2:4:5 and their least common multiple is 300. What is the sum of the smallest and the largest of the three numbers?

Arnau is running a luggage shop. A brand-new item priced at 30% above the cost price did not sell well. So he took 39 dollars off the price, and found that the bags sold very well. If the profit for each bag is now 10% of the cost price, what is the cost...

The roots of the polynomial f(x)=7x2+31x+c=0 are reciprocals of each other. What is the value of c?

As x ranges over all real values, what is the minimum value of the polynomial x4−14x2+303?

How many distinct geometric progressions are there, such that the first term is 1, the last term is 1024 and every term is an integer?

You are planning to lay square tiles on an entire 21125cm by 54925cm rectangular floor without any overlapping. If all the square tiles must be of the same size, what is the least possible number you can lay?

Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?

Adam and Bob went apple picking in an orchard. At the end of the day, they counted the number of apples they picked. They realized that if Adam picked 39 more apples, he would have picked twice as many as Bob picked. Also, if Bob picked 39 more apples, he...

15 - 2n = 13 if you're looking for n then n = 1.

N + 2N = 4N + 5 if you're looking for N, then N = -5

Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?