maximum

256 Questions
128 Answers

-1

105

0

+818

integers

If $a$ and $b$ are positive integers for which $ab - 3a + 4b = 131$, what is the minimal possible value of $|a - b|$?

maximum 2 oct. 2023

-1

141

0

+818

help with quadratic

Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.

maximum 2 oct. 2023

-2

81

1

+818

counting problem

In the array below, in how many different ways can we start with the letter A and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCH"?
A
RRR
C lire plus ..

maximum 1 oct. 2023

-2

132

0

+818

need help

Here is a problem about a triangle.
A square is inscribed in a right triangle, as shown below. The legs of the triangle are 1 and 3. Find the area of the square. lire plus ..

maximum 1 oct. 2023

-1

83

0

+818

need help

In triangle $ABC$, $\angle A = 30^\circ$ and $\angle B = 90^\circ$. Point $X$ is on side $\overline{AC}$ such that line segment $\overline{BX}$ bisects $\angle ABC$. If $BC = 12$, then find the area of triangle $BXA$.

maximum 1 oct. 2023

-1

138

0

+818

help counting

Syd chooses two different primes, both of which are greater than 20, and multiplies them. The resulting product is less than 800. How many different products could Syd have ended up with?

maximum 1 oct. 2023

-2

118

1

+818

need help

In a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. How many ways are there to color the five squares, so that at least one square is yellow, and at least one square lire plus ..

maximum 30 sept. 2023

-2

126

0

+818

help with counting

In the Olympic women's skating competition, the gold medal goes to first place, silver to second, and bronze to third. If there are 19 skaters, including 2 Americans and 5 Canadians, in how many ways can the medals be awarded to three of the 19 skaters lire plus ..

maximum 30 sept. 2023

-2

117

1

+818

palindromes

A palindrome is a number that is the same when read forwards and backwards, such as 43234. Find the number of 4-digit palindromes that are divisible by 8.

maximum 30 sept. 2023

-2

94

1

+818

inequality

Find the smallest integer that satisfies the inequality: (x - 5)(x + 5)(x - 3) > 0.

maximum 25 sept. 2023

+818

-1

Do not post AoPS homework.

maximum20 janv. 2025