`x` and `y`, two nonzero integers, satisfy the equation `frac{3x-2y}{x+y}=5`. What is the value of `frac{3x+2y}{x-y}`?

5 years ago, the combined age of three friends was 10 years. In how many years will their combined age be 100 years?

The dog Vega and her little puppy, Storm, can together eat 1 bone in 8 minutes. Vega eats 4 times faster than Storm.

How long will it take Vega to eat three bones on her own?

Calculate the sum of all three-digit numbers `bar(abc)` such that ``bar(ab)` xx `bar(cc)` xx `bar(abc)` = `bar(abcabc)``.

Find the area marked A.

Let `a, b, c, d` and `e` be different integers, such that `(3-a)(3-b)(3-c)(3-d)(3-e) = 18`.

Calculate `a + b + c + d + e`.

In an isosceles triangle, the altitude of each leg is `24 cm`, and the altitude of the base is `20 cm`. Find the area of the triangle.

George the farmer has two fields for sowing fruits, which have areas in the ratio `3:4`. He plants the smaller field with raspberries and blackberries in the ratio `4:5`.

In what ratio should he plant in the larger field if he wants to plant an equal area of raspberries and strawberries?

Let "Ø" be a binary operation, for which:

1) `x` Ø `(y + z)` = `(x `Ø `y) - z`

2) `(y + z)` Ø `x` = `(y Ø x)` + `z`

3) `1 Ø 1 = 1`

What is the value of 2017 Ø 2016?

A train has speed 5m/s, and a bird has speed 10m/s. It takes 80 seconds for the bird to fly from the back of the train to the front, and back again.

How long, in m, is the train?

Find the 30^{th} term of this sequence: `sqrt(6), 2sqrt(3), 3sqrt(2), 2sqrt(6), sqrt(30)`.

4 boats (at the corner of this rectangle) are headed to rescue a sinking ship at X. The distances are marked.

How far is boat B from the sinking ship?

George rides to school by bicycle. If he rides at 5 km/h, he will be late by 2 minutes. If he travels at 6 km/h, he arrives 4 minutes early.

How far is George's home from his school, in km?

In how many ways can we choose two basketball teams consisting of 5 players each from a group of 10 students?

`ABCD` is a square, side length 5. `M` is on side `BC` such that `CM:MB = 2:3`. `N` is on the diagonal `BD` such that `BN:ND = 2:3`. Find length `MN`.

A mathematics competition has no more than 700 participants. If the organiser divides them into groups of 5 students, 3 students will be left over. If they are divided into groups of 7 students, 5 students will be left over. If they are divided into groups of 11 students, then 9 students will be left over.

How many students are participating in the competition?

How many pairs of positive integers `(x, y)` exist such that:

`x + y <= 100` and `frac{3/x - y}{3/y - x} = 13`

My dad and mom's ages total 80 years. I'm 13, and my younger sisters are 10 and 6 years old.

After a few years, the three children's total ages will be 59% of my parents' total ages. How old will I be then?

Let `A` be the product of the digits of the number `1^2017 + 2^2017 + 3^2017 + 4^2017`.

Let `B` be the product of the digits of the number `2017^1 + 2017^2 + 2017^3 + 2017^4`.

Find `A + B`.

If `x` and `y` are such that `x + y = 4` and `x^2 + y^2 = 6`, determine the value of `x^3 + y^3`.

A cube-pile of `5*5*5` small white cubes is painted blue on the outside, but not on the base. How many of the small cubes are colored blue in some way?

What is the 2018^{th} decimal place of `frac{1}{7}`?

If `x + y = sqrt(7)` and `x - y = sqrt(3)`, what does `x*y` equal?

Triangle `ABC` is equilateral with side length 2. `O` is an arbitrary point inside triangle `ABC`. `x, y` and `z` are the perpendicular distances of O from the sides of the triangle.

Find `x + y + z`.

George has 25% more candies than Dolly. Dolly has 36% less than Filip. What percentage more candies does Filip have than George?

Let `bar{abcd}` be a four-digit number such that `bar{abcd}` + `bar{abc}` + `bar{ab}` + `a` = 2018.

Find the product `a*b*c*d`.

Samira's orchard grows apples, peaches and plums. There are more than 80, but fewer than 100 trees.

One-third of the trees are apple trees, and three-sevenths are peach trees. How many plum trees are at Samira's orchard?

How many different routes are there from A to B, without backtracking or repeating roads / points?

Let `a, b` and `c` (where `c < 0`) be such that `ab = 1, bc = 2, ca = 3`. Calculate `a*b*c`.

In triangle `ABC`, the angle bisectors of angle `A` and angle `B` form an angle of 150 degrees.

Find Angle C, in degrees.

The number of sides of polygon A is 60% larger than the number of sides of polygon B. The sum of interior angles of polygon B is 40% smaller than the sum of internal angles of polygon A.

Determine the total number of sides in these two polygons.

If `a + b + c = 0` and `a^2 + b^2 + c^2 = 2`, what is the value of `ab + bc + ca`?

Determine the value of `sqrt(11 - 6sqrt(2)) ` + `sqrt(7 - 4sqrt(3))` + `sqrt(5 + 2sqrt(6))`.

A positive integer is written on each of the six sides of a given cube. For each vertex, we calculate the product of the numbers which are written on the neighbouring sides for that vertex (the sides adjacent to that vertex). If the sum of the numbers at the vertices is 1001, what is the sum of the numbers written on the cube sides?

Calculate the sum of all four-digit numbers which can be formed with the digits 1, 2, 3 and 4. (repetition is not allowed)

In the country Chessland, there are more than 22 but fewer than 36 teams in the national chess league. Every team plays every other team twice.

15% of all matches finished in a draw. Determine the number of matches that finished in a draw.

The measures of the interior angles in a convex polygon are in arithmetic progression. If the smallest angle is 110 and the largest angle is 170, find the size of the third angle.

How many whole numbers less than 100,000 contain at least one 7?

*For e.g.: 750 contains a 7, but 650 does not.*