ZzZPMO2025_PART1

Simplify: 1 - 1/3 + 1/5 - 1/7 + 1/11.

• 940/1155

• 941/1155

• 942/1155

• 943/1155

If 30% of p is q, and 20% of q is 12, what is 50% of p + q?

• 1/2(q + 12)

• 130

• 3/10p + 1/2q

• 100

Which of the following is equal to ∛54 + ∜4?

• ∛128

• ∛56

• ∛54·4

• ∜112

Let ABCD be a square with each side of length 1 unit. If M is the intersection of its diagonals and P is the midpoint of MB, what is the square of the length of AP?

• 3/4

• 5/8

• 1/2

• 3/8

How many ordered pairs (x, y) of positive integers satisfy 2x + 5y = 100?

• 8

• 9

• 10

• 11

Find the area of the circle that circumscribes a right triangle whose legs are of lengths 6 cm and 10 cm.

• 34π cm²

• 68π cm²

• 102π cm²

• 136π cm²

How many real roots does the equation log(x² - 3x)₃ 4 = 2/3 have?

• 0

• 2

• 3

• 4

• 6

• 7

• 8

• 9

Let 0 < x < 1. Which of the following has the largest value?

Find the sum of all the 4-digit positive numbers with no zero digit.

• 36644635

• 36644645

• 36445335

• 36446355