nmw2023

In set theory, this function is used for studying the continuum function and the cardinal exponentiation function.

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

• 1 2 (q + 12)

• 130

• 3/10 p + 1/5 q

• 100

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.

• 34pi

• 68pi

• 102pi

• 136pi

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

• 0

• 2

• 3

• 4

Find the largest integer value of n such that 1×3×5×7×· · ·×31×33×35 is divisible by 3^n .

• 6

• 7

• 8

• 9

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

• x^3

• x^2 + x

• x^2 + x^3

• x^4

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

• 36644635

• 36644645

• 36445335

• 36446355

Find the number of real roots of the equation x^5 − x^4 + x^3 − 4x^2 − 12x = 0

• 0

• 1

• 3

• 5