MathCounts Warmup/Workout 6

If

 $A\ =\ 2^3-3^2+4\left(5+1\right)\ and\ B\ =\ 7^2-2\left(3\ +1\right)^2$  What is the value of  $A-B$  ?

What is the ratio of the area of square ABCD to that of square BDEF in the figure shown?

• 1/3

• 1/2

• 1/4

• 1/5

• 2/3

What is the MEDIAN of the first ten prime numbers?

Let the value of a word equal the sum of the values of its letters. Suppose MATH has value M + A + T + H = 85 and M = 8, A = 3H, T = 73 and H = 1. If S = 3M - 15 and N = 2H + S, what is the value of SAMANTHA?

What is the reminder when the sum of  $10^2-4^2$  is divided by 8?

Hugo has a solid like the one shown, comprised of 32 unit cubes. He paints each face a solid red and then separates the solid into 32 individual unit cubes. What is the probability that a randomly selected unit cube has exactly one painted face?

• 1/20

• 7/10

• 3/16

• 5/14

• 9/21

If x equals twice its reciprocal, what is the value of x⁴?

A robotic vacuum cleaner vacuums one hotel room in 3/10 of an hour. At this rate, how many rooms of the same size will it vacuum in 3 hours?

Nya starts with an integer N and repeatedly subtracts 6. Mya starts with an integer M and repeatedly adds 8.

When Nya and Mya each have performed their respective repeated operation 13 times, both have a resulting value of 25. What is the value of N + M?

 $\left(1\ +\ \frac{1}{2}\right)\left(1\ +\ \frac{1}{3}\right)\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{19}\right)\ ?$  

What is the value of: