ACT Number & Quantity 4

A storage facility is currently offering a special rate to customers who sign contracts for 6 months or more. According to this special rate, the first month's rent is $1, and for each month after the first month, customers pay the regular monthly rental rate. The table below shows the storage unit sizes available, the floor dimensions, and the regular monthly rental rate. All the units have the same height.

Refer to the image.

Daria will sign a contract to rent a Size 3 unit for 12 months at the current special rate. The amount Daria will pay for 12 months at the current special rate represents what percent decrease from the regular rental rate for 12 months?

• 8.25%

• 8.33%

• 8.42%

• 9.00%

• 9.09%

A storage facility is currently offering a special rate to customers who sign contracts for 6 months or more. According to this special rate, the first month's rent is $1, and for each month after the first month, customers pay the regular monthly rental rate. The table below shows the storage unit sizes available, the floor dimensions, and the regular monthly rental rate. All the units have the same height.

Refer to the image.

Size 5 units can be subdivided to form other sizes of units. What is the greatest number of Size 1 units that can be formed from a single Size 5 unit?

• 2

• 4

• 8

• 10

• 16

For the complex number i and an integer x, which of the following is a possible value of i^x ?

• 0

• 1

• 2

• 3

• 4

Let m and n be 2 positive integers, such that m < n. Which of the following compound inequalities must be true?

The component forms of vectors u and v are given by u = ⟨5,3⟩ and v = ⟨2,−7⟩. Given that 2u + (−3v) + w = 0, what is the component form of w ?

• ⟨-16, 15⟩

• ⟨-4, -27⟩

• ⟨3, 10⟩

• ⟨4, 27⟩

• ⟨16, -15⟩

Hai has $100 available to buy USB drives to back up data for his business computers. Each USB drive has a price of $8, and Hai will pay a sales tax of 7% of the total price of the USB drives. What is the maximum number of USB drives Hai can buy?

• 11

• 12

• 13

• 14

• 15

For how many integers x is the equation 3^{x + 1} = 9^x−2 true?

• 0

• 1

• 2

• 3

• An infinite number

If 115% of a number is 460, what is 75% of the number?

• 280

• 300

• 320

• 345

• 400

A certain computer performs 1.5 × 10⁸ calculations per second. How many seconds would it take this computer to perform 6.0 × 10¹⁶ calculations?

• 2.5 × 10⁻⁹

• 2.5 × 10⁻⁹

• 4.0 × 10²

• 4.0 × 10⁸

• 9.0 × 10²⁴