Sprint #2

What is the value of (3⁻⁴·18¹²·8⁻²)/(27⁶·4³) ? (A) 12 (B) 6 (C) 9 (D) 18 (E) Other

C

What is the value of 99 × 101 × 99? (A) 998801 (B) 988901 (C) 989801 (D) 989901 (E) Other

D

Geoff writes down the number 1. He then creates a list of numbers using the following process: He flips a fair coin. If the coin shows heads, he adds 1 to the preceding number in the list, and writes down the result as the next number in the list. If the coin shows tails, he subtracts 1 from the preceding number in the list, and writes down the result as the next number in the list. Using thisprocess, Geoff generates a list that has 12 numbers, including the first number of 1. For example,one such list might be 1, 2, 1, 2, 3, 4, 3, 2, 3, 4, 5, 6. How many distinct 12-number lists can Geoff create that have 8 as their last term? (A) 55 (B) 36 (C) 78 (D) 45 (E) Other

A

Sydney flips a fair coin five times. What is the probability that Sydney gets at least two more tails than heads? (A) 3/16 (B) 3/8(C) 5/16 (D) 1/4 (E) Other

A

The roots of x² + 5x + q = 0 differ by 2. If q can be written as a fraction in lowest terms as a/b, what is the value of a + b? (A) 25 (B) 20 (C) 15 (D) 21 (E) Other

A

Triangle ABC is equilateral, with a side length of 24. Point D is located on AB such that (AD)/(DB) =1/3 . What is the shortest distance from D to AC? (A) 3√3 (B) 4 (C) 6 (D) 4√3 (E) Other

A

Two right triangles have the same area. The first right triangle has legs of lengths 8 and 24. The second right triangle has legs with lengths that sum to 28. What is the perimeter of the second triangle? (A) 48 (B) 56 (C) 42 (D) 54 (E) Other

A

A showing of the latest Marvel movie ended at 9:33 PM. If the movie was 128 minutes long, what time did the movie start? (A) 7:40 PM (B) 7:25 PM (C) 7:20 PM (D) 7:35 PM (E) Other

B

If 9³ⁿ=27¹⁻ⁿ, what is the value of 1/ₙ? (A) 1/3 (B) 3 (C) 1/9(D) 27 (E) Other

B

In an arithmetic sequence of numbers, the difference between consecutive terms is constant. For example, 1, 4, 7, 10 is an arithmetic sequence, since consecutive terms differ by 3. In another arithmetic sequence, the 14th term is 73 and the 22nd term is 113. What is the first term of this sequence? (A) 6 (B) 8 (C) 5 (D) 9 (E) Other

B

Luke added up all of the even whole numbers less than nineteen. What was Luke's result? (A) 94 (B) 90 (C) 86 (D) 92 (E) Other

B

Matt cut a piece of wire into three segments of equal length. Matt then bent each segment into a circle with a radius of 9/π. What was the length of Matt's original piece of wire? (A) 27 (B) 54 (C) 27π (D) 18π (E) Other

B

The product of two whole numbers is 36. If the larger number is 9 more than the smaller number, what is the sum of the two numbers? (A) 17 (B) 15 (C) 18 (D) 14 (E) Other

B

A pack of 12 trading cards can be purchased for $0.75. Kirk has been saving his allowance and has $6.00 that he plans to use to buy packs of trading cards. How many cards can Kirk buy with the money he has saved? (A) 108 (B) 84 (C) 96 (D) 60 (E) Other

C

How many 8's are in five 12's and six 6's? (A) 10 (B) 8 (C) 12 (D) 14 (E) Other

C

How many days is fifty-two weeks and one day? (A) 364 (B) 368 (C) 365 (D) 367 (E) Other

C

Three rectangles all have an area of 36. The first rectangle has a width of 12, the second rectangle has a width of 8, and the third has a width of 9. What is the shortest perimeter of any of the three rectangles? (A) 26 (B) 22 (C) 25 (D) 24 (E) Other

C

What is the value of (2 −1/5) (2 −4/5)? (A) 21/5 (B) 2 3/25 (C) 2 4/25 (D) 2 1/10 (E) Other

C

At the corner store, Macy bought two packs of gum at a cost of $0.85 per pack, and paid the cashier $2. How much change did Macy receive from the cashier? (A) $0.40 (B) $0.10 (C) $0.20 (D) $0.30 (E) Other

D

If Y is a digit and the three-digit number 1Y1 is a multiple of 9, what is the value of Y? (A) 4 (B) 5 (C) 8 (D) 7 (E) Other

D

If x♣y = x2 − 2x − y 2 + 1, then what is the value of (5♣3)♣6? (A) 4 (B) −1 (C) 1 (D) 0 (E) Other

D

Kendrick ran the 100-meter dash three times, recording times of 10.4 seconds, 10.9 seconds, and 10.5 seconds. What was Kendrick's average time, in seconds, in the 100-meter dash? (A) 10.7 (B) 10.5 (C) 10.55 (D) 10.6 (E) Other

D

The perimeter of a triangle is the sum of the lengths of the three sides of the triangle. A triangle has perimeter 32. One side of the triangle has length 14 and the other two sides of the triangle are equal in length. What is the length of one of the other two sides? (A) 13 (B) 11 (C) 7 (D) 9 (E) Other

D

28. In a geometric sequence, each term is equal to the preceding term multiplied by a constant. For example, 2, 10, 50, 250 is a geometric sequence since each term is 5 times the previous term. In a particular geometric sequence, the sum of the fourth and fifth terms is 960, and the sum of the second and third terms is 60. What is the sum of all possible values of the first term of this sequence? (A) 3 (B) 13 (C) 11 (D) 5 (E) Other

E

At Commercialstick Baseball Stadium, the Deluxe Hamburger costs $9, while the Deluxe Hotdog costs $6.50. Amanda purchased some Deluxe Hotdogs and Deluxe Hamburgers for her friends. If Amanda spent $75, how many Deluxe Hotdogs and Deluxe Hamburgers did she purchase alto- gether? (A) 12 (B) 8 (C) 6 (D) 9 (E) Other

E

Hexadecimal is base 16, with the extra digits A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15. What is the base 10 value of the three-digit hexadecimal number CCC? (A) 3260 (B) 3244 (C) 3228 (D) 3292 (E) Other

E

In trapezoid ABCD, base AB = 12, base CD = 28, diagonal BD = 13, and diagonal AC = 37. What is the area of trapezoid ABCD? (A) 216 (B) 224 (C) 248 (D) 252 (E) Other

E

Julie is currently 8 1/3% older than Kayla. In eight years, Julie will be 6 1/4% older than Kayla. How old is Julie currently in years? (A) 21 (B) 24 (C) 28 (D) 30 (E) Other

E

What is the sum of the single-digit whole numbers that do not evenly divide 24? (A) 14 (B) 16 (C) 25 (D) 12 (E) Other

E

Working together, Philip and Brian swept the porch in six minutes. When Philip swept the porch by himself, he took eighteen minutes. Assuming each person sweeps at a constant rate, how long, in minutes, does it take Brian to sweep the porch by himself? (A) 10 (B) 6 (C) 12 (D) 8 (E) Other

E