Sprint Round
A collection of an equal number of dimes and quarters is worth $28.00. How many coins are in the collection? (A) 160 (B) 80 (C) 120 (D) 180 (E) Other
A
A rectangular prism with dimensions 10×3×M has the same volume as a rectangular prism with dimensions 9×5×N. What is the value of M N? (A) 3 2 (B) 1 2 (C) 2 3 (D) 2 (E) Other
A
All three vertices of △ABC lie on a circle that has diameter AC and center O. If ∠AOB = 60◦ and the radius of the circle is 7, find BC. (A) 7√3 (B) 21√2/2 (C) 7√6 (D) 14 (E) Other
A
If a⋆b = a·b+a+b, what is 4⋆6? (A) 34 (B) 28 (C) 39 (D) 35 (E) Other
A
The volume of a rectangular prism is 1000 cubic units. What is the least possible surface area of the rectangular prism, in square units? (A) 600 (B) 720 (C) 625 (D) 624 (E) Other
A
What is 2345 + 5432 + 2345 + 5432? (A) 15554 (B14445 (C) 25554 (D) 14444 (E) Other
A
What is 5/12 + 1/4 − 1/5? (A) 7/15 (B) 8/15 (C) 1/2 (D) 13/30 (E) Other
A
What is the base 10 value of 505056 +16 +50506? (A) 7776 (B) 8192 (C) 7777 (D) 10000 (E) Other
A
What is the only prime number between 110 and 120? (A) 113 (B) 117 (C) 119 (D) 115 (E) Other
A
What is the perimeter of a right triangle with one leg of length 16 and an area of 240? (A) 80 (B) 64 (C) 84 (D) 50 (E) Other
A
Daniel is mixing Gatorade for his soccer team. He needs one scoop of powdered drink mix for each cup of water. If there are two cups in a pint and two pints in a quart, and a quart is onequarter of a gallon, how many scoops of powdered drink mix will Daniel need for five gallons of water? (A) 20 (B) 80 (C) 40 (D) 60 (E) Other
B
Find the remainder when 1+2+3+···+47 is divided by 16. (A) 12 (B) 8 (C) 4 (D) 1 (E) Other
B
How many positive divisors does the number 343343 have? (A) 18 (B) 20 (C) 16 (D) 28 (E) Other
B
Nicki sent twenty-four text messages in an hour. At the same rate, how many hours will it take her to send seventy-two text messages? (A) 41 2 (B) 3 (C) 4 (D) 2 (E) Other
B
What is 225% of (11×4000+11×400+11×40+11×4)? (A) 109998 (B) 109989 (C) 109999 (D) 108888 (E) Other
B
What is the value of 111×333? (A) 33963 (B) 36963 (C) 33663 (D) 36663 (E) Other
B
A baseball game lasted 185 minutes and ended at 9:20. At what time did it start? (A) 6:05 (B) 6:20 (C) 6:15 (D) 6:30 (E) Other
C
A box contains 3 blue balls and 7 yellow balls. If two balls are chosen from the box without replacement, what is the probability that they are the same color? Express your answer as a common fraction. (A) 1/2 (B) 3/5 (C) 8/15 (D) 7/15 (E) Other
C
A standard fair six-sided die is rolled 3 times. What is the probability that the sum of the three values that were rolled is 9? (A) 1 9 (B) 7 36 (C) 25 216 (D) 1 8 (E) Other
C
An equilateral triangle has side length of 9. What is its perimeter? (A) 30 (B) 21 (C) 27 (D) 18 (E) Other
C
Beckyisholdingapieceofpaperthat'sintheshapeofanisoscelestrianglewithbaseof32inches and height of 32 inches. She makes a cut parallel to the base that is 20 inches in length, creating a trapezoid and a smaller isosceles triangle. What is the area of the smaller isosceles triangle, in square inches? (A) 216 (B) 400 (C) 200 (D) 240 (E) Other
C
What is the average (mean) of eight, ten, twelve, and six? (A) 7 (B) 11 (C) 9 (D) 10 (E) Other
C
A piece of wire is bent into a regular pentagon shape with side length 15 inches. The wire is restraightened and then bent into an equilateral triangle shape. How many inches is the side length of this triangle? ( (A)50 (B) 30 (C) 15 (D) 25 (E) Other
D
If x√x = 49, what is the value of 1/x³? Express your answer as a common fraction. (A) 343 (B) 1 49 (C) 2401 (D) 1 2401 (E) Other
D
The area of regular hexagon ABCDEF is 72. What is the area of triangle FCE? (A) 18√2 (B) 12√3 (C) 18 (D) 24 (E) Other
D
The ratio of the angles of a triangle is 2:3:5. What is the degree measure of the smallest angle? (A) 18◦ (B) 30◦ (C) 72◦ (D) 36◦ (E) Other
D
In how many distinct ways can the letters in the word TIMMY be arranged? (A) 40 (B) 120 (C) 20 (D) 30 (E) Other
E
Jae turns a crank that's connected to gear A, which then turns gear B. For every five complete revolutions of the crank and gear A, gear B makes six revolutions. If gear A has 60 teeth, how many teeth does gear B have? (A) 60 (B) 48 (C) 54 (D) 72 (E) Other
E
What is the largest prime factor of (20200+2020)2 +(20200−2020)2? (A) 2 (B) 5 (C) 103 (D) 11 (E) Other
E
What is the sum of all odd, single-digit prime numbers? (A) 16 (B) 8 (C) 12 (D) 10 (E) Other
E
