Algebra
When expressed as a common fraction, what is the value of (2+4+6+8+···+1340+1342)/(3+6+9+12+···+2010+2013)?
2/3
Massaru has 3 pencils in his bookbag. Two pencils are blue and one is red. If he randomly selects two pencils, what is the probability that they are the same color? Express your answer as a common fraction.
1/3
What fraction is equivalent to 0.712712712...? Express your answer as a common fraction?
47/66
The line y = 3/4x + 2 is reflected over the y-axis, and the resulting line is then reflected over the x-axis. What is the slope of this third line? Express your answer as a common fraction.
3/4
What is the sum of the solutions to the equation G = (12)/(7 - G), where G is the absolute value of x, |x|?
0
A cookie recipe requires 4 cups of flour to make 5 dozen cookies. If Amy needs to make 15 dozen cookies, how many cups of flour will she need?
12 cups
Two distinct numbers are selected simultaneously and at random from the set {1, 2, 3, 4, 5}. What is the probability that their product is an even number? Express your answer as a common fraction.
7/10
What is the value of the least positive base ten number which requires six digits for its binary representation?
32
A rectangular box has a volume of 480 cubic inches. The height of the box is 5 inches. The ratio of the length of the box to the width of the box is 3 to 2. What is the measure of the width of the box?
8 inches
Let N be the greatest integer multiple of 36 all of whose digits are even and no two of whose digits are the same. Find the remainder when N is divided by 1000.
640
A large box of popcorn sells for $1.20. You want to sell a smaller box, such that each dimension will be 1/2 the corresponding dimension of the larger box. What is the proportional price, in dollars, to charge for the smaller box if price is determined solely by volume?
$0.15
Two distinct numbers are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8, and 9 and their product is computed. Express as a common fraction the probability that the product is a prime number.
1/9
What is the greatest possible value of a^(b^c) , where a, b and c are distinct positive integers less than 4?
9
The interior height of a can of Zip’s Deluxe Paint is 4 3/4 inches, and the inside diameter of the can is 4 1/6 inches. How many cubic inches are in the volume of the can? Express your answer to the nearest whole number.
65 cubic inches
A positive integer is called ascending if, in its decimal representation, there are at least two digits and each digit is less than any digit to its right. How many ascending positive integers are there?
502
How many terms are in the expansion of the expression [(3x + 2y)2 (3x − 2y)2]3 after it is simplified to lowest terms?
7 terms
How many whole numbers from 100 to 600 inclusive contain the digit 5 exactly once?
153
What is the greatest integer less than 100 that cannot be written as a sum of two primes?
97
What is the area of the triangle formed by the lines y=5, y=1+x, and y=1-x?
16 squared units
Eb D Db C B Bb?
A
Each number in the set {5, 9, 10, 13, 14, 18, 20, 21, 25, 29} was formed by adding two of the numbers in the set a, b, c, d, e where a < b < c < d < e. What is the value of c?
7
Reals p, q, r are chosen randomly from the interval from 0 to 6. What is the probability that no two of p, q, r have absolute difference less than 1?
8/27
The total area of four squares, each with whole-number side measurements, is 23 square inches. In inches, what is the positive difference between the perimeter of the largest square and the perimeter of the smallest square?
8
The medians of a particular right triangle drawn from the vertices of the acute angles are 5 units and sqrt(40) units. What is the length of the median drawn from the right angle? Express your answer as a decimal to the nearest tenth.
3.6 units
A point whose coordinates are both integers is called a lattice point. How many lattice points lie on the graph of x2 - y2 = 20002?
98 points