Mystery
What is the absolute value of the product of all the integers from - 6 to 3, inclusive?
0
A common brick, in the shape of a rectangular solid, measures 5 by 9 by 23 centimeters. How many square centimeters are in its total surface area?
734
A = { positive multiples of 5 that are less than 200 }
B = { positive multiples of 7 that are less than 200 }
How many numbers are in both sets A and B (the intersection of sets A and B) ?
5
Heidi wrote the number 1 on one slip of paper. She wrote the number 2 on two slips of paper, the number 3 on three slips of paper, the number 4 on four slips of paper, the number 5 on five slips of paper, and the number 6 on six slips of paper. All of the slips of paper were placed into a box. Sally withdrew one slip of paper from the box. The probability, written as a fraction in lowest terms in lowest terms, that the number Sally withdrew is an odd number is X / Y. What is the sum of X + Y ?
10
There are two possible values of X that make this equation true:
( X - 8 ) ( X + 5 ) = 0
What is the sum of those two values?
3
On April 13, 1987, Rick was 8 times as old as Pat while Kelly was 3 times as old as Pat. Rick is 20 years older than Kelly. How old was Pat on April 13 in the year 2023?
40
The edge of one cube is 3 centimeters longer than the edge of another cube. The difference between their volumes is 1,413 cubic centimeters. How many centimeters are in the length of the larger cube?
14
Of the 287 8th graders at the Northborough Melican Middle School:
209 are less than six feet tall,
156 have dark hair,
123 are less than six feet tall and have dark hair.
How many students are at least six feet tall and do not have dark hair?
45
The probability that Evan will successfully make a basket during a basketball game is 2 / 5. If the probability that he misses a basket on three consecutive shots is A / B, written as a fraction in lowest terms, then what is the product of AB ?
3,375
In a right triangle, the length of one leg is 2 centimeters shorter than twice the length of the other leg. If the area of the triangle is 132 square centimeters, then how many centimeters are in the length of the longer leg?
22
Two cars are travelling in the same direction. The car that is in the lead is going 48 miles per hour while the second car is going 60 miles per hour. How many miles apart are the two cars 45 minutes before the faster car catches up to the slow car?
9
A water tank in the shape of a cylinder has an inside diameter of 24 feet and a height of 87 feet. A cubic foot of water is 7.5 gallons. A rock, in the shape of a sphere with a diameter of 8 feet, is dropped into a full tank of water and sinks to the bottom of the tank. To the nearest whole number of gallons, how many gallons of water remain in the tank ? Use pi=3.14
293,025
M = { 2, 3, 5, 7, 11, 13 }
A = { 9, 18, 27, 36, 45, 54, 63 }
T = { 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 }
H = { 3, 5, 7, 9 }
If P = (M n H) U (A n T) then what is the product of all the numbers in set P ? (Translation: P is the union of the intersection of sets M and H and the intersection of sets A and T.)
3,674,160
A vendor is selling balloons at the parade. She has 7 red, 4 green, and 5 blue balloons remaining. Cagney and Lacey each select a balloon without one seeing what the other has chosen. The probability, written as a fraction in lowest terms, that Cagney and Lacey each select a balloon of the same color is K / M. What is the sum of K + M ?
157
DOUBLE JEOPARDY!
-15