Logic and patterns
Only one of the following is true, which is it?
A) All of the below
B) All of the above
C) This one
D) None of the above
E) None of the above
D
How many distinct ways can you arrange the four letters A B C and D, using each only once?
24
Mordecai has assembled 106 pieces from his puzzle at 3 pm. In the next two hours he places 23 more. Then his cat messes it up and there are only 87 pieces left on the table. How many pieces does Mordecai need to find?
42
A triangle with an area of 27 sq feet has a base of 9 feet. What is its height in feet?
6 ft
James and Jimmy have 174 Pokemon cards all together. James has 24 more cards than Jimmy. How many cards does Jimmy have?
75
What percent of the permutations of the digits 1, 3 5 and 9 are odd?
100%
Rolling a fair 20 sided die, what is the probability the result is a prime number as a percent?
40%
The Milton family barn had 48 square yards of usable space originally. They recently added an additional room that is 6 yards by 12 yards, all usable. Next week they have to install a new piece of equipment that has a base which takes up 15 square yards. How much usable space will they have after the installment?
105
A cone and cylinder have identical bases, and have identical volumes. If the cone is 9 meters tall, how tall is the cylinder?
3 meters
Sam's age and his brothers age added together is half of the sum of their parents ages. Sam is 4 years older than his brother, and their parents are both 42. How old is Sam's brother?
19 years old
In the pattern of numbers
2, 5, 10, 17, 26
What would come next?
37
Jack has three different types of socks. 2 pairs of white short socks, 3 pairs of gray long socks, and 1 pair of black long socks. If all of his socks are loose in the drawer, how many socks does he need to grab without looking to ensure that he has at least one matching pair?
4
Aaliyah made 3 jello cubes from a mold with side lengths of 4 inches. She wants to serve her 6 friends equal volumes. How many cubic inches does each person get?
32
A ballroom is in the shape of rectangle such that the length is 3 times the width. If the perimeter is 800 feet, what is the area?
30,000 sq ft
Charlie has 3 times as many cousins as Stan. Stan has half as many cousins as Emma. Emma has four more cousins than Kai. If Kai has 2 cousins, how many more cousins does Charlie have than Emma?
3
7^5 ends in what number?
7
What is the probability that 3 fair six sided dice roll to a sum of four as a simplified fraction?
1/72
Jay calculated 19 factorial. Joel calculated 17 factorial. How many times larger is Jay's number than Joel's number?
342
A trapezoid has base lengths of 6 inches and 2 feet, and a height of 36 inches. What is its area in square feet?
3.75 sq ft
Jalen pays $100 in January for a year long grocery superstore membership and spends $275 a month on groceries. Alex spends $320 a month on groceries. At the end of which month has Jalen spent less money on groceries this year than Alex?
March
Find the missing number in the pattern:
1, 0.5, 0.25, X, 0.0625
0.125
There is a bag full of slips of paper with the numbers one through 10, with each number appearing one time. If I pull out two pieces of paper out without replacement, what is the probability that their sum is greater than 18? Represent as a simplified fraction.
1/45
Zoe was playing with her calculator. She types in 3 and multiplies it by itself 6 times. Then she divides by 3 five times. She hits the squared button. Then she divides that by the factorial of three minus one. Then she divides that by 2. What does her screen say?
8.1
I have a pool in the shape of a rectangular prism with a volume of 48,000 liters. It's floor is 8 by 3 meters. 1 cubic centimeter is equal to 1 milliliter. What is the depth of my pool in meters?
2 meters
Mr. Rodriguez bought 30 calculators for his class, and he also purchased a set of white board markers that cost $15.50. Since he's a teacher, he was offered 20% off of his purchase as part of a special promotion. Before tax his total was $132.40. What was the original cost of each calculator?
$5