Algebra
What is the value of 5 x 13 - 12 / 3 x 7 + 52 ?
62
(5 x 13) - (12 / 3 x 7) + 25
65 - (4 x 7) + 25
65 - 28 + 25
65 - 3
62
What is the interior angle measure of a regular nonagon (nine-sided polygon), in degrees?
140 degrees
How many two-digit integers are multiples of 7?
13
7x14 = 98, so there are 14 multiples of 7 below 100, but 7 is not a two-digit number.
Mr. Blubber selects a random whole number that is not greater than 20. What is the probability that it is prime? Express your answer as a percentage.
40%
Primes below 20 are 2,3,5,7,11,13,17, and 19. There are 8 of them and 20 possible choices (0 is a whole number), so the probability is 8 / 20 = 4 / 10 = 40 / 100 = 40%.
True or False? The sides of a scalene triangle are all equal in length.
Find the value of:
2024! / (2022! + 2023!)
2023
2024! / (2022! + 2023!) =
2024! / (2022! + 2023 * 2022!) =
2024! / (2024 * 2022!) =
2023
The diagonals of a rhombus are of lengths 30 and 40. What is the perimeter of the rhombus?
100
What is the smallest odd whole number with three distinct prime factors?
105
3 x 5 x 7 = 15 x 7 = 105There are five different light switches in a room. The room is sufficiently bright when at least three of the light switches are on. How many ways can the switches be turned on such that the room is sufficiently bright?
16
5c3 = 10
5c4 = 5
5c5 = 1
10+5+1 = 16
True or False? (0.46)^2 < 0.46
TRUE
DAILY DOUBLE
You must wager at least $5 and at most your current total.
Each term of the sequence 3, 16, 29, 42, . . . is 13 more than the term that precedes it. What is the integer value of the first term of the sequence that is greater than 300?
A rectangle of height 10 and width 24 is inscribed in a circle. What is the circumference of that circle? Express your answer in terms of pi.
26 pi
Mr. Blubber is thinking of a whole number. If he divides it by 5, there is a remainder of 3. If he divides it by 7, there is a remainder of 4. What is the number Mr. Blubber is thinking of, given that his number lies between 70 and 100?
88
5 x 13 = 85, so 88 mod 5 = 3
7 x 12 = 84, so 88 mod 7 = 4
A drawer has 10 black pens, 10 red pens, 10 blue pens, and 10 green pens. What is the minimum number of pens Mr. Blubber has to draw from the drawer to guarantee that he has three pens of the same color?
9 pens
With 8 pens, he could have 2 of each color. The 9th pen guarantees that he will have 3 of the same color.
True or False? The answer to this question is "TRUE”
Both answers are correct
What is the value of x+y+z when 3x+y−10z = 21 and 5x+7y+18z = 11?
4
The lengths of two sides of an isosceles triangle are 61 feet and 22 feet. What is the area of the triangle?
660 sq ft
What is the sum of all the 3-digit multiples of 4 which use the digits 2, 3, and 4 each exactly once?
756
324 + 432 = 756
DAILY DOUBLE
You must wager at least $5 and at most your current total.
At a strange restaurant, there are 2 choices for appetizer (salad or soup), 2 choices for the main course (steak or chicken skewers), and a whopping 30 choices for dessert. In how many ways can Mr. Blubber select a meal consisting of an appetizer, a main course, and a dessert if he does not get both salad and steak?
True or False? 221 is a prime number.
FALSE
13 x 17 = 221
If the average of 26/n, 6/5, and 10/7 is 1, what is n?
70
A circle with radius 4 is centered at the origin (0, 0). The line x = 2 divides the circle into two parts. What is the area of the smaller part? Express your answer in terms of pi.
16/3 pi - 4 sqrt(3)
The number 2023 is raised to the 2023rd power, and then the result is multiplied by 34. What is the units digit of the resulting number?
8
The units digit of the powers of 3 are 3, 9, 7, 1, for every 4 powers of 3. Since 2023 % 4 = 3, the units digit of 20232023 = 7. Multiplying 7 x 4 = 28, so the answer is 8.
Four girls and four boys randomly sit down at a circular table with exactly 8 seats. What is the probability that two girls are sitting next to each other? Express your answer as a common fraction.
34/35
The only configuration where two girls are NOT sitting next to each other is alternating boys and girls. The probability of this occurring is:
4/7 * 3/6 * 3/5 * 2/4 * 2/3 * 1/2 =
4 * 3 * 6 * 2 / 7! =
1 / (5 * 7) =
1/35.
So the answer is 1 - 1/35 = 34/35.
True or False? 34 x 57 = 1928.
FALSE
34 x 57 = 1938