Algebra
Find the sum of the numbers: 2 + 5 + 8 + ... + 98 + 101
1751, Note that the numbers increase by 3, so 2 + 3k = 101, so
k = 33. Therefore, there are 34 numbers.
We divide into pairs (2 + 101) + (5 + 98) + ⋯ = 17 ∙ 103 = 1751
Bruno wants to hide the Math Team budget in a secure safe with a 4-digit password. In secret, Daniel learns from Bruno that the password is the largest 4-digit number that is divisible by 7 and can be written in 4 different digits. What is the password?
9870, (since 987 is biggest 3 digit number divisible by 7 that doesn't have same digits in it)
In 2050, The elevator in the 20-story school called Hcet Nylkoorb is broken: it can either go up 8 floors or go down 13 floors. Is it possible to get from the 20th floor to the first floor using the elevator? (please say in how many attemps you can get there OR why you can't there)
No - There is only one way to go: 20-7-15-2-10-18-5-13, but you can’t leave from the 13th floor
Isfar bought 5 energy drinks for the next academic week. 3 of them are strawberry flavored, 1 is orange flavored, 1 is "classic" flavored. In how many ways can Isfar drink all these energy drinks?
5! : 3! = 20
What is the ending digit of the difference
1 · 2 · 3 · 4 · … · 2021 − 1 · 3 · 5 · … · 2019 · 2021?
5 - first number will have end digit of 0 because 2 * 5 = 10 and second number will have end digit of 5 because it's divisible by 5 and odd. 10 - 5 = 5
The clock shows 9:15. What is the angle between the minute and hour hands?
172.5 degrees (180 - 7.5 = 172.5) (7.5 is dispalcement of of hour hand from 9)
In order to get pocket money from his parents, Nikita needs to find the number of positive integer pair solutions to the equation:
(1+2a)(2+2b)(2a+b)=32ab
The fraction 32/49 is written on the board. In one action, Martin can either add 1 to the denominator, or subtract 1 from the numerator, or reduce the fraction, or multiply the numerator and denominator by the same number. After what minimum number of actions can he obtain the fraction 2/3?
never - 32/49 < 2/3, all those actons are decreasing/keeping the same original fraction.
In parallelogram ABCD the bisectors of angles A and D intersect at the midpoint of side BC.
Find AD if AB = 5.
10 - ∠BEA = ∠EAD, since BC ∥ AD, then ABE is isosceles, so AB = BE. Therefore,
AD = BC = 2AB = 10
Adir says that if the next week he will have 2 or more big tests in one day when he is cooked. What is the chance that he is cooked if there are 3 tests next week?
(5^3 - 5 * 4 * 3)/ 125 = 65/125
Mr. G-K forgot the code from his locker with calculators. The code for the locker is a two-digit number. Mr. G-K forgot the code, but he remembers that the sum of the digits of this number, added to their product, is equal to the number itself. Write all possible versions of the code so that Mr. G-K can open the locker faster.
19, 29, 39, 49, 59, 69, 79, 89, 99
(x + y) + x · y = 10x + y
x · y = 9x
y = 9 and x is any other digit except 0