The area of this shape is:

( 3 + 5 ) x 2 : 2 = 8 ( m² )

Answer: ... 

Last number is 998

First number is 100

Number wth three digits that share for 2 is:

( 998 - 100 ) : 2 + 1 = 450 ( numbers )

Answer: ... 

To be able to buy 9 bottles of fruit juice at the cheapest price, they should appoint 4 people to buy 8 bottles for: (7 + 1) x 4 = 32 (dollars)
The total amount they will pay to buy 9 bottles is: 32 + 7 = 39 (dollars)

If there are two people at a party, they can shake hands once. There
is no one else left to shake hands with, so there is only one
handshake total.

 2 people, 1 handshake

If there are three people at a party, the first person can shake hands 
with the two other people (two handshakes).  Person two has already 
shaken hands with person one, but he can still shake hands with person 
three (one handshake).  Person three has shaken hands with both of 
them, so the handshakes are finished.  2 + 1 = 3.

 3 people, 3 handshakes
If there are four people at a party, person one can shake hands with 
three people, person two can shake hands with two new people, and 
person three can shake hands with one person.  3 + 2 + 1 = 6.

 4 people, 6 handshakes

Are you seeing a pattern?

If you have five people, person five shakes four other hands, person 
four shakes three other hands, person three shakes two other hands, 
and person two shakes one hand.  Another way to see it is,

 Person 5  Person 4  Person 3  Person 2

    4    +    3    +    2    +    1    =   10 handshakes total  


====================================================
People at Party               Number of Handshakes

     2                                           1
     3                      1 + 2              = 3
     4                      1 + 2 + 3          = 6
     5                      1 + 2 + 3 + 4      = 10
     6                      1 + 2 + 3 + 4 + 5  = 15
     .
     .
     .                                             n(n-1)
     n                      1 + 2 + ...+ (n-1) =  --------
                                                      2
8(8-1)/2= 28
Each man shakes hands with everyone except his own wife: 28-4=24
No women shake hands with each other: 24 -((4x3):2)= 18

Calling the two-digit number written by Anna was: ab then the number Ben wrote was abab
The structural analysis of the number we are:
Abab = 100 x ab + ab = 101 x ab
The result of the division is: abab: ab = 101 x ab: ab = 101

4 horses are there: 4 x 4 = 16 (legs)
11 people are there: 11 x 2 = 22 (legs)
4 horses and 11 people are there: 16 x 22 = 38 (legs)

                                                              Answer: 38 legs

Because Zack's number is odd, the last digit of this number may be 1 or 9
Because Mr. Zack chose 4 numbers, we type the number 1 (the number of thousands is the same as the unit)
Inferred: Number to find the last digit is 9
When 9 turns 1800 (up - side - down), we get number 6
Inferred: The thousands digit is the number 6
We have: 10 - 8 = 2
Because the hundreds of new digits minus the tens digit of the old number are 2. Inference: The hundreds digit of the new number is 0 and the tens digit of the old number is 8.
We have: 8 - 0 - 1 (remember) = 7
So: The number Zack made at the beginning is: 6089

The number of 4-digit numbers is: (9999 - 1000): 1 + 1 = 9000 (number)
If you do not use numbers 2 and 3, then you have eight digits left to form units, tens and hundreds. Since zeros can not be used to make thousands of digits, there are only seven digits left to make thousands. According to the kernel rule, we have: 8 x 8 x 8 x 7 = 3584 (number)
Inference: A 4-digit number containing two digits, or three or both, is 9000 - 3584 = 5416 (number).

Total height of 2 boys are: 131.6 x 2 = 263.2(cm)
Total height of 4 girls are: 128.3 x 4 = 513.2(cm)
Total height of all children are: 263.2 + 513.2 = 776.4(cm)
The average height of all children are: 776.4 : 6 = 129.4(cm)

                                                                       Answer: 129.4cm

48 cards = 1/3  of the remainder
The remainder = 72 cards = 60% of his cards
His cards = 72 x 100 : 60 = 120 (cards)

                                       Answer: 120 cards

The girls of the pupils were absent: 30 x 40 : 100 = 12(girls)

                                                                         Answer: 12 girls

Transform the inequality we get:
1 <x - 3 and 1 <3 - x. Inferred: x> 4 and x <2 (1)
X - 3 <100 and 3 - x <100. Findings: x <103 and x> 2 (1)
From (1) and (2) we deduce: -97 <x <2 and 4 <x <103
Consider: -97 <x <2, we have: The number of integers satisfying is: [1 - (-96)]: 1 + 1 = 98 (number)
Consider: 4 <x <103, we have: The integer number satisfying is: (102 - 5]: 1 + 1 = 98 (number)
So: The integer number satisfying 1 <│x - 3│ <100 is: 98 + 98 = 196 (number)

We have:
1\(^2\) = 1. Inferred: 12 has the last digit of 1
2​\(^2\) = 4. Inferred: 22 has the last digit of 4
3​\(^2\)  = 9. Inferred: 32 has the last digit of 9
4​\(^2\) = 16. Inferred: 42 has the last digit of 6
5\(^2\) = 25. Given: 52 has the last digit of 5
6\(^2\) = 36. Inferred: 62 has the last digit of 6
7\(^2\) = 49. Inferred: 72 has the last digit of 9
8\(^2\) = 64. Inference: 82 has the last digit of 4
9\(^2\) = 81. Inferred: 92 has the last digit of 1
10\(^2\) = 100. Describe: 102 has the last digit of 0
11\(^2\) = 121. Inference: 112 has the last digit of 1
Calculate:1\(^2\) + 2\(^2\) + 3\(^2\) + 4\(^2\) + 5\(^2\) + 6\(^2\) + 7\(^2\) + 8\(^2\) + 9\(^2\) + 10\(^2\) with the last digits: 1 + 4 + 9 + 6 + 5 + 6 + 9 + 4 + 1 + 0 = 45
We have: 1\(^2\) + 2\(^2\) + ... + 2009\(^2\) + 2010\(^2\) with digits ending in: 5
We have: 2011\(^2\) + 2012\(^2\) + ... + 2016\(^2\) + 2017\(^2\) with the digits ending in: 1 + 4 + 9 + 6 + 5 + 6 + 9 = 40
Inferred: 1\(^2\) + 2\(^2\) + 3\(^2\) + ... 2016\(^2\) + 2017\(^2\) with digits ending in: 5

Call a, a + 1, a + 2, ..., a + 9 are 10 consecutive natural numbers Alex wrote
* Suppose we remove the number a: (a + 1) + (a + 2) + ... + (a + 9) ≥ 490
Deduced:
9a + (1 + 2 + ... + 9) ≥ 490
9a + 45 ≥ 490
9a ≥ 490 - 45
9a ≥ 445
A ≥ 445: 9
A ≥ 49
* Suppose we remove the number a + 9, the sum: a + (a + 1) + (a + 2) + ... + (a + 8) ≤ 490
Deduced:
9a + (1 + 2 + ... + 8) ≤ 490
9a + 36 ≤ 490
9a ≤ 490 - 36
9a ≤ 454
A ≤ 445: 9
A ≤ 50
Describe: a = 49 or 50
* If: a = 49, we have: 49 + 50 + 51 + ... + 58 = (58 + 49) x 10: 2 = 535
Inferred: Deleted number: 535 - 490 = 45 (type is not in the above sequence)
* If: a = 50, we have: 50 + 51 + ... + 59 = (59 + 50) x 10: 2 = 545
Inferred: Deleted number: 545 - 490 = 55 (Received)
So: The number Alex deleted was 55

We have the law of the expression that in a fraction the numerator is greater than the denominator of 1 unit. Think of: b = a - 1
Simple expression is: a / 2 = 2015. Inferred: a = 4030
Deduced: b = 4029
Deduced: a + b = 4030 + 4029 = 8059

Number of prize winners: 2562 - 1602 = 960 (you)
Call a number of Gold Medal students
Because: The number of Silver medal students is twice the number of Gold medal students, the number of Bronze medal students twice the number of Silver medal students, Won the bronze medal. Inference: The number of Gold Medal students is:
A + 2a + 4a + 8a = 960
15a = 960
A = 960: 15
A = 64
Because: There are 12.5% of the students winning the gold medal has an absolute score of 300 points. Find out: The number of Gold medalists scoring an absolute 300 points is: 64 x 12.5: 100 = 8 (you)

Number of prize winners: 2562 - 1602 = 960 (you)
Call a number of Gold Medal students
Because: The number of Silver medal students is twice the number of Gold medal students, the number of Bronze medal students twice the number of Silver medal students, Won the bronze medal. Inference: The number of Gold Medal students is:
A + 2a + 4a + 8a = 960
15a = 960
A = 960: 15
A = 64
Because: There are 12.5% of the students winning the gold medal has an absolute score of 300 points. Find out: The number of Gold medalists scoring an absolute 300 points is: 64 x 12.5: 100 = 8 (you)

Since the topic does not say how many students each class has, we can assume that the number you bought a candy is the maximum you can have.
Since 5 blocks have 40 students, the largest number of students in a class is: 40 - 4 = 36 (you). Inferred: 36 of this friend bought 36 candy
Because of the different classes of candy purchased different candy so that we have the number of candies of the remaining 4 blocks are: 2, 3, 4, 5. Inception: The total candy of the remaining 4 blocks are: 2 + 3 + 4 + 5 = 14 (tablet)
We have: 36 + 14 = 50
So: The number of students buying 1 candy is: 36 friends

The price of 71 pencils is: 71 x 2 = 142 (dollars)
We have: 71: 3 = 23 (residual 2)
The amount discounted when buying 71 pencils is: 1 x 23 = 23 (dollars)
The amount of money Trump paid when buying 71 pencils was: 142 - 23 = 119 (dollars).
The price of 67 ball pens is: 67 x 3 = 201 (dollars)
We have: 67: 5 = 13 (residual 2)
The amount discounted when buying 67 ball pens is: 2 x 13 = 26 (dollars).
The amount of money Trump paid when buying 67 ball pens is: 201 - 26 = 175 (dollars).
The total amount of money Trump paid for 71 pencils and 67 ball pens was 119 + 201 = 294 (dollars).