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Who Made the Error?
A teacher gave her class an assignment to create a math puzzle that would challenge the class.
One student was asked to present their problem. The student wrote a large multi-digit number
on the board and asked the other students to tell about the divisors of the number one by one.
The 1student said, "The number is divisible by 2."
The 2nd student said, "The number is divisible by 3."
The 3rd student said, "The number is divisible by 4." (and so on)
The 30th student said, "The number is divisible by 31."
The teacher then commented that exactly two other students who spoke consectutively, gave
incorrect statements. Which two students made incorrect statements? Justify your answer,

Respuesta :

The power of a factor of a dividend in the divisor must be less than or equal to its power in the dividend, for the dividend to be divisible by the divisor

The students that made incorrect statements are the 15th and 16th students

The reason the above values are correct are given as follows:

The given parameters are;

The number written on the board = A large multi digit number

The numbers given as the divisor of the large number are;

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31

The students said to give incorrect statements = Two students that spoke consecutively

Given that two consecutive numbers are incorrect, we have;

The numbers do not have multiples that are less than 31, therefore, the number cannot be any of 1 to 15

Also, we have;

3 × 6 = 18

4 × 5 = 20

3 × 7 = 21

2 × 11 = 22

4 × 6 = 24

2 × 13 = 26

4 × 7 = 28

5 × 6 = 30

However, we have 16 = 2⁴, which is the highest power of 2 in the range, 1

to 32 and likely to be larger than the required size of the even number

divisor, such that it will not divide the large number given the numbers of 2s

in 16,  is larger than the number of 2s in the large number, which

gives the two possible numbers as 16 and 17

Therefore, the students that made incorrect statements are the 15th and 16th students

Learn from more math puzzles here:

https://brainly.com/question/15801840