Question

P1. A teacher wrote a large number on the board and asked the students to tell about the

divisors of the number one by one.

The 1st student 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 students, who spoke consecutively, spoke

wrongly.

Which two students spoke wrongly? Explain your answer with appropriate justification.​

Answer 1

Answer:

16 & 17 numbers

15th & 16th Student

Step-by-step explanation:

As per question data students said that

number is divisible by

2 , 3, 4, .......................................................... 30 , 31

The teacher then commented that exactly two students, who spoke consecutively, spoke  Wrongly

Means That number is not divisible by those two numbers

Two numbers are consecutive

From 2 to 15 numbers can be wrong

as their number multiplied by 2 will be true  

so  

first possible  

pair = 16 , 17  ( where 17 is already prime so not dependent upon other divisors till 31)

16 can have factors 2 , 4 & 8  

LCM of 2 , 4 & 8 = 8 so 16 is also one of the possibility not being divisor

(1 6 , 17 ) can be the solution

Now let check further pairs till 31

Any number can not be wrong which is multiplication of two divisors (having no common Factor)

(17 , 18) & (18, 19)   - ( 18 can be wrong as 18 = 2 * 9)

(19 , 20) & (20, 21)   - ( 20 can be wrong as 20 = 4 * 5)

(21 , 22) & (22, 23)   - ( 22 can be wrong as 22 = 2 * 11)

(23 , 24) & (24, 25)   - ( 24 can be wrong as 24 = 3 * 8)

(25 , 26) & (26, 27)   - ( 26 can be wrong as 26 = 2 * 13)

(27 , 28) & (28, 29)   - ( 24 can be wrong as 28 = 4 * 7)

(29 , 30) & (30 , 31)  - ( 30 can be wrong as 30 = 5 * 6)

So number 16 & 17  by students 15th & 16th