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.
Answers
Answer:
Students spoke wrongly is number 16 and 17.
Step-by-step explanation:
Given : 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.
To find : Which two students spoke wrongly?
Solution :
Follow the steps:
Step 1 - The secret numbers are consecutive so one is even and one is odd.
Step 2 - It can't be any two consecutive numbers if it is not divisible by 2 and 3.
For example, it also wouldn't be divisible by 6 or 8 or 9, etc, which would violate the condition.
Step 3 -These two numbers cannot have multiples that are less than 31. Eliminating 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
Step 4 - It can't be like the number 21 because if it's divisible by 3 and 7, it will be divisible by 21.
Step 5 - Eliminating all of those, we get that the answer is
Students number 16 & 17.
Therefore, Students spoke wrongly is number 16 and 17.