Question

A teacher challenges his class 7 students to try and 'invent' a divisibility test for 12. After discussing among themselves, the class comes up with 4 different answers, which are given below. Only one of them is correct. Which of these is a divisibility test for 12?

Answer 1

Answer

If a number is divisible by 3 and 4 both, then that number is divisible by 12.

Example=4416

Step-by-step explanation:

Step 1: To check divisibilty by 3

     add all the digits e.g. 4+4+1+6=15

      15 is divisible by 3

      Hence 4416 is divisible by 3.

Step 2: To check divisibility by 4

       Last 2 digit is 16

       16 is divisible by 4

       Hence 4416 is divisible by 4

Therefore 4416 is divisible by 12

Answer 2

• Divisibility for 12 :- The number should pa ss the divisibility tests for 3 and 4 .

Complete Question :- A teacher challenges his class 7 students to try and 'invent' a divisibility test for 12. After discussing among themselves, the class comes up with 4 different answers, which are given below. Only one of them is correct. Which of these is a divisibility test for 12 ?

A) The number should pa ss the divisibility tests for 2 and 6.

B) The number should pa ss the divisibility tests for 3 and 4.

C) The number should pa ss the divisibility tests for 2 and 10.

D) None of these - there is no divisibility test for 12.

Concept used :-

• Divisibility rule of 2 :- If unit digit of a number is 0,2,4,6 or 8 then, the number is divisible by 2 .
• Divisibility rule of 3 :- If sum of all digits of a number is divisible by 3, the given number is also divisible by 3 .
• Divisibility rule of 4 :- If last two digits { hundred place digit and unit place digit } are divisible by 4, the given number is also divisible by 4 .
• Divisibility rule of 6 :- If a number is divisible by 2 and 3 both, the given number is also divisible by 6 .
• Divisibility rule of 10 :- if unit digit of a number is equal to zero, the given number is divisible by 10 .

Solution :-

checking all 4 different answers given by students,

A) The number should pa ss the divisibility tests for 2 and 6.

Example :- 126

→ Unit digit = 6 , so given number is divisible by 2 .

also,

→ sum of number = 1 + 2 + 6 = 9 => 9 ÷ 3 = Remainder 0 . so given number is divisible by 3 .

since 126 is divisible by 2 and 3 both, it must be divisible by 6 also .

now, checking for 12 :-

→ 126 ÷ 12 = 10.5 or remainder is not equal to zero .

therefore, we can conclude that, if a number should pa ss the divisibility tests for 2 and 6, it may not pa ss the divisibility tests for 12 .

Hence, Answer (A) is incorrect .

B) The number should pa ss the divisibility tests for 3 and 4.

Example :- 792

checking if last two digits of the number are divisible by 4 :-

→ 792 ÷ 4 = 198 quotient and zero remainder .

So, 792 is divisible by 4 .

now,

→ sum of digit = 7 + 9 + 2 = 18 => Divisible by 3 { 6 × 3. }

So, 792 is divisible by 3 .

now, checking for 12 :-

→ 792 ÷ 12 = 66 quotient and zero remainder .

therefore, we can conclude that, if a number should pa ss the divisibility tests for 3 and 4, the given number is also divisible by 12 .

Hence, Answer (B) is correct .

C) The number should pa ss the divisibility tests for 2 and 10.

Example :- 200

Unit digit = 0, so given number is divisible by 2 and 10 both .

now, checking for 12 :-

→ 200 ÷ 12 = 16 quotient and 8 remainder .

since remainder is not equal to zero . Therefore, we can conclude that, if a number should pa ss the divisibility tests for 2 and 10, it may not pa ss the divisibility tests for 12 .

Hence, Answer (C) is incorrect .

∴ Answer (B) The number should pa ss the divisibility tests for 3 and 4 is correct answer .

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