Question

find the two-digit numbers a and b such that the number 65ab0 is divisible by 66.

Answer 1

Answer:

Therefore value of a is 0 and b is 1

Number is 65010

Step-by-step explanation:

Any term divisible by 2x3x11 shall be divisible by 66

1. Digit at unit place is 0 , therefore it is divisible by

2. Now, to check if it is divisible by 3 , sum of all digits shall be divisible by 3

6+5+a+b=11+a+b

Let us take the minimum value as 12 (not less than 11 ) divisible by 3

11+a+b=12

a+b=1

Either a=1 or b=1 (could not be a rational number)………………..(1)

3. A number is divisible by 11 if sum of odd digits minus sum of even digits is either 0 or divisible by 11

6+a-5-b=1+a-b

Let us take difference of sum of odd and even digits as 0

i.e. 1+a-b= 0

a-b=-1

a=b-1

Let b=1 (from equation (1)

a=1-1=0

Let b=0, a=-1 (not possible )

Therefore value of a is 0 and b is 1

Number is 65010