Question

If 6a5342b is divisible by both 5 and 3, then the least possible value of a' is ...
a) 1
b) 0
c)2
d) 3

please explain clearly
if u explain clearly then I marked u as braineliest​

Answer 1

Given info : 6a5342b is divisible by both 5 and 3.

To find : the least possible value of a is ...

solution : divisibility of 5 : every number is divisible by 5 if its last digit is either 0 or 5.

so the number 6a5342b is divisible by 5 only when b = 0 or 5 ...(1)

divisibility of 3 : every number is divisible by 3 if sum of digit of that number is integral multiple of 3.

so the number 6a5342b is divisible by 3 when 6 + a + 5 + 3 + 4 + 2 + b = 18 + a + b = integral multiple of 3.

we see, 18 is divisible by 3. it is integral multiple of 3, isn't it ?

case 1 : so if we take, b = 0 [from eq (1) ] then  a = 0 to make the number divisible by both 5 and 3.

case 2 : but if we take b = 5 , then a = 1 [ 18 + 1 + 3) = 24 which is integral multiple of 3. so, it is divisible by both 5 and 3. ]

but we have to find the least possible value of a. which we get from case 1, don't we ?

so the least value of a is 0.