Question

A number 476*#0 is divisible by both three and 11 find the non-zero digits in the hundreds and tens place

Answer 1

Answer:

Step-by-step explanation:

Let the number be 476ab0

476ab0 is divisible by 3

⇒ 4 + 7 + 6 + a + b + 0 is divisible by 3

⇒ 17 + a + b is divisible by 3 - - - - - - - (i)

476ab0 is divisible by 11

[(4 + 6 + b) - (7 + a + 0)] is 0 or divisible by 11

⇒ [3 + (b - a)] is 0 or divisible by 11 - - - - - - - -(ii)

Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation (i) and Equation (ii).

if a = 6 and b = 2,

17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer

if a = 8 and b = 2,

17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)

[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11 --- Does not meet equation(ii).Hence this is not the answer

if a = 6 and b = 5,

17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer

if a = 8 and b = 5, 17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1 [3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2 Since these values satisfies both equation 1 and equation 2, this is the answer