Find A as required(i) The greatest 2 digit number 9A is divisible by 2

1.	Find A as required(i) The greatest 2 digit number 9A is divisible by 2.(ii) The least number 567A is divisible by 3.(iii) The greatest 3 digit number 9A6 is divisible by 6.(iv) The number A08 is divisible by 4 and 9.(v) The number 225A85 is divisible by 11.
Answer» (i) A number is divisible by 2 if it is an even number. Greatest 2 digit even number is 98. ∴ A = 8 (ii) A number is divisible by 3 if the sum of its digits is divisible by 3 Sum of digits of 567A = 5 + 6 + 7+ A = 18 + A ∴ 18 is divisible by 3 ∴ A may be 0 The number will be 5670 (iii) A number is divisible by 6 if it is divisible by both 2 and 3 9A6 is even and so divisible by 2 If A = 9 then the sum of digits will be = 24 which is divisible by 3. The number will be 996 and A = 9 (iv) 08 is divisible by 4, so A08 is divisible by 4. If A = 1 then the sum of digits will be 9 which is divisible by 9. The number will be 108 and A = 1 (v) 5 + A + 2 – (8 + 5 + 2) = 7 + A – 15 = -8 + A ∴ A = 8

Find A as required(i) The greatest 2 digit number 9A is divisible by 2.(ii) The least number 567A is divisible by 3.(iii) The greatest 3 digit number 9A6 is divisible by 6.(iv) The number A08 is divisible by 4 and 9.(v) The number 225A85 is divisible by 11.

Answer»

(i) A number is divisible by 2 if it is an even number.

Greatest 2 digit even number is 98.

∴ A = 8

(ii) A number is divisible by 3 if the sum of its digits is divisible by 3

Sum of digits of 567A = 5 + 6 + 7+ A = 18 + A

∴ 18 is divisible by 3

∴ A may be 0

The number will be 5670

(iii) A number is divisible by 6 if it is divisible by both 2 and 3

9A6 is even and so divisible by 2

If A = 9 then the sum of digits will be = 24 which is divisible by 3.

The number will be 996 and A = 9

(iv) 08 is divisible by 4, so A08 is divisible by 4.

If A = 1 then the sum of digits will be 9 which is divisible by 9.

The number will be 108 and A = 1

(v) 5 + A + 2 – (8 + 5 + 2)

= 7 + A – 15

= -8 + A

∴ A = 8