Question

replace * in the 289* so that the number is divisible by 5 but not 10 ​

Answer 1

Answer:

Given that, the number 66784∗ is divisible by 9.

To find out: The smallest value of ∗.

We know that, a number is divisible by 9, if the sum of its digits is divisible by 9.

The sum of digits of the give number =6+6+7+8+4+∗

⇒31+∗

The smallest number after 31 which is divisible by 9 is 36.

Hence, for the smallest value of ∗, the sum of digits should be 36.

∴ 31+∗=36

⇒∗=36−31=5

Hence, the smallest value of ∗ for which the number 66784∗ is divisible by 9, is 5.

Answer 2

Given:

Replace * in the 289* so that the number is divisible by 5 but not 10

Solution:

Know that,

Divisibility by 5: A number is always divisible by 5 if its last digit is 5 or 0.

Divisibility by 10: A number is always divisible by 10 if its last digit is 0.

Therefore, * in the 289* should be replaced by 5 so that the number is divisible by 5 but not 10.

Hence, the number is 2895 that is divisible by 5 but not 10.