Question

The digit by which ‘*’ should be replaced in 635 * 722 so that the number formed is divisible by 22
i) 0
(ii) 4
(iii) 3
(iv) none of these.

Answer 1

Step-by-step explanation:

If the difference between the sum of digits of odd places and the sum of digits of even places of a number is divisible by 11 or it is zero then that number is divisible by 11.

(i) 64∗2456

Now,

6−4+∗−2+4−5+6=16+∗−11

=5+∗

We can now observe that 5+x is divisible by 11 if x=6.

Hence, there should be 6 at the place of ∗ for the number to be divisible by 11.

(ii) 86∗6194

Now,

8−6+∗−6+1−9+4=13+∗−21

=−8+∗

We can now observe that −8+x is divisible by 11 if x=8.

Hence, there should be 8 at the place of ∗ for the number to be divisible by 11.

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