Question

Q10. In each of the following replace * by a digit so that the number formed is divisible by 11:
()64*2456 (ii) 86*6194

Answer 1

Answer:

i) 6

ii) 8

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Step-by-step explanation:

(i) 64×2456

It is divisible by 11

The difference between the sum of digits of odd places and sum of digits of even place is divisible by 11 or it is zero

Now 6+4+∗+6−5+2+4 [ which is divisible by 11 ]

16+∗−11 is divisible by 11

5+x is divisible by 11

∴∗is 6.

(ii) 86×6194

It is divisible by 11

The difference between the sum of digits of odd places and sum of digits of even places is divisible by 11 or its is zero.

Now 4+1+∗+8=13+∗

9+6+6=21

21−(13+∗) is divisible by 11

21−13−∗ is divisible by 11

8−∗ is divisible by 11

∴∗ is 8.

Answer 2

(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.