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Q.

Prove that a 4-digit palindrome is always divisible by 11.


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a

1001

b

1001

c

2001

d

3001 

answer is A.

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Detailed Solution

Concept- A palindromic number is a number that remains the same when its digits are reversed.
For Example – 090 ,121 , 111, 131, 252 etc
To prove that,
a 4-digit palindrome is always divisible by 11.
Numbers are as follows – 1001,1111,1221,1331 etc
These numbers can be written as :
1001 = 330 + 11 = 11(90+1)
1111 = 1100 + 11 = 11(100 + 1)
1221 = 1210 + 10 = 11(110+1)
 and so on……
Hence, the correct option is 1.
 
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