Anti divisible palindromes!
Number Theory
Level
5
What is the probability that a palindrome chosen between 1000 and 10 000 at random will not be divisible by 7?
The answer is 0.8.
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A 4 digit palindrome can be expressed as 1000p+100q+10q+p Because It is A palindrome.
Using the divisibility for 7, We get,
100p+10q+q-2p=0 (Mod 7)
= 98p +11q= 0 (Mod 7)
We Know that 98 is completely Divisible by 7, So, Any multiple of 98 will also be divisible by 7.
Thus, We need to Solve
11q= 0 (Mod 7)
Which leads us to 2 solutions i.e. 0 and 7.
Now, There exist 90 palindromes Between 1000 and 10,000.
Thus the Probability of the Number NOT Being divisible by 7 Is
9 0 7 2 = 0 . 8
Cheers! xD