A number theory problem by Anandmay Patel
Number Theory
Level
2
A 5 digit number is divisible by 91 and 11.If the second digit from the left is 1, what is the product of the third digit and fourth digit from the left?
The answer is 0.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
91 and 11 are prime.So the 5 digit number is 1001(91x11) multiplied by some integer.Now by inspection,we find that the integer must be a 2 digit number so that the final number(1001 multiplied by the integer) is a 5 digit number.
Any 2 digit number is of the form 10a+b,where a,b are natural numbers less than 10.So 1001 x (10a+b)=ab0ab. Now, we are required to find the product of the 3rd and the 4th digit from the left of the 5 digit number. But the 3rd digit from left is 0.So product and our final answer is 0.