CAT Quantitative Aptitude Questions | CAT Number Theory - Digits questions

The question is about Digits. Some details about a 80 digits number is given and we need to find out the 44^th digit of that number . Dealing with digits and base system of a number is a vital component in CAT Number Systems. A range of CAT questions can be asked based on this simple concept in the CAT Exam.

Question 8: N is an 80-digit positive integer (in the decimal scale). All digits except the 44^th digit (from the left) are 2. If N is divisible by 13, find the 44^th digit?

1. 5
2. 6
3. 1
4. 2

Explanatory Answer

Method of solving this CAT Question from Number Theory - Digits: How does one find the 44th digit of an 80-digit number?

Any number of the form abcabc is a multiple of 1001. 1001 is 7 * 11 * 13. So, any number of the form abcabc is a multiple of 13.

42 digits ......... 43 44 .... remaining 36 digits
222222 ..... 222222 2 a 222222............222222
Or we can write this 80 digit number as,
222222 ......2222220000000 ............000000 (It has 42 2's and 38 0's and it is divisible by 13)
+ 00000 .......00000 2 a 000000............000000 (43^rd digit is 2 and 44^th digit is a)
+ 00000 ..........000000 222222.............222222 (It has 36 2's in the end and it is divisible by 13)

We are left with a two digit number 2a. 26 is a multiple of 13, so the 44^th digit should be 6.

The question is "If N is divisible by 13, find the 26^th digit?"

Hence the answer is "6"

Choice B is the correct answer.