CAT Quantitative Aptitude Questions | CAT Number Systems - Remainders

CAT Questions | Number Theory | Remainders - Large number CAT Questions

The question is from CAT Number Theory - Remainders. A large number is given and we need to find out the remainder when the first 100 digits is divided by 9. Get practice by solving CAT questions from Remainders.

Question 11: Consider a large number N = 1234567891011121314………979899100. What is the remainder when first 100 digits of N is divided by 9?

1. 0
2. 8
3. 1
4. 5

Best CAT Coaching in Chennai

Crash course - Early Bird discount Starts Sat, June 29th, 2019

Method of solving this CAT Question from Number Theory - Remainders: Check how many times digits from 1 to 9 occur in first 100 digits of N.

N is nothing but first 100 natural numbers written in ascending order!
The first 99 natural numbers will give us 9 + (90 * 2) =189 digits.
So let us consider first 49 numbers. Number of digits = 9 + (40 * 2) = 89
11 more is needed to make 100 digits. So we can include 50, 51, 52, 53, 54 and 5

Hence the first 100 digits of N goes like this 1234567891011121314.......5253545
We need to find the sum of the above number to check for divisibility by 9.
From 1 to 50, each of the digits 1 to 4 occurs 14 times, digit 5 occurs 6 times and each of 6 to 9 occurs 5 times

Sum of digits from 1 to 4 = 10
Sum of digits from 6 to 9 = 30
Therefore, sum of digits from 1 to 50 = 10 * 15 + 5 * 6 + 30 * 5 = 330
Sum of digits from 51 to 54 plus a 5 = 5 * 4 + ( 1 + 2 + 3 + 4) + 5 = 20 + 15 = 35
Total sum = 330 + 35 = 365
When 365 is divided by 9, we get 5 as the remainder!

The question is "What is the remainder when first 100 digits of N is divided by 9?"

Choice D is the correct answer.

Signup Now!

CAT Coaching in ChennaiEnroll at 29000/-

Next Weekend Batch Starts Sat, June 29th, 2019

Best CAT Coaching in ChennaiEarly Bird discount of 7000

Personalised attention, Small batch sizes.

CAT Online Coaching | CAT Number Systems questions Videos On YouTube

Other useful sources for Number System Questions | Number Theory Remainders Sample Questions

Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
10-C, Kalinga Colony, Bobbili Raja Salai
K.K.Nagar, Chennai. India. Pin - 600 078

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com