Number System Questions with Solutions
The number system is the foundation of quantitative aptitude. It covers the different types of numbers (natural numbers, whole numbers, integers, rational and irrational numbers, primes and composites) and the rules that govern them. Exam questions test divisibility rules, unit digits of large powers, remainders, factors and multiples, HCF and LCM, and the number of trailing zeros in a factorial. Most of these questions can be solved in under a minute once you know the pattern. Unit digits repeat in cycles of four, and divisibility by 11 depends on the difference between the sums of alternate digits. Number properties also appear inside questions on simplification, averages and series, so strong basics here save time across the whole quant section. Practise the questions below to build speed with divisibility, remainders, unit digits and HCF-LCM. Every question has a step-by-step solution and, where possible, a shortcut method.
- Q21.
The integers 34041 and 32506, when divided by a 3-digit integer n, leave the same remainder. What can be the value of n?
A. 289B. 307C. 367D. 493mediumAsked in NIMCET 2019View solution › - Q22.
Each of A, B and C is a different digit among 1 to 9. How many different values of the sum of A, B and C are possible, if ABA × AA = ACCA?
A. 1B. 3C. 7D. 8hardAsked in NIMCET 2019View solution › - Q23.
Among the given numbers below, the smallest number which, when divided by 9, 10, 15 and 20, leaves the remainders 4, 5, 10 and 15 respectively, is
A. 85B. 535C. 355D. 265easyAsked in NIMCET 2024View solution › - Q24.
Ramu visits Delhi every 15 days and Samu goes to Delhi every 20 days. They met at Delhi 5 days back. After how many days, from today, will they meet at Delhi next time?
A. 35B. 55C. 60D. 65easyAsked in NIMCET 2024View solution › - Q25.
The number of all even integers between 99 and 999 which are not multiples of 3 and 5 is
A. 240B. 250C. 245D. 235mediumAsked in NIMCET 2025View solution › - Q26.
A two-digit number is such that the product of its digits is 12. If 36 is added to the number, the digits interchange their places. What is the number?
A. 26B. 38C. 25D. 24easyAsked in NIMCET 2025View solution › - Q27.
Consider a sequence formed by concatenating the positive integers in increasing order: 12345678910111213... Which among the following is the 2028th digit in this infinite sequence?
A. 7B. 1C. 4D. 2mediumAsked in NIMCET 2025View solution ›