CDS 2018: How to Solve Number System Questions

Updated On -

Feb 12, 2018

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Shivani Tiwari

Content Curator

CDS is a national level entrance examination conducted by UPSC twice a year. CDS exam is scheduled to be conducted on February 5, 2017. The main objective of this exam is to select candidates for recruitment in Indian Defence forces. Mathematics ection is a key factor in CDS to ensure good score in the exam. The mathematics paper consists of 120 questions in UPSC CDS. The duration of the examination is 120 minutes.

How to solve Number system questions In CDS exam?

Number system is one of the most important topics of elementary mathematics. It helps in boosting overall score of the candidate. This section contains approximately 15% of weightage in CDS exam. Number system is the fundamental section of any topic in mathematics. Here, the paper pattern for number system in elementary mathematics section.

Topics No. of questions
Basic of number system 4
Surds & Indices 2
Factors 3

Candidates need to focus on the questions of every topic. Here, we are providing concepts and methods for each topic. Candidates can follow these concepts to score better in number system questions.

Basics of number system

Candidates must be good in calculations, counting, analysis etc. They need to solve these questions in less time by shortcut tricks. For example:

Q: 1397*1397 =?

Ans: (1397)2

= (1400-3)2

= 1951609; By formulae (a2-2ab+b2)


These questions need only some practice to solve in single attempt. Candidate need to focus on particular type questions in HCF & LCM. Here is the example of that type of question which are asked in CDS exam:

Q: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:

Ans: Clearly, the numbers are (23*13) and (23*14)

Therefore, the larger number = 23*14 = 322

Surds and Indices

These questions look complicated and tricky but candidates can solve it in few seconds by an easy method. For example:

Q: If 5a = 3125, then the value of 5(a-3) is:

Ans: 5a = 3125,

5a = 55,

a= 5,

therefore, 5(a-3)= 5(5-3)= 52=25


In these questions, the method is depending upon simple arithmetic rules. It needs to only give clear attention for a while. For example:

Q: (6 + 4) *5

Ans: first solve the numbers inside the bracket 6 + 4 = 10, then 10*5 = 50.


This is the simplest question of mathematics in CDS exam. It gives bonus marks in elementary, e.g.,

Q: Find the prime factors of 102.

Ans: The prime factors of 102 are 2, 3 and 17.

Tips to solve Number system questions in CDS exam

There are some important tips to solve number system questions in CDS 2018. Candidates can go through following points that will help in their preparation strategy:

  • Make use of NCERT books up to 10th class to know the number system concepts. This is the best way to solve these questions.
  • Solve the types of number system questions without using pen and paper. Memorize the concepts and revise it regularly.
  • Solve minimum 50 questions daily of this topic from easy to high level of difficulty.
  • Candidate need to focused on questions related to HCF & LCM, finding unit place and products of numbers.
  • The best way to solve number system questions quickly is to work on fundamentals of calculations and analyze.
  • Learn the shortcuts for each type question, it helps to solve questions in less time.

*The article might have information for the previous academic years, please refer the official website of the exam.