The number 9730 - 1430 is divisible by : 

This question was previously asked in
CDS Elementary Mathematics 16 April 2023 Official Paper
View all CDS Papers >
  1. 37 but not 83  
  2. 83 but not 37 
  3. Both 37 and 83  
  4. Neither 37 nor 83  

Answer (Detailed Solution Below)

Option 3 : Both 37 and 83  
Free
UPSC CDS 01/2025 General Knowledge Full Mock Test
8.2 K Users
120 Questions 100 Marks 120 Mins

Detailed Solution

Download Solution PDF

Concept:

an - bn, (where n is even number) is always divisible by (a - b) & (a + b)

Calculation:

We have 9730 - 1430

By using the above concept, 

9730 - 1430 is divisible by

(97 - 14) = 83

And

(97 + 14) = 111 = 37 × 3

∴ 9730 - 1430 is divisible by both 37 and 83.  

Latest CDS Updates

Last updated on Jul 7, 2025

-> The UPSC CDS Exam Date 2025 has been released which will be conducted on 14th September 2025.

-> Candidates can now edit and submit theirt application form again from 7th to 9th July 2025.

-> The selection process includes Written Examination, SSB Interview, Document Verification, and Medical Examination.  

-> Attempt UPSC CDS Free Mock Test to boost your score.

-> Refer to the CDS Previous Year Papers to enhance your preparation. 

Get Free Access Now
Hot Links: teen patti online game teen patti pro teen patti flush teen patti rich online teen patti real money