send mail to support@abhimanu.com mentioning your email id and mobileno registered with us! if details not recieved
Resend Opt after 60 Sec.
By Loging in you agree to Terms of Services and Privacy Policy
Claim your free MCQ
Please specify
Please verify your mobile number
Login not allowed, Please logout from existing browser
Please update your name
Subscribe to Notifications
Stay updated with the latest Current affairs and other important updates regarding video Lectures, Test Schedules, live sessions etc..
Your Free user account at abhipedia has been created.
Remember, success is a journey, not a destination. Stay motivated and keep moving forward!
Refer & Earn
Enquire Now
My Abhipedia Earning
Kindly Login to view your earning
Support
A number leaves a remainder 3 on division by 14, and leaves a remainder k on division by 35. How many possible values can k take?
3
2
5
4
N/8 remainder = 3 N = 8q + 3 q can be in one of 3 forms 3p 3p + 1 3p + 2 N = 8(3p) + 3 or 8(3p + 1) + 3 or 8(3p + 2) + 3 24p + 3 or 24p + 11 or 24p + 19 N/24 possible remainders are 3, 11, 19 Why did we choose to write q as 3p, 3p + 1 or 3p + 2? 8 x 3 = 24, this is why we chose 3p, 3p + 1, 3p + 2 So, if we are given that remainder on dividing N by 8, then there will be a set of possibilities for the remainder of division of N by 24 (or any multiple of 8) N/42 remainder = 11 N/7 remainder = ? N/42 remainder = 11 N = 42q + 11 42q + 11 divided by 7 42q leaves no remainder 11/7 remainder = 4 So, if we are given that remainder on dividing N by 42, then we can find the remainder of dividing N by 7 (or any factor of 42) Now, let us address the question A number leaves a remainder of 3 on division by 14, or it can be written as 14n + 3 On division by 70, the possible remainders can be 3, 17 (3 + 14), 31 (3 + 28), 45 (3 + 42), or 59 (3 + 56). The number can be of the form 70n + 3 70n + 17 70n + 31 70n + 45 70n + 59 Now, we need to divide this number by 35 70n + 3 divided by 35, the remainder will be 3. 70n + 17 divided by 35, the remainder will be 17. 70n + 31 divided by 35, the remainder will be 31. 70n + 45 divided by 35, the remainder will be 10. 70n + 59 divided by 35, the remainder will be 24. On division by 35, the possible remainders are 3, 17, 31, 10 or 24. There are 5 possible remainders
Report error
Access to prime resources