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
How many positive integers are there from 0 to 1000 that leave a remainder of 3 on division by 7 and a remainder of 2 on division by 4?
32
36
24
19
Number should be of the form 7n + 3 and 4m + 2. The LCM of 7 and 4 is 28. So, let us see what are the possible remainders when we divide this number by 28. A number of the form 7n + 3 can be written as 28K + 3 or 28k + 10 or 28 + 17 or 28k + 24. A number of the form 4m + 2 can be written as 28l + 2, 28l + 6, 28l + 10, 28l + 14, 28l + 18, 28l + 22, 28l + 26. Within these, the only common term is 28K + 10. The numbers in this sequence are 10, 38, 66.....990. We still need to figure out how many numbers are there in this sequence. We are going in steps of 28, so let us see if we can write these numbers in terms of 28p + r. 10 = 28 * 0 + 10 38 = 28 * 1 + 10 66 = 28 * 2 + 10 94 = 28 * 3 + 10 .......... 990 = 28 * 35 + 10 There are 36 numbers in this sequence.
Report error
Access to prime resources