0

Guest

Courses New

The number of ordered pairs (m,n),m,n€{1,2,.......50} such that 6 n + 9 m is a multiple of 5.

  1. The number of ordered pairs (m,n),m,n€{1,2,.......50} such that  6n +9m is a multiple of 5.

Grade:12th pass

2 Answers

Tony
108 Points
5 years ago
I have done it with modulus(remainder) function. Modulus of 6^m will be 1 ^m anr that of 4^n is (-1)^n.
The key is to find a relation between m and n. For this question, if you take modulus 5, you get 1m +(-1)n = 1+(-1)n. The first thing to notice is that this is independent of m. Therefore, every value of m is possible. Thus, there are 50 possible m values. To make this equal to 0, you want n to be odd. Thus, there are 25 possible n values. Therefore, there are (50)(25)=1250 number of possible pairs.
Tony
108 Points
5 years ago
Sry bro , by mistake in the above answer I have took the question as 6^m but it is 6^n.
Sry for that.Method is still same but bro just swap m with n wherever written in above answer!

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More