Quant- Numbers Problem

This topic has expert replies
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: 08 Apr 2020

Quant- Numbers Problem

by Neellkanth » Wed Apr 08, 2020 3:55 am
Given that:

4m+n=20; and
|n|≤20

How many ordered pairs (m,n) exist in which m and n both are integers?

Junior | Next Rank: 30 Posts
Posts: 15
Joined: 30 May 2020

Re: Quant- Numbers Problem

by orthodoxparadox » Sat May 30, 2020 10:57 pm
Let us try it for all n from -20 to 20. We can only choose such n that 20 - n is divisible by 4, since m is also an integer. Since 20 is divisible by 4, n must also be divisible by 4.

So values would be -20, -16, -12, -8, -4, 0, 4, 8, 12, 16, 20 => 11 values in total.

Junior | Next Rank: 30 Posts
Posts: 13
Joined: 01 Aug 2020

Re: Quant- Numbers Problem

by Ignite » Sat Aug 01, 2020 10:19 pm
4m+n=20; and |n|≤20

When,
m = 0, n = 20
m = 1, n = 16
m = 2, n = 12
m = 3, n= 8
m= 4, n =4
m=5, n = 0

But, n can also take negative values upto -20
So there will be
m= 6, n = -4
m=7, n = -8
m= 8, n=-12
m=9, n =-16
m=10, n =-20

Thus, there are 11 ordered pairs.

Thanks,
Ignite

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 6578
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

Re: Quant- Numbers Problem

by [email protected] » Tue Jul 12, 2022 1:23 am
Neellkanth wrote:
Wed Apr 08, 2020 3:55 am
Given that:

4m+n=20; and
|n|≤20

How many ordered pairs (m,n) exist in which m and n both are integers?
Solution:

We see that:

m = (20 - n)/4 = 5 - n/4 = integer

Since n is also an integer, n must be a multiple of 4. Since |n| ≤ 20, n can be 20, 16, 12, 8, 4, 0, -4, -8, -12, -16, or -20. Since there are 11 values of n, there are 11 ordered pairs (m, n).

Answer: 11