Study hall Remainder question

[AmunaGmat]

Hi Ron and happy new year :)

In this problem from study hall:

If M and N are positive intergers, what is the remainder when N is divided by M.
1. N= 7m +3

I have the same question as one of the student, Rishi. He said he assumed that M>3 and you replied by saying do not assume anything. I do not think this is an Assumption but the truth, because we know that remainders should be less than the divisor. What I mean is e.g remainders of 7 will be 1, 2, 3, 4, 5 & 6 and never equal or greater than 7.

Am I missing something?

[jnelson0612]

Hi Ron and happy new year :)

In this problem from study hall:

If M and N are positive intergers, what is the remainder when N is divided by M.
1. N= 7m +3

I have the same question as one of the student, Rishi. He said he assumed that M>3 and you replied by saying do not assume anything. I do not think this is an Assumption but the truth, because we know that remainders should be less than the divisor. What I mean is e.g remainders of 7 will be 1, 2, 3, 4, 5 & 6 and never equal or greater than 7.

Am I missing something?

Yes, I think you are getting a little turned around here. We derive N from an equation involving M. M can be any positive integer; there are no constraints on M in this equation. We use values of M to obtain values of N and only then do we think about remainders when N is divided by M.

I look at this and think that I should choose numbers:
When M=1, N=10. 10(N) divided by 1(M) has quotient 10, remainder 0.
When M=2, N=17. 17 divided by 2 has quotient 8, remainder 1.

Right there I would say that statement 1 is not sufficient, because I have two different values for remainders.

[AmunaGmat]

Hi Ron and happy new year :)

In this problem from study hall:

If M and N are positive intergers, what is the remainder when N is divided by M.
1. N= 7m +3

I have the same question as one of the student, Rishi. He said he assumed that M>3 and you replied by saying do not assume anything. I do not think this is an Assumption but the truth, because we know that remainders should be less than the divisor. What I mean is e.g remainders of 7 will be 1, 2, 3, 4, 5 & 6 and never equal or greater than 7.

Am I missing something?

Yes, I think you are getting a little turned around here. We derive N from an equation involving M. M can be any positive integer; there are no constraints on M in this equation. We use values of M to obtain values of N and only then do we think about remainders when N is divided by M.

I look at this and think that I should choose numbers:
When M=1, N=10. 10(N) divided by 1(M) has quotient 10, remainder 0.
When M=2, N=17. 17 divided by 2 has quotient 8, remainder 1.

Right there I would say that statement 1 is not sufficient, because I have two different values for remainders.

Thanks a lot J. I got the point!!!

[tim]

glad to hear it!