How to solve this kind of remainder problem.

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brucejin

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N is an integer greater than 5, and when 205 is divided by N, the remainder is 5.
For how many distinct positive integers N is this statement true?

I know given 205/N = m + 5/N.
m is an integer.

Then what to do?

Thanks
 
Hello, brucejin!

You're on your way . . .

\(\displaystyle N\) is an integer greater than 5.
When 205 is divided by \(\displaystyle N\), the remainder is 5.
For how many distinct positive integers \(\displaystyle N\) is this statement true?

\(\displaystyle \text{I know given: }\:\frac{205}{N} \:=\: m + \frac{5}{N},\:m\text{ is an integer.}\)

Then what to do?
Click to expand...

Multiply your equation by \(\displaystyle N\!:\;\;205 \:=\:mn + 5 \quad\Rightarrow\quad Nm \:=\:200\)

Hence, \(\displaystyle N\) is a factor of 200, where \(\displaystyle N > 5.\)

Therefore: .\(\displaystyle N \;=\;8, 10, 20, 25, 40, 50, 100, 200\quad\hdots \quad \boxed{8}\text{ values.}\)

 
soroban said:
Hello, brucejin!

You're on your way . . .

\(\displaystyle N\) is an integer greater than 5.
When 205 is divided by \(\displaystyle N\), the remainder is 5.
For how many distinct positive integers \(\displaystyle N\) is this statement true?

\(\displaystyle \text{I know given: }\:\frac{205}{N} \:=\: m + \frac{5}{N},\:m\text{ is an integer.}\)

Then what to do?
Click to expand...

Multiply your equation by \(\displaystyle N\!:\;\;205 \:=\:mn + 5 \quad\Rightarrow\quad Nm \:=\:200\)

Hence, \(\displaystyle N\) is a factor of 200, where \(\displaystyle N > 5.\)

Therefore: .\(\displaystyle N \;=\;8, 10, 20, 25, 40, 50, 100, 200\quad\hdots \quad \boxed{8}\text{ values.}\)
Click to expand...

Ok...but aren't N and n two different variables? If we are going to GIVE the answers to students, shouldn't those answers be accurate?

My humble opinion, of course.
 
soroban said:
\(\displaystyle N \;=\;8, 10, 20, 25, 40, 50, 100, 200\quad\hdots \quad\)
Click to expand...


Yeah, and what will the instructor think about the answer when the student mindlessly copies down and turns in "8,10,20,25,40,50,100,200..." ?

Also, Soroban consistently advertises that he's the other guy who completes students' homework, but who's the first guy?

Is it the big Glenn, the fast Eddie, Arthur O?

I think that it's well past time for Soroban to update his signature line. (Better yet, it's time for Soroban, Glenn, Eddie, Arthur, et al, to stop completing homework as a general approach, and start providing guidance and alternate examples instead, as the vast majority of the regulars here decided quite some time ago.)

My bombastic opinions, of course.

 
Re:

mmm4444bot said:
My bombastic opinions, of course.
Click to expand...
bom?bas?tic?
–adjective (of speech, writing, etc.) high-sounding; high-flown; inflated; pretentious.
Also, bom?bas?ti?cal.

Synonyms:
pompous, grandiloquent, turgid, florid, grandiose. Bombastic, flowery, pretentious, verbose all describe a use or a user of language more elaborate than is justified by or appropriate to the content being expressed. Bombastic suggests language with a theatricality or staginess of style far too powerful or declamatory for the meaning or sentiment being expressed: a bombastic sermon on the evils of cardplaying. Flowery describes language filled with extravagant images and ornate expressions: a flowery eulogy. Pretentious refers specifically to language that is purposely inflated in an effort to impress: a pretentious essay designed to demonstrate one's sophistication. Verbose characterizes utterances or speakers that use more words than necessary to express an idea: a verbose speech, speaker.

Gee Mark, youza quite the guy :D
 


Denis, you missed about two dozen synonyms.

Here's four that I had in mind, when I employed that adjective: loudmouthed, ranting, overblown, and arrogant.

(You already knew that I'm quite a guy, right? I know that you've read my profile.)

 
Re:

mmm4444bot said:
Also, Soroban consistently advertises that he's the other guy who completes students' homework, but who's the first guy?
Click to expand...

It was Skeeter - who has not done homework for a while....
 
Re: Re:

Denis said:
mmm4444bot said:
...Better yet, it's time for Soroban, Glenn, Eddie, Arthur, et al, ...
Click to expand...
You forgot stapel :p
Click to expand...

Denis - I might be missing your point totally - but stapel is one of the tutors who insists on having work shown.

If I am not mistaken, she is the one who commented "..... or wait for one of the two guys who would do the homework for you" - This was before the days of eddie, glen, arthur, et al.
 
Re: Re:

Subhotosh Khan said:
Denis - I might be missing your point totally - but stapel is one of the tutors who insists on having work shown.
Click to expand...
YES, you're missing my "joke like" intent...stapel is "cruel" :)
 
brucejin said:
… sorry for my tough question which caused you guy so much trouble.
Click to expand...


(1) Your question is not tough.

(2) The off-topic discussion that developed in this thread (for which I take full responsibility) is not something over which you need to apologize.

 
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