>>>>>>> +10V
>>>>>>> |
>>>>>>> |
>>>>>>> C
>>>>>>>+5V--------------B
>>>>>>> E
>>>>>>> |
>>>>>>> 1K
>>>>>>> |
>>>>>>> gnd
>>>>>>>(drawn like a real schematic, on a whiteboard)
>>>>>>>What is the base voltage? (one answer: 0.6!)
>>>>>>>What is the emitter voltage?
>>>>>>>What is the collector voltage?
>>>>>>>What is the base current?
>>>>>>>What is the emitter current?
>>>>>>>What is the collector current?
>>>>>>>Any other comments?
>>>>>>Germanium or silicon?
>>>>>>PNP or NPN? ;)
>>>>>>Roberto Waltman
>>>>>>[Running for cover...]
>>>>>For a (slightly) more advanced test..
>>>>>>> -10V
>>>>>>> |
>>>>>>> 1K
>>>>>>> |
>>>>>>> C
>>>>>>>-5V--------------B NPN >>>>>>> E
>>>>>>> |
>>>>>>> gnd
>>>>One more question: What is the pressure of the magic smoke inside the
>>>>transistor?
>>>If it's a jellybean NPN, the E-B junction is going to be just fine
>>>(typically they break down around 8-9V and are rated for at least 5V),
>>>and the answers are, as JL says, going to be about the same as his
>>>example except for the higher base current due to typically low
>>>reverse beta. But it fits a different visual pattern, being an NPN
>>>with E grounded-- it's probably not obvious that it's a
>>>"collector-follower".
>> That's way overkill for a first question interview. If some kid
>> doesn't know about reverse beta, I wouldn't chuck him out right away.
>> I measured a BFT25 as having reverse beta about 4.
> And each time some one comments on that, I still try to think of an >application where that would prosper? Maybe something in speed switching >. etc..
> Kind of reminds me of ECL logic in a way.
>Jamie
I have used a BFT25 to ground an AC-coupled analog signal, in a
gain-switching application. You need a lot of base current to clamp
the negative part of the swing, since reverse beta is low.
Precision electronic instrumentation
Picosecond-resolution Digital Delay and Pulse generators
Custom laser drivers and controllers
Photonics and fiberoptic TTL data links
VME thermocouple, LVDT, synchro acquisition and simulation
>>>>>>>> +10V
>>>>>>>> |
>>>>>>>> |
>>>>>>>> C
>>>>>>>>+5V--------------B
>>>>>>>> E
>>>>>>>> |
>>>>>>>> 1K
>>>>>>>> |
>>>>>>>> gnd
>>>>>>>>(drawn like a real schematic, on a whiteboard)
>>>>>>>>What is the base voltage? (one answer: 0.6!)
>>>>>>>>What is the emitter voltage?
>>>>>>>>What is the collector voltage?
>>>>>>>>What is the base current?
>>>>>>>>What is the emitter current?
>>>>>>>>What is the collector current?
>>>>>>>>Any other comments?
>>>>>>>Germanium or silicon?
>>>>>>>PNP or NPN? ;)
>>>>>>>Roberto Waltman
>>>>>>>[Running for cover...]
>>>>>>For a (slightly) more advanced test..
>>>>>>>> -10V
>>>>>>>> |
>>>>>>>> 1K
>>>>>>>> |
>>>>>>>> C
>>>>>>>>-5V--------------B NPN
>>>>>>>> E
>>>>>>>> |
>>>>>>>> gnd
>>>>>One more question: What is the pressure of the magic smoke inside the
>>>>>transistor?
>>>>If it's a jellybean NPN, the E-B junction is going to be just fine
>>>>(typically they break down around 8-9V and are rated for at least 5V),
>>>>and the answers are, as JL says, going to be about the same as his
>>>>example except for the higher base current due to typically low
>>>>reverse beta. But it fits a different visual pattern, being an NPN
>>>>with E grounded-- it's probably not obvious that it's a
>>>>"collector-follower".
>>> That's way overkill for a first question interview. If some kid
>>> doesn't know about reverse beta, I wouldn't chuck him out right away.
>>> I measured a BFT25 as having reverse beta about 4.
>> And each time some one comments on that, I still try to think of an
>>application where that would prosper? Maybe something in speed switching
>>. etc..
>> Kind of reminds me of ECL logic in a way.
>>Jamie
> I have used a BFT25 to ground an AC-coupled analog signal, in a
> gain-switching application. You need a lot of base current to clamp
> the negative part of the swing, since reverse beta is low.
>>> [ Please reply to the group,
>>> return address is invalid ]
>>Now we are getting somewhere.
>>Also need to know the Hfe to answer the Ib and Ie parts.
>>Might also be good to know the temperature and the transistor part number.
>I'd be happy for the applicant to make some assumptions (stated, if he
>likes) and give me ballpark numbers. *Without* cranking up Spice on
>his laptop.
<speffS...@interlogDOTyou.knowwhat> wrote:
>On Wed, 24 Oct 2012 18:41:33 +0000 (UTC), Willem
><wil...@turtle.stack.nl> wrote:
>>k...@att.bizzzzzzzzzzzz wrote:
>>) I originally discounted 2s and 5s because the only 9*0 ends in zero (assumed
>>) that the '9' made a difference - it doesn't). Obviously, there is also 2
>>) times 5 in each decade, so there are 408 (x0) + 40 (x100) +4 (x1000) + 409
>>) (2x5) = 861.
>>I have no idea what you mean with 9*0 and why they should make a difference.
>>Also, you still made a mistake, 861 is not the right answer.
>>>> In order to insure my place in infamy, I created my own irrelevant
>>>> questions. Well, not exactly a question, more of a process. I would
>>>> show the applicant a PCB from the company product, and ask them to
>>>> identify components that they've worked with in the past, and give a
>>>> short description on what they do. Ostensively, this was to gauge
>>>> experience. Most would recognize about 25% of the major RF
>>>> components, which was about what I would expect. I then explained
>>>> what the board did, what products it was used in, some of the parts
>>>> they missed, and generally filled in the blanks.
>>>> I would then give the applicant a tour of the factory, production
>>>> line, grab a cup of coffee, and return to my messy office where I
>>>> would hand the applicant the exact same PCB, and ask the exact same
>>>> question. The real test was whether they were paying attention and
>>>> how much of my explanation they were able to recall. 50% recognition
>>>> was typical. Exceptional engineers and techs, which unfortunately we
>>>> couldn't afford to hire, would come very close to 100% recognition and
>>>> recall.
>>>> Other companies use the interview for testing problem solving skills.
>>>> <http://en.wikipedia.org/wiki/Microsoft_Interview>
>>>> Now, that's what I call relevant questions. However, it's
>>>> occasionally abused by asking the applicant to solve a real problem
>>>> with a current product. I once interviewed at a company that did that
>>>> to me. I was presented with a large schematic of the product, and
>>>> asked to critique the design. After a few minutes of hasty back of
>>>> the envelope calculations, I declared the product to be over-designed,
>>>> a tolerance accumulation nightmare, and that there were several active
>>>> stages that were superfluous. I offered specific recommendations on
>>>> what should be changed. I then expect to be thanked for my brilliant
>>>> insights. Instead, I was diplomatically thrown out the door. It
>>>> seems that the manager that was conducting the interview had designed
>>>> the product, and did not take kindly to criticism. So much for a
>>>> relevant problem solving interview.
>>> You didn't want to work there, so it was a great interview.
>>> (drawn like a real schematic, on a whiteboard)
>>> What is the base voltage? (one answer: 0.6!)
>> During the dot.com bubble, I worked for a software company that would
>> (by way of analogy) have employed the person on the grounds that they at
>> least knew which was the base.
> With that answer? Are you sure? ;-)
>> Apparently, the management thought that
>> any 'programmer' was better than no programmer.
> Been there. It's taken some convincing, at times, to get management to
> understand that sometimes more people = less work. It's often too late to
> improve a schedule, by *any* means.
Getting a manager to understand that doing nothing is the best course when something is running late - that's quite a feat.
>>>>>>>> +10V
>>>>>>>> |
>>>>>>>> |
>>>>>>>> C
>>>>>>>>+5V--------------B
>>>>>>>> E
>>>>>>>> |
>>>>>>>> 1K
>>>>>>>> |
>>>>>>>> gnd
>>>>>>>>(drawn like a real schematic, on a whiteboard)
>>>>>>>>What is the base voltage? (one answer: 0.6!)
>>>>>>>>What is the emitter voltage?
>>>>>>>>What is the collector voltage?
>>>>>>>>What is the base current?
>>>>>>>>What is the emitter current?
>>>>>>>>What is the collector current?
>>>>>>>>Any other comments?
>>>>>>>Germanium or silicon?
>>>>>>>PNP or NPN? ;)
>>>>>>>Roberto Waltman
>>>>>>>[Running for cover...]
>>>>>>For a (slightly) more advanced test..
>>>>>>>> -10V
>>>>>>>> |
>>>>>>>> 1K
>>>>>>>> |
>>>>>>>> C
>>>>>>>>-5V--------------B NPN >>>>>>>> E
>>>>>>>> |
>>>>>>>> gnd
>>>>>One more question: What is the pressure of the magic smoke inside the
>>>>>transistor?
>>>>If it's a jellybean NPN, the E-B junction is going to be just fine
>>>>(typically they break down around 8-9V and are rated for at least 5V),
>>>>and the answers are, as JL says, going to be about the same as his
>>>>example except for the higher base current due to typically low
>>>>reverse beta. But it fits a different visual pattern, being an NPN
>>>>with E grounded-- it's probably not obvious that it's a
>>>>"collector-follower".
>>>That's way overkill for a first question interview. If some kid
>>>doesn't know about reverse beta, I wouldn't chuck him out right away.
>>>I measured a BFT25 as having reverse beta about 4.
>> And each time some one comments on that, I still try to think of an >>application where that would prosper? Maybe something in speed switching >>. etc..
>> Kind of reminds me of ECL logic in a way.
>>Jamie
> I have used a BFT25 to ground an AC-coupled analog signal, in a
> gain-switching application. You need a lot of base current to clamp
> the negative part of the swing, since reverse beta is low.
If you're in need for a low saturated switch and don't want to use mos
then I guess this would work..
But, beware of what you place at the emitter, I would think you need
to stay belong the zenering of the emitter..
<jlar...@highlandtechnology.com> wrote:
>You didn't want to work there, so it was a great interview.
Actually, I did want to work there, and probably would have been
willing to tolerate the manager. In retrospect, all he was doing was
defending his design and avoided hiring a potential troublemaker (me).
>This is my first-pass qualifier question.
I noticed that nobody actually answered the problem. So....
> +10V
> |
> C
>+5V--------------B
> E
> |
> 1K
> |
> gnd
>What is the base voltage?
5V
>What is the emitter voltage?
Assuming silicon, and not germanium,
5V - 0.6V = 4.4V
>The best interview is to work on a real design problem, together on a
>whiteboard, for a couple of hours.
Agreed. The last engineer I hired (back in the early 1980's) was one
of maybe a dozen applicants that were filtered by HR. My boss gave me
about an hour each as he didn't want me to spend 12 days on
interviews. I wasn't hugely interested in what they knew. I was
interested in their willingness and abilities to learn new things. My
little memory test trick was my primary tool. There's not much that
can be done in an hour, especially with constant interruptions.
Eventually, about 4 people in engineering grilled the applicant. We
then compared notes and passed it on to whomever was going to make the
final decision. The overall batting average was lousy. We hired one
clown that instantly retired on the job. Another specialized in
finding excuses not to show up to work. Yet another acted like he was
still working for his previous employer. Spending a day with the
applicant would have brought much of this to the surface, but that
didn't happen.
There's also a problem hiring engineers in very small companies. At
literally all of my employers, engineers were directly involved in all
aspects of product development, production, QA, and documentation. We
needed a very versatile engineer, capable of doing more than just
engineering. I didn't care if the candidate knew how to do
everything. However, I did care if he was able to learn new skills. I
was hired at one company to do RF design work, but spent the first 6
months cleaning up my predecessors mess on the production line.
>I also like to ask people what they designed last, and to describe
>some circuits.
Yep. We also did that. However, I ran into one odd problem with an
engineer from Japan. I could see that he was competent. However, I
had great difficulty determining what he did at his previous employer.
It wasn't a big secret as it was all on his resume. Yet, he wouldn't
talk about it. I eventually determined that in Japan, he was
considered part of a team. Discussing a project without the inclusion
of the team was like taking personal credit for the teams
accomplishments. When I switched my questions to reflect the
accomplishments of the team, the answers were forthcoming.
>"John Larkin" <jlar...@highlandtechnology.com> wrote in message >news:hcug88p745bp6jfpe1g6rbrmhpkv61an5h@4ax.com...
>> On Wed, 24 Oct 2012 19:22:24 -0400, Jamie
>> <jamie_ka1lpa_not_valid_after_ka1l...@charter.net> wrote:
>>>John Larkin wrote:
>>>> On Wed, 24 Oct 2012 16:44:06 -0400, Spehro Pefhany
>>>> <speffS...@interlogDOTyou.knowwhat> wrote:
>>>>>>>>>This is my first-pass qualifier question.
>>>>>>>>> +10V
>>>>>>>>> |
>>>>>>>>> |
>>>>>>>>> C
>>>>>>>>>+5V--------------B
>>>>>>>>> E
>>>>>>>>> |
>>>>>>>>> 1K
>>>>>>>>> |
>>>>>>>>> gnd
>>>>>>>>>(drawn like a real schematic, on a whiteboard)
>>>>>>>>>What is the base voltage? (one answer: 0.6!)
>>>>>>>>>What is the emitter voltage?
>>>>>>>>>What is the collector voltage?
>>>>>>>>>What is the base current?
>>>>>>>>>What is the emitter current?
>>>>>>>>>What is the collector current?
>>>>>>>>>Any other comments?
>>>>>>>>Germanium or silicon?
>>>>>>>>PNP or NPN? ;)
>>>>>>>>Roberto Waltman
>>>>>>>>[Running for cover...]
>>>>>>>For a (slightly) more advanced test..
>>>>>>>>> -10V
>>>>>>>>> |
>>>>>>>>> 1K
>>>>>>>>> |
>>>>>>>>> C
>>>>>>>>>-5V--------------B NPN
>>>>>>>>> E
>>>>>>>>> |
>>>>>>>>> gnd
>>>>>>One more question: What is the pressure of the magic smoke inside the
>>>>>>transistor?
>>>>>If it's a jellybean NPN, the E-B junction is going to be just fine
>>>>>(typically they break down around 8-9V and are rated for at least 5V),
>>>>>and the answers are, as JL says, going to be about the same as his
>>>>>example except for the higher base current due to typically low
>>>>>reverse beta. But it fits a different visual pattern, being an NPN
>>>>>with E grounded-- it's probably not obvious that it's a
>>>>>"collector-follower".
>>>> That's way overkill for a first question interview. If some kid
>>>> doesn't know about reverse beta, I wouldn't chuck him out right away.
>>>> I measured a BFT25 as having reverse beta about 4.
>>> And each time some one comments on that, I still try to think of an
>>>application where that would prosper? Maybe something in speed switching
>>>. etc..
>>> Kind of reminds me of ECL logic in a way.
>>>Jamie
>> I have used a BFT25 to ground an AC-coupled analog signal, in a
>> gain-switching application. You need a lot of base current to clamp
>> the negative part of the swing, since reverse beta is low.
William Elliot wrote:
> On Tue, 23 Oct 2012, Robert Baer wrote:
>>> On 23/10/2012 4:20 PM, Sylvia Else wrote:
>>>> On 23/10/2012 12:31 PM, RichD wrote:
>>>>> What are the last 3 digits of 171 ^ 172?
>>> Indeed thinking along similar lines, one can write 171 as (170 + 1).
>>> So we need (170 + 1)^172 mod 1000.
>>> Again, only the last three terms can be non-zero mod 1000.
>>> a) (172 * 171) / 2 * 170^2
>>> b) 172 * 170
>>> c) 1
>>> a) is 56 * 171 * 170^2.
>>> 170^2 is 900 mod (square the 7, and drop the leading 4).
>>> Now mutiply by the 6 and 1, and drop the leading 5, gives 400.
>>> b) is 2 * 170 + 70 * 70 mod 1000 = 340 + 900 mod 1000.
>>> So the sum is 400 + 340 + 900 + 1 mod 1000, or, unsurprisingly 641.
>> I am reminded of another "puzzle": how many terminal zeros are there in
>> 4089! (4089 factorial)?
William Elliot wrote:
> On Tue, 23 Oct 2012, Butch Malahide wrote:
>> On Oct 23, 11:59 pm, William Elliot<ma...@panix.com> wrote:
>>> On Tue, 23 Oct 2012, Robert Baer wrote:
>>>> I am reminded of another "puzzle": how many terminal zeros are there in
>>>> 4089! (4089 factorial)?
>>>> In order to insure my place in infamy, I created my own irrelevant
>>>> questions. Well, not exactly a question, more of a process. I would
>>>> show the applicant a PCB from the company product, and ask them to
>>>> identify components that they've worked with in the past, and give a
>>>> short description on what they do. Ostensively, this was to gauge
>>>> experience. Most would recognize about 25% of the major RF
>>>> components, which was about what I would expect. I then explained
>>>> what the board did, what products it was used in, some of the parts
>>>> they missed, and generally filled in the blanks.
>>>> I would then give the applicant a tour of the factory, production
>>>> line, grab a cup of coffee, and return to my messy office where I
>>>> would hand the applicant the exact same PCB, and ask the exact same
>>>> question. The real test was whether they were paying attention and
>>>> how much of my explanation they were able to recall. 50% recognition
>>>> was typical. Exceptional engineers and techs, which unfortunately we
>>>> couldn't afford to hire, would come very close to 100% recognition and
>>>> recall.
>>>> Other companies use the interview for testing problem solving skills.
>>>> <http://en.wikipedia.org/wiki/Microsoft_Interview>
>>>> Now, that's what I call relevant questions. However, it's
>>>> occasionally abused by asking the applicant to solve a real problem
>>>> with a current product. I once interviewed at a company that did that
>>>> to me. I was presented with a large schematic of the product, and
>>>> asked to critique the design. After a few minutes of hasty back of
>>>> the envelope calculations, I declared the product to be over-designed,
>>>> a tolerance accumulation nightmare, and that there were several active
>>>> stages that were superfluous. I offered specific recommendations on
>>>> what should be changed. I then expect to be thanked for my brilliant
>>>> insights. Instead, I was diplomatically thrown out the door. It
>>>> seems that the manager that was conducting the interview had designed
>>>> the product, and did not take kindly to criticism. So much for a
>>>> relevant problem solving interview.
>>> You didn't want to work there, so it was a great interview.
>>> (drawn like a real schematic, on a whiteboard)
>>> What is the base voltage? (one answer: 0.6!)
>> During the dot.com bubble, I worked for a software company that would
>> (by way of analogy) have employed the person on the grounds that they at
>> least knew which was the base.
> With that answer? Are you sure? ;-)
>> Apparently, the management thought that
>> any 'programmer' was better than no programmer.
> Been there. It's taken some convincing, at times, to get management to
> understand that sometimes more people = less work. It's often too late to
> improve a schedule, by *any* means.
Well, there IS a way...fire absolutely everybody and dump the company..
On Oct 23, Sylvia Else <syl...@not.at.this.address> wrote:
> >>> I saw this posed as an interview question:
> >>> (usual exponent notation)
> >>> What are the last 3 digits of 171 ^ 172?
> >>> Presumably, one is given pen and paper.
> >>> Is there a trick here? The second digit isn't too tough,
> >>> but the third is a lot of work.
> >> That's a really stupid interview question for an electronic design
> >> position.
> > It would be a valid question if you apply for a job as a stock broker.
?
> Perhaps not even then. All the offered solutions require knowledge of
> congruences, which is part of basic number theory. Unless a person has
> done a maths degree, or happens to have encountered it in passing (my
> situation), they're unlikely to be sure that the required steps are
> mathematically valid.
It's a firm that does financial modeling. They're recruiting people
to write code, for statistical analysis etc.; quants, not brokers.
It's a very good question for such a position. OF course, you want
someone unafraid of math, but better yet, it requires some original
thinking, a problem that wasn't on the exam.
>>>>> In order to insure my place in infamy, I created my own irrelevant
>>>>> questions. Well, not exactly a question, more of a process. I would
>>>>> show the applicant a PCB from the company product, and ask them to
>>>>> identify components that they've worked with in the past, and give a
>>>>> short description on what they do. Ostensively, this was to gauge
>>>>> experience. Most would recognize about 25% of the major RF
>>>>> components, which was about what I would expect. I then explained
>>>>> what the board did, what products it was used in, some of the parts
>>>>> they missed, and generally filled in the blanks.
>>>>> I would then give the applicant a tour of the factory, production
>>>>> line, grab a cup of coffee, and return to my messy office where I
>>>>> would hand the applicant the exact same PCB, and ask the exact same
>>>>> question. The real test was whether they were paying attention and
>>>>> how much of my explanation they were able to recall. 50% recognition
>>>>> was typical. Exceptional engineers and techs, which unfortunately we
>>>>> couldn't afford to hire, would come very close to 100% recognition and
>>>>> recall.
>>>>> Other companies use the interview for testing problem solving skills.
>>>>> <http://en.wikipedia.org/wiki/Microsoft_Interview>
>>>>> Now, that's what I call relevant questions. However, it's
>>>>> occasionally abused by asking the applicant to solve a real problem
>>>>> with a current product. I once interviewed at a company that did that
>>>>> to me. I was presented with a large schematic of the product, and
>>>>> asked to critique the design. After a few minutes of hasty back of
>>>>> the envelope calculations, I declared the product to be over-designed,
>>>>> a tolerance accumulation nightmare, and that there were several active
>>>>> stages that were superfluous. I offered specific recommendations on
>>>>> what should be changed. I then expect to be thanked for my brilliant
>>>>> insights. Instead, I was diplomatically thrown out the door. It
>>>>> seems that the manager that was conducting the interview had designed
>>>>> the product, and did not take kindly to criticism. So much for a
>>>>> relevant problem solving interview.
>>>> You didn't want to work there, so it was a great interview.
>>>> (drawn like a real schematic, on a whiteboard)
>>>> What is the base voltage? (one answer: 0.6!)
>>> During the dot.com bubble, I worked for a software company that would
>>> (by way of analogy) have employed the person on the grounds that they at
>>> least knew which was the base.
>> With that answer? Are you sure? ;-)
>>> Apparently, the management thought that
>>> any 'programmer' was better than no programmer.
>> Been there. It's taken some convincing, at times, to get management to
>> understand that sometimes more people = less work. It's often too late to
>> improve a schedule, by *any* means.
> Well, there IS a way...fire absolutely everybody and dump the company..
That certainly an option but it doesn't meet the stated goals.
> > What are the last 3 digits of 171 ^ 172?
> > Is there a trick here?
> a = 171; d = 1000
> b = 172 = 128 + 32 + 8 + 4
> Calculate:
> a^2 mod d = 241
> a^4 = (a^2)^2 mod d = 241^2 mod d = 81
> a^8 = (a^4)^2 mod d
> a^32 = (a^8)^4 = [(a^8)^2]^2 mod d
> a^128 = (a^32)^4 = [(a^32)^2]^2 mod d
> and use those results to calculate
> a^172 = a^128 a^32 a^8 a^4 mod d.
Yes, that's probably what they expect, and would
get you the job. It's not too much work.
I did it by looking at periodicities in the second digit, as one
does the multiplications. But that became excessive, in
the third digit.
But I wonder if there are some obscure number theory short
cuts. Which might give you a leg up on other candidates,
though it's doubtful the interviewers expect that.
On Oct 22, Sylvia Else <syl...@not.at.this.address> wrote:
> > What are the last 3 digits of 171 ^ 172?
> > Presumably, one is given pen and paper.
> > Is there a trick here? The second digit isn't too tough,
> > but the third is a lot of work.
> Don't know about a trick. After noting the (*) result below using a
> caculator, I managed to get the right answer from scratch on a
> whiteboard, but I doubt I'd have managed to do it in an interview
> environment.
> Anyway, since we're only looking at the last three digits, we can do
> calculations mod 1000.
In modulo arithmetic, I thought the modulo had to be a prime number.
> Doing 171^2 by long multiplication, keeping only the last three digits
> gives 241.
> 241^2 by long multiplication, keeping only the last three digits is 81.
> So 171^4 = 81 mod 1000 (this is the * result) and 171^172 = 81^43 mod
> 1000 = 9^86 mod 1000.
> Now 9 is 10 - 1, so we have 171^172 = (10 - 1)^86 mod 1000.
> If we were to expand that using the binomial theorem, all the terms
> would by multiples of 1000, and therefore unimportant, except the last
> three.
> The last three are
> a)(86 * 85) / 2 * 10^2 * (-1)^84,
> b) 86 * 10^1 * (-1)^85, and
> c)(-1)^86.
> a) can also be written 43 * 85 * 100, and since we're taking it modulo
> 1000, we need only multiply the 3 by the 5, giving 15, and keep only the
> 5, so a) is 500 mod 1000.
> b) is -860
> c) is 1
> So the result is 500 - 860 + 1 = -359 mod 1000.
> But that's negative, so add 1000 to make it positive, and the answer is 641.
