stumbled around this question on some practise test i found online.
No Idea how to solve this with MGMAT strategies.
can anyone help ? thanks
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- NabeelZ316
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- RonPurewal
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Re: How many zeros does 100! end with?
NabeelZ316 Wrote:stumbled around this question on some practise test i found online.
as per the forum rules, you need to cite the original source of the problem, including all answer choices.
you also need to provide the official correct answer.
please familiarize yourself with the forum rules before posting. thank you.
- NabeelZ316
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Re: How many zeros does 100! end with?
RonPurewal Wrote:NabeelZ316 Wrote:stumbled around this question on some practise test i found online.
as per the forum rules, you need to cite the original source of the problem, including all answer choices.
you also need to provide the official correct answer.
please familiarize yourself with the forum rules before posting. thank you.
sorry. here
is the question
so the source is practise question from gmat club
answer choices:
A. 20
B. 24
C. 25
D. 30
E. 32
correct answer is B
THANK U
- RonPurewal
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Re: How many zeros does 100! end with?
GMAT Club is just another forum, though. does GMAT Club actually produce its own problems? (if not, we still need a citation of the original source)
__
in any case—
please do not just post a problem and say "please advise", or "i had no idea how to solve this".
first of all, this is almost certainly not true. you probably STARTED the problem in some way... and then got stuck at some SPECIFIC point(s) along the way.
assuming that's the case... please post SPECIFIC QUESTIONS about the issue(s) you're having with the problem.
• what was your approach?
• what did you understand?
• what didn't you understand?
• where did you get stuck?
• did you try any alternate approaches?
etc.
thanks.
__
in the unlikely event that this actually is true—i.e., if you actually looked at this problem and GENUINELY thought, "wow, i have NO idea how to do this AT ALL"—then don't study this problem right now!
in that case, you're better off leaving the problem and returning to it later.
...in other words, if this is what's happening, then you're basically asking us for the the equivalent of an "answer key".
• the problem should come with an answer key (right?) ...so, in that case, you'd want to refer to the answer key.
• if we just "walk you through" the entire problem... that's not going to help you develop your problem-solving skills! moreover, you'd be wasting the problem, and GMAT problems are a fairly precious resource.
__
in any case—
please do not just post a problem and say "please advise", or "i had no idea how to solve this".
first of all, this is almost certainly not true. you probably STARTED the problem in some way... and then got stuck at some SPECIFIC point(s) along the way.
assuming that's the case... please post SPECIFIC QUESTIONS about the issue(s) you're having with the problem.
• what was your approach?
• what did you understand?
• what didn't you understand?
• where did you get stuck?
• did you try any alternate approaches?
etc.
thanks.
__
in the unlikely event that this actually is true—i.e., if you actually looked at this problem and GENUINELY thought, "wow, i have NO idea how to do this AT ALL"—then don't study this problem right now!
in that case, you're better off leaving the problem and returning to it later.
...in other words, if this is what's happening, then you're basically asking us for the the equivalent of an "answer key".
• the problem should come with an answer key (right?) ...so, in that case, you'd want to refer to the answer key.
• if we just "walk you through" the entire problem... that's not going to help you develop your problem-solving skills! moreover, you'd be wasting the problem, and GMAT problems are a fairly precious resource.
- NabeelZ316
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Re: How many zeros does 100! end with?
Hmm I tried searching for the source but unfortunately couldn't find the exact source. Anyway, I was just curious to know what the MGMAT approach for this question could be.
When I look at this question, I go 1x2x3x4x5......x99x100 = ANS and then look for zeros but I know this is not the right way to solve.
So thats why I decided to post here.
Thank you
When I look at this question, I go 1x2x3x4x5......x99x100 = ANS and then look for zeros but I know this is not the right way to solve.
So thats why I decided to post here.
Thank you
- RonPurewal
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Re: How many zeros does 100! end with?
well... i guess this question is sufficiently generic that we can discuss it (i.e., it's not really "special" enough to be legitimately under copyright).
still, though -- as i mentioned already -- it won't do you any good if i just TELL you how to solve the problem.
also, there's no such thing as "the MGMAT solution" to a problem! the point is to develop a mentality of investigation and pattern recognition, and to develop general problem-solving skills.
• think about numbers that end with ONE zero.
...what do these numbers have in common?
...where does that zero COME from? (what PRODUCES it?)
...can you make up a test that will correctly determine this?
• think about numbers that end with TWO zeroes.
...what do these numbers have in common?
...where do those 0's COME from? (what PRODUCES them?)
...can you make up a test that will correctly determine this?
• after you figure out these two situations, you should be able to generalize enough to solve this problem.
still, though -- as i mentioned already -- it won't do you any good if i just TELL you how to solve the problem.
also, there's no such thing as "the MGMAT solution" to a problem! the point is to develop a mentality of investigation and pattern recognition, and to develop general problem-solving skills.
• think about numbers that end with ONE zero.
...what do these numbers have in common?
...where does that zero COME from? (what PRODUCES it?)
...can you make up a test that will correctly determine this?
• think about numbers that end with TWO zeroes.
...what do these numbers have in common?
...where do those 0's COME from? (what PRODUCES them?)
...can you make up a test that will correctly determine this?
• after you figure out these two situations, you should be able to generalize enough to solve this problem.
- hcgoldberg
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Re: How many zeros does 100! end with?
Since this is a few days stale and I am myself curious on the answer, I will take a swing at it. Many apologies if I am breaking the rules by posing an answer to someone else's question...
Also this question definitely shows up somewhere in my MGMAT CAT or OG from 2017, but don't remember exactly where.
Super cool question.
So as Ron said, a 0 at the end occurs during a factor of 10. A factor of ten occurs when you have factors of 2 and 5 in equal amounts. So one way to do this is to figure out 100! then break it down to the prime factors then figure out the number of 2^x * 5^x where the x's are equal. This would be madness because calculating 100! ain't gonna happen.
Thus you need another way to think about how many factors of 2 or 5 exist. If you went after 2, it would be quite hard because there are a ton of factors of 2 in every number between 1 and 100. HOWEVER, there is a countable amount of 5's in the numbers between 1 and 100. One quick (and incomplete) way to figure this out is find the number of multiples of 5 between 1 and 100. This would give you 20. This is incomplete because some of those multiple of 5 do indeed have more than one five in them (e.g., 25). Where else are there two fives? 50, 75, 100. Thus if you count all of the numbers with the single factors of 5, you get 20. Then you get another 4 fives from the numbers with two factors of five. Then just to be safe, are there any numbers with three factors of 5? Nope, because we know that 5^3 is 125, which is larger than 100. Therefore we have a total of 24 factors of 5 in 100! And again since we know there are going to be many more than 24 factors of 2 in 100!, we can say with confidence that there will be 24 factors of 10 in 100! Lastly to go back to where we started X factors of 10 equals X zeros at the end. So bam, that's 24 trailing zeros in 100! folks.
When I saw the answer to this question the first time, I was blown away that I would have to think like this on the GMAT test. I'm just lucky now that I ran into before test day.
Happy holidays,
Harry
Also this question definitely shows up somewhere in my MGMAT CAT or OG from 2017, but don't remember exactly where.
Super cool question.
So as Ron said, a 0 at the end occurs during a factor of 10. A factor of ten occurs when you have factors of 2 and 5 in equal amounts. So one way to do this is to figure out 100! then break it down to the prime factors then figure out the number of 2^x * 5^x where the x's are equal. This would be madness because calculating 100! ain't gonna happen.
Thus you need another way to think about how many factors of 2 or 5 exist. If you went after 2, it would be quite hard because there are a ton of factors of 2 in every number between 1 and 100. HOWEVER, there is a countable amount of 5's in the numbers between 1 and 100. One quick (and incomplete) way to figure this out is find the number of multiples of 5 between 1 and 100. This would give you 20. This is incomplete because some of those multiple of 5 do indeed have more than one five in them (e.g., 25). Where else are there two fives? 50, 75, 100. Thus if you count all of the numbers with the single factors of 5, you get 20. Then you get another 4 fives from the numbers with two factors of five. Then just to be safe, are there any numbers with three factors of 5? Nope, because we know that 5^3 is 125, which is larger than 100. Therefore we have a total of 24 factors of 5 in 100! And again since we know there are going to be many more than 24 factors of 2 in 100!, we can say with confidence that there will be 24 factors of 10 in 100! Lastly to go back to where we started X factors of 10 equals X zeros at the end. So bam, that's 24 trailing zeros in 100! folks.
When I saw the answer to this question the first time, I was blown away that I would have to think like this on the GMAT test. I'm just lucky now that I ran into before test day.
Happy holidays,
Harry
- RonPurewal
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Re: How many zeros does 100! end with?
that ^^ is a correct analysis.
incidentally, i'm also going to lock the thread, since (as per what you said about possible sources) the problem definitely doesn't belong in this folder.
^^ this problem is a very nice illustration of the kind of thinking you'll have to do for this exam.
you don't need ANY "special" knowledge to solve this problem. (really, you don't need to KNOW anything other than that 0's at the ends of whole numbers come from being multiples of 10... and even that you could figure out by just looking at a few examples.)
beyond that, the problem is pretty much purely based on pattern recognition.
...and, at the end of the day, pattern recognition is EASILY the most important skill tested on the quant section.
incidentally, i'm also going to lock the thread, since (as per what you said about possible sources) the problem definitely doesn't belong in this folder.
When I saw the answer to this question the first time, I was blown away that I would have to think like this on the GMAT test
^^ this problem is a very nice illustration of the kind of thinking you'll have to do for this exam.
you don't need ANY "special" knowledge to solve this problem. (really, you don't need to KNOW anything other than that 0's at the ends of whole numbers come from being multiples of 10... and even that you could figure out by just looking at a few examples.)
beyond that, the problem is pretty much purely based on pattern recognition.
...and, at the end of the day, pattern recognition is EASILY the most important skill tested on the quant section.
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