Author 
Message 
TAGS:

Hide Tags

SC Moderator
Joined: 13 Apr 2015
Posts: 1706
Location: India
Concentration: Strategy, General Management
GPA: 4
WE: Analyst (Retail)

If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing
[#permalink]
Show Tags
26 Apr 2016, 04:14
Question Stats:
52% (01:45) correct 48% (02:14) wrong based on 60 sessions
HideShow timer Statistics
If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing zeros does n have? A) 94 B) 95 C) 96 D) 97 E) 98 Question: Self Made OA after 12 hours
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Aug 2009
Posts: 6785

If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing
[#permalink]
Show Tags
26 Apr 2016, 04:44
Vyshak wrote: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing zeros does n have?
A) 22
B) 23
C) 24
D) 25
E) 26
Question: Self Made OA after 12 hours n = 5 * 10 * 15 * 20 * 25 ........... * 500, take out 5 from each term  \(n= 5^{\frac{500}{5}}*1*2*3*...99*100 = 5^{100}*100!..\) since there are enough of 5s lets see how many 2s are there.. \([\frac{100}{2}]+[\frac{100}{4}]+[\frac{100}{8}]+[\frac{100}{16}]+[\frac{100}{32}]+[\frac{100}{64}] = 50+25+12+6+3+1 = 97..\) so it will have 97 trailing Zeroes Vyshak, a good Q, but please look into the answer or there may be some typo in Qs
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor




SC Moderator
Joined: 13 Apr 2015
Posts: 1706
Location: India
Concentration: Strategy, General Management
GPA: 4
WE: Analyst (Retail)

Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing
[#permalink]
Show Tags
26 Apr 2016, 04:56
chetan2u wrote: Vyshak wrote: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing zeros does n have?
A) 22
B) 23
C) 24
D) 25
E) 26
Question: Self Made OA after 12 hours n = 5 * 10 * 15 * 20 * 25 ........... * 500, take out from each \(n= 5^{\frac{500}{5}}*1*2*3*...99*100 = 5^{100}*100!..\) since there are enough of 5s lets see how many 2s are there.. \([\frac{100}{2}]+[\frac{100}{4}]+[\frac{100}{8}]+[\frac{100}{16}]+[\frac{100}{32}]+[\frac{100}{64}] = 50+25+12+6+3+1 = 97..\) so it will have 97 trailing Zeroes Vyshak, a good Q, but please look into the answer or there may be some typo in Qs Thanks Chetan . Updated the answer choices.



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4011
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing
[#permalink]
Show Tags
26 Apr 2016, 08:41
Vyshak wrote: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing zeros does n have?
A) 94
B) 95
C) 96
D) 97
E) 98
Question: Self Made OA after 12 hours n = 5 * 10 * 15 * 20 * 25 ........... * 500 n =5 (1*2*3*4*5.......100) n = 5 * 100! No of zeroes in 100! is 24 100/5 = 20 20/5 = 4 No of 2's in 100! is 97 100/2 = 50 50/5 = 25 25/2 = 12 12/ 2 = 6 6/2 =3 3/1 = 1 Now the fun begins 100! has 24 5's so it will have 24 trailing zeros, there is also one additional 5 and 73 two's left, definitely the blue part ca form at least one 0 Hence total number of zeroes will be 24 + 1 = 25 trailing zeroes...
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Math Expert
Joined: 02 Aug 2009
Posts: 6785

Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing
[#permalink]
Show Tags
26 Apr 2016, 08:59
Abhishek009 wrote: Vyshak wrote: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing zeros does n have?
A) 94
B) 95
C) 96
D) 97
E) 98
Question: Self Made OA after 12 hours n = 5 * 10 * 15 * 20 * 25 ........... * 500
n =5 (1*2*3*4*5.......100)n = 5 * 100! No of zeroes in 100! is 24 100/5 = 20 20/5 = 4 No of 2's in 100! is 97 100/2 = 50 50/5 = 25 25/2 = 12 12/ 2 = 6 6/2 =3 3/1 = 1 Now the fun begins 100! has 24 5's so it will have 24 trailing zeros, there is also one additional 5 and 73 two's left, definitely the blue part ca form at least one 0 Hence total number of zeroes will be 24 + 1 = 25 trailing zeroes...Hi, you have gone wrong in highlighted portion n = 5 * 10 * 15 * 20 * 25 ........... * 500 is NOT equal to n =5 (1*2*3*4*5.......100) BUT 5^100*(1*2*...100).. since you are taking out 5 from each term..
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Intern
Joined: 15 Apr 2016
Posts: 1

Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing
[#permalink]
Show Tags
28 Apr 2016, 13:59
Hi Chetan,
How did you go from 5^100*100! to 97?
Thanks, Diego.



Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing
[#permalink]
Show Tags
28 Apr 2016, 14:26



Math Expert
Joined: 02 Aug 2009
Posts: 6785

Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing
[#permalink]
Show Tags
28 Apr 2016, 19:28
dordonez12 wrote: Hi Chetan,
How did you go from 5^100*100! to 97?
Thanks, Diego. Hi, bunuel has already given you a link to check on. Otherwiseto check zeroes in th eend of a number, we require to know how many 10s are there in it.. 400 has two 10s, 10000 has four 10s and so on.. Now what is 100! It is 1*2*3*4*...*99*100  product of all numbers till 100.. How many 10s will it have.. will depend on number of 2s and 5s it will have.. we have seen that it has excess 5s in 5^100, so we check for number of 2s.. \([\frac{100}{2}]+[\frac{100}{4}]+[\frac{100}{8}]+[\frac{100}{16}]+[\frac{100}{32}]+[\frac{100}{64}] = 50+25+12+6+3+1 = 97..\) Now let me explain you withslightly smaller number.. say we are to find 2s in 15!.. \([\frac{15}{2}]+[\frac{15}{4}]+[\frac{15}{8}]+[\frac{15}{16}]\) Now 15/2 gives us how many multiple of 2s are there till 15 so 15/2 = 7.5 , we take only integer value , so 7 what are they 2,4,6,8,10,12,147 values now 15/4 gives us those number of 2s that add on due to multiples of 4; 15/4 = 3.75 what are they  4,8,12 3 values similarly number of multile of 8s, since they have three 2s 8 = 2*2*2 we have counted two 2s through above method, so 15/8 = 1.8 , so 1 value 8 beyond that 15/16 = 0.9, since it does not hane any 16s in it.. so TOTAL 2s = SUM of all the above
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Current Student
Joined: 12 Aug 2015
Posts: 2651

Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing
[#permalink]
Show Tags
02 May 2016, 18:44
Hey Vyshak and Everyone ...!!! I have some serious concerns about this question. I have seen many questions on the gmatclub to calculate the trailing zeros which can be done via easy manipulation of the number of two's and five's ad the numbers involved were small. Don't you think The Formula you guys use for calculating the number of trailing zeros is a bit out of concept here ; Since the numbers involved are always small. Do you really think GMAT will ask us this ? I am seriously asking question as if the answer is YES then i might well learn the formula stated above . Regards StoneCold
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



SC Moderator
Joined: 13 Apr 2015
Posts: 1706
Location: India
Concentration: Strategy, General Management
GPA: 4
WE: Analyst (Retail)

Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing
[#permalink]
Show Tags
02 May 2016, 22:38
stonecold wrote: Hey Vyshak and Everyone ...!!! I have some serious concerns about this question. I have seen many questions on the gmatclub to calculate the trailing zeros which can be done via easy manipulation of the number of two's and five's ad the numbers involved were small. Don't you think The Formula you guys use for calculating the number of trailing zeros is a bit out of concept here ; Since the numbers involved are always small. Do you really think GMAT will ask us this ? I am seriously asking question as if the answer is YES then i might well learn the formula stated above . Regards StoneCold Hi, This concept tests the 2's and 5's required to form zeros in a given expression and I don't see it as a formula. Its always better to understand the question and logic behind it rather than to learn the logic as a trick. This question can be solved in under 2 mins and can very well be tested in exam.



Current Student
Joined: 12 Aug 2015
Posts: 2651

Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing
[#permalink]
Show Tags
02 May 2016, 23:12
Vyshak wrote: stonecold wrote: Hey Vyshak and Everyone ...!!! I have some serious concerns about this question. I have seen many questions on the gmatclub to calculate the trailing zeros which can be done via easy manipulation of the number of two's and five's ad the numbers involved were small. Don't you think The Formula you guys use for calculating the number of trailing zeros is a bit out of concept here ; Since the numbers involved are always small. Do you really think GMAT will ask us this ? I am seriously asking question as if the answer is YES then i might well learn the formula stated above . Regards StoneCold Hi, This concept tests the 2's and 5's required to form zeros in a given expression and I don't see it as a formula. Its always better to understand the question and logic behind it rather than to learn the logic as a trick. This question can be solved in under 2 mins and can very well be tested in exam. No offence I still disagree Anyways Please Provide an alternative solution for people who don't want to use the formula I tried counting two's and zero's Now without using the formula  How can someone count the number of two's between 1 and 100 in two minutes? When its a small umber then counting the number of two;s is easy Any other way out? Regards StoneCold
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



SVP
Joined: 06 Nov 2014
Posts: 1887

If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing
[#permalink]
Show Tags
Updated on: 03 May 2016, 00:36
stonecold wrote: No offence I still disagree Anyways Please Provide an alternative solution for people who don't want to use the formula I tried counting two's and zero's Now without using the formula  How can someone count the number of two's between 1 and 100 in two minutes? When its a small umber then counting the number of two;s is easy Any other way out? Regards StoneCold Hi StoneCold, Whenever I type a reply to you, I am always afraid of that STUNNER :D About the question, yes you cannot calculate the number of 2's in between 1 and 100 in under 2 minutes, That is the precise reason why you need to remember the formula. And, yes this can very well be tested on the GMAT.



Math Expert
Joined: 02 Aug 2009
Posts: 6785

Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing
[#permalink]
Show Tags
03 May 2016, 00:33
stonecold wrote: Vyshak wrote: stonecold wrote: Hey Vyshak and Everyone ...!!! I have some serious concerns about this question. I have seen many questions on the gmatclub to calculate the trailing zeros which can be done via easy manipulation of the number of two's and five's ad the numbers involved were small. Don't you think The Formula you guys use for calculating the number of trailing zeros is a bit out of concept here ; Since the numbers involved are always small. Do you really think GMAT will ask us this ? I am seriously asking question as if the answer is YES then i might well learn the formula stated above . Regards StoneCold Hi, This concept tests the 2's and 5's required to form zeros in a given expression and I don't see it as a formula. Its always better to understand the question and logic behind it rather than to learn the logic as a trick. This question can be solved in under 2 mins and can very well be tested in exam. No offence I still disagree Anyways Please Provide an alternative solution for people who don't want to use the formula I tried counting two's and zero's Now without using the formula  How can someone count the number of two's between 1 and 100 in two minutes? When its a small umber then counting the number of two;s is easy Any other way out? Regards StoneCold Hi, I would say even if I do not know the formula, I will get to that by just moving on because formula comes out of the approach itself.. lets count 2s in 1 to 100 it could be in the form of 2s, 4s,8s etc.. how may multiples of 2 in 100 = 100/2 = 50.. how many multiples of 4 in 100 = 100/4 = 25....Actually its 25 of 4s which means 50 of 2s, but 25 of these have been counted in multiples of 2.. how many multiples of 8 in 100 = 100/8 = 12.5....so 12 how many multiples of 16 in 100 = 100/8 = 6....so 6 how many multiples of 32 in 100 = 100/32 = 3....so 3 how many multiples of 64 in 100 = 100/64 = 1....so 1. Add all of them to get your answer.. the formula is actually the addition of the step wise approach you take to find the number of 2s..
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



NonHuman User
Joined: 09 Sep 2013
Posts: 8073

Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing
[#permalink]
Show Tags
24 Sep 2017, 09:40
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing &nbs
[#permalink]
24 Sep 2017, 09:40






