GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Jun 2018, 09:58

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

SC Moderator
Joined: 13 Apr 2015
Posts: 1684
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing [#permalink]

### Show Tags

26 Apr 2016, 04:14
1
6
00:00

Difficulty:

75% (hard)

Question Stats:

52% (01:46) correct 48% (02:11) wrong based on 58 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

OA after 12 hours
Math Expert
Joined: 02 Aug 2009
Posts: 5886
If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing [#permalink]

### Show Tags

26 Apr 2016, 04:44
4
1
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

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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

SC Moderator
Joined: 13 Apr 2015
Posts: 1684
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
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
1
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

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: 3504
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
1
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

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: 5886
Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing [#permalink]

### Show Tags

26 Apr 2016, 08:59
1
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

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..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.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: 46128
Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing [#permalink]

### Show Tags

28 Apr 2016, 14:26
dordonez12 wrote:
Hi Chetan,

How did you go from 5^100*100! to 97?

Thanks,
Diego.

Check Trailing Zeros Questions and Power of a number in a factorial questions in our Special Questions Directory.

Hope it helps.
_________________
Math Expert
Joined: 02 Aug 2009
Posts: 5886
Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing [#permalink]

### Show Tags

28 Apr 2016, 19:28
1
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 2,4,6,8,10,12,14--7 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
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154
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 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 GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

SC Moderator
Joined: 13 Apr 2015
Posts: 1684
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
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 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.
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154
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 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 GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

SVP
Joined: 06 Nov 2014
Posts: 1888
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.

Originally posted by OptimusPrepJanielle on 03 May 2016, 00:16.
Last edited by OptimusPrepJanielle on 03 May 2016, 00:36, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 5886
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 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.

the formula is actually the addition of the step wise approach you take to find the number of 2s..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Non-Human User
Joined: 09 Sep 2013
Posts: 6999
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.
_________________
Re: If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing   [#permalink] 24 Sep 2017, 09:40
Display posts from previous: Sort by

# If n = 5 * 10 * 15 * 20 * 25 ........... * 500, how many trailing

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.