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

It is currently 15 Oct 2019, 15:08

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If 60! is written out as an integer, with how many

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 15 Aug 2013
Posts: 228
Re: How many zeroes at the end of 60!?  [#permalink]

Show Tags

New post 19 May 2014, 18:06
VeritasPrepKarishma wrote:
russ9 wrote:
How do we know that there aren't more factors of 2 vs. 5? If there were more factors of 2, would we modify the equation to account for powers of 2 in the denominator?

Thanks!


The point is that you need both a 2 and a 5 to make a 10. If I have 100 2s but only 3 5s, I can make only 3 10s. No number of 2s alone can make a 10. So even if there are many more 2s, they are useless to us because we have limited number of 5s.


Hi Karishma and @WoundedTiger, makes sense. Thanks!

Would it make sense to compare the 2's in the denominator as well and choose the one's that have the lower exponent out of the two or are the 5's ALWAYS going to be less than the 2's?
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: How many zeroes at the end of 60!?  [#permalink]

Show Tags

New post 19 May 2014, 19:41
russ9 wrote:
VeritasPrepKarishma wrote:
russ9 wrote:
How do we know that there aren't more factors of 2 vs. 5? If there were more factors of 2, would we modify the equation to account for powers of 2 in the denominator?

Thanks!


The point is that you need both a 2 and a 5 to make a 10. If I have 100 2s but only 3 5s, I can make only 3 10s. No number of 2s alone can make a 10. So even if there are many more 2s, they are useless to us because we have limited number of 5s.


Hi Karishma and @WoundedTiger, makes sense. Thanks!

Would it make sense to compare the 2's in the denominator as well and choose the one's that have the lower exponent out of the two or are the 5's ALWAYS going to be less than the 2's?


Every second number has a 2 while every fifth number has a 5. So number of 2s will always be greater than the number of 5s.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern
Intern
avatar
Joined: 26 Apr 2015
Posts: 3
Re: If 60! is written out as an integer, with how many  [#permalink]

Show Tags

New post 29 Apr 2015, 20:09
Awesome learning from this post ; Thanks everyone
Manager
Manager
avatar
B
Joined: 08 Nov 2015
Posts: 56
GMAT 1: 460 Q32 V22
Re: If 60! is written out as an integer, with how many  [#permalink]

Show Tags

New post 25 Sep 2016, 03:36
Orange08 wrote:
If 60! is written out as an integer, with how many consecutive 0’s will that integer end?

A. 6
B. 12
C. 14
D. 42
E. 56



Correct answer is C.

60/5 + 60/25. Quotient is 12 + 2 = 14
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4778
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: If 60! is written out as an integer, with how many  [#permalink]

Show Tags

New post 25 Sep 2016, 08:11
Orange08 wrote:
If 60! is written out as an integer, with how many consecutive 0’s will that integer end?

A. 6
B. 12
C. 14
D. 42
E. 56


10 Sec Solution

60/5 = 12
12/5 = 2

So, Trailing Zeroe's will be 14 ( 12 + 2 ) , answer will be (C) 14

_________________
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 )
Intern
Intern
avatar
B
Joined: 17 Dec 2016
Posts: 38
GMAT 1: 540 Q38 V26
Reviews Badge
Re: If 60! is written out as an integer, with how many  [#permalink]

Show Tags

New post 10 Feb 2017, 15:52
Orange08 wrote:
Many thanks.
silly question probably - can real test contain such question?


Regarding the concept, which Bunuel mentioned, yes. However, I would expect the wording to be different.
Manager
Manager
avatar
B
Joined: 23 Dec 2013
Posts: 138
Location: United States (CA)
GMAT 1: 710 Q45 V41
GMAT 2: 760 Q49 V44
GPA: 3.76
Reviews Badge
Re: If 60! is written out as an integer, with how many  [#permalink]

Show Tags

New post 22 May 2017, 20:28
1
Orange08 wrote:
If 60! is written out as an integer, with how many consecutive 0’s will that integer end?

A. 6
B. 12
C. 14
D. 42
E. 56


Here it's best to think about the problem conceptually. If we want to know then number of consecutive zeroes at the end of 60!, then we are really asking for the number of pairs of 2's and 5's. Since there are more multiples of 2 than 5 within 1-60, 5 will be the limiting factor/agent.

As a result, we can simplify find the number of multiples of 5 between 1 and 60 (12) then add two more for 50 and 25 that each contribute an extra five. The total number of 5's in this prime factorization is thus 12+2 =14.
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4002
Location: Canada
Re: If 60! is written out as an integer, with how many  [#permalink]

Show Tags

New post 19 Apr 2018, 16:07
Top Contributor
1
Orange08 wrote:
If 60! is written out as an integer, with how many consecutive 0’s will that integer end?

A. 6
B. 12
C. 14
D. 42
E. 56


60! = (1)(2)(3)(4)(5)(6) . . . (57)(58)(59)(60)

KEY CONCEPT: For every pair of one 2 and one 5, we get a product of 10, which accounts for one zero at the end of the integer.
So, the question is "How many pairs of one 2 and one 5 are "hiding" in the product?"

Well, there is no shortage of 2's hiding in the product. In fact, there are FAR MORE 2's than 5's. So, all we need to do is determine how many 5's are hiding in the product.
60! = (1)(2)(3)(4)(5)(6) . . . (57)(58)(59)(60)
= (1)(2)(3)(4)(5)(6)(7)(8)(9)(2)(5)(11)...(3)(5)...(4)(5)...(5)(5)...(6)(5)...(7)(5)...(8)(5)...(9)(5)...(2)(5)(5)...(11)(5)...(56)(57)(58)(59)(12)(5)
In total, there are 14 5's hiding in the product.
And there are MORE THAN 14 2's hiding in the product.

So, there are 14 pairs of 2's and 5'2, which means the integer ends with 14 zeros

Answer:C

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Intern
Intern
avatar
Joined: 15 Sep 2018
Posts: 3
Re: If 60! is written out as an integer, with how many  [#permalink]

Show Tags

New post 15 Sep 2018, 12:34
I'm a bit confused with the concept of "Trailing zeros".
According to wikipedia, "Trailing zeros to the right of a decimal point, as in 12.3400, do not affect the value of a number and may be omitted if all that is of interest is its numerical value. This is true even if the zeros recur infinitely". However, zeros to the left of a decimal point are introduced as "trailing zeros" in this forum. I just wanted to clarify the meaning of "trailing zeros" here.

Thank you!!
Senior PS Moderator
User avatar
D
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 737
GMAT 1: 740 Q50 V40
GMAT 2: 770 Q51 V42
GMAT ToolKit User Reviews Badge
Re: If 60! is written out as an integer, with how many  [#permalink]

Show Tags

New post 15 Sep 2018, 13:46
1
owlette wrote:
I'm a bit confused with the concept of "Trailing zeros".
According to wikipedia, "Trailing zeros to the right of a decimal point, as in 12.3400, do not affect the value of a number and may be omitted if all that is of interest is its numerical value. This is true even if the zeros recur infinitely". However, zeros to the left of a decimal point are introduced as "trailing zeros" in this forum. I just wanted to clarify the meaning of "trailing zeros" here.

Thank you!!


It is certain that 60! will not be a decimal but a integer. Anything larger than 5! Ends in a zero. A trailing zero here is the number of zeros to the right of first non-zero digit and to the left of the decimal point. Integer 2 can be written as 2.0
So 60! = ABCxx0000xx0.0


Hope you get the usage.
Best,
Gladi

Posted from my mobile device
_________________
Regards,
Gladi



“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58340
Re: If 60! is written out as an integer, with how many  [#permalink]

Show Tags

New post 16 Sep 2018, 01:21
1
owlette wrote:
I'm a bit confused with the concept of "Trailing zeros".
According to wikipedia, "Trailing zeros to the right of a decimal point, as in 12.3400, do not affect the value of a number and may be omitted if all that is of interest is its numerical value. This is true even if the zeros recur infinitely". However, zeros to the left of a decimal point are introduced as "trailing zeros" in this forum. I just wanted to clarify the meaning of "trailing zeros" here.

Thank you!!


Links below should help:

Everything about Factorials on the GMAT
Power of a Number in a Factorial Problems
Trailing Zeros Problems

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
_________________
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8048
Location: United States (CA)
Re: If 60! is written out as an integer, with how many  [#permalink]

Show Tags

New post 15 Mar 2019, 18:45
Orange08 wrote:
If 60! is written out as an integer, with how many consecutive 0’s will that integer end?

A. 6
B. 12
C. 14
D. 42
E. 56


To determine the number of trailing zeros in a number, we need to determine the number of 5-and-2 pairs within the prime factorization of that number.

Since we know there are fewer 5s in 60! than 2s, we can find the number of 5s and thus be able to determine the number of 5-and-2 pairs.

To determine the number of 5s within 60!, we can use the following shortcut in which we divide 60 by 5, then divide the quotient of 60/5 by 5 and continue this process until we no longer get a nonzero quotient.

60/5 = 12

12/5 = 2 (we can ignore the remainder)

Since 2/5 does not produce a nonzero quotient, we can stop.

The final step is to add up our quotients; that sum represents the number of factors of 5 within 60!.

Thus, there are 12 + 2 = 14 factors of 5 within 60!

Since there are 14 factors of 5 within 60!, there are 14 5-and-2 pairs and thus 14 trailing zeros.

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Intern
avatar
B
Joined: 03 Apr 2018
Posts: 38
Premium Member CAT Tests
Re: If 60! is written out as an integer, with how many  [#permalink]

Show Tags

New post 20 Sep 2019, 05:55
Is there any other way to count the number of trailing zeroes? What if we forget the formula in exam - can I calculate by counting 2s*5s and number of 10s (10, 20, 30, 40,..). This way I counted 13 trailing zeroes and not 14. Can someone please explain.
GMAT Club Bot
Re: If 60! is written out as an integer, with how many   [#permalink] 20 Sep 2019, 05:55

Go to page   Previous    1   2   [ 33 posts ] 

Display posts from previous: Sort by

If 60! is written out as an integer, with how many

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne