It is currently 19 Nov 2017, 07:25

### 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

# 14! is equal to which of the following?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 42247

Kudos [?]: 132677 [0], given: 12331

14! is equal to which of the following? [#permalink]

### Show Tags

20 Apr 2016, 01:04
Expert's post
2
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

87% (00:30) correct 13% (00:29) wrong based on 100 sessions

### HideShow timer Statistics

14! is equal to which of the following?

A. 87,178,291,200
B. 88,180,293,207
C. 89,181,294,209
D. 90,000,000,003
E. 91,114,114,114
[Reveal] Spoiler: OA

_________________

Kudos [?]: 132677 [0], given: 12331

Senior Manager
Joined: 11 Nov 2014
Posts: 362

Kudos [?]: 54 [0], given: 17

Location: India
WE: Project Management (Telecommunications)
Re: 14! is equal to which of the following? [#permalink]

### Show Tags

20 Apr 2016, 01:48
For sure it ends even number
that's A / E

since we have 10 in the multiplication, its A (ending with 0)

Kudos [?]: 54 [0], given: 17

Manager
Joined: 10 Apr 2016
Posts: 56

Kudos [?]: 9 [2], given: 7

Concentration: Strategy, Entrepreneurship
GMAT 1: 520 Q29 V30
GPA: 3.01
Re: 14! is equal to which of the following? [#permalink]

### Show Tags

20 Apr 2016, 02:02
2
KUDOS
Every factorial higher than 4! will have 0 as a units digit, so answer must be A
_________________

Took the Gmat and got a 520 after studying for 3 weeks with a fulltime job. Now taking it again, but with 6 weeks of prep time and a part time job. Studying every day is key, try to do at least 5 exercises a day.

Kudos [?]: 9 [2], given: 7

Math Expert
Joined: 02 Aug 2009
Posts: 5210

Kudos [?]: 5840 [2], given: 117

Re: 14! is equal to which of the following? [#permalink]

### Show Tags

20 Apr 2016, 02:56
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
14! is equal to which of the following?

A. 87,178,291,200
B. 88,180,293,207
C. 89,181,294,209
D. 90,000,000,003
E. 91,114,114,114

since 14! is PRODUCT of all numbers till 14, it should end in 0s in units and tens place.. as lower integer value of [] in $$[\frac{14}{5}] + [\frac{14}{5^2}]= 2$$
ONLY A has two 0s in end..
A
_________________

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

Kudos [?]: 5840 [2], given: 117

Intern
Joined: 29 Nov 2014
Posts: 4

Kudos [?]: [0], given: 4

Re: 14! is equal to which of the following? [#permalink]

### Show Tags

20 Apr 2016, 07:44
chetan2u wrote:
Bunuel wrote:
14! is equal to which of the following?

A. 87,178,291,200
B. 88,180,293,207
C. 89,181,294,209
D. 90,000,000,003
E. 91,114,114,114

since 14! is PRODUCT of all numbers till 14, it should end in 0s in units and tens place.. as lower integer value of [] in $$[\frac{14}{5}] + [\frac{14}{5^2}]= 2$$
ONLY A has two 0s in end..
A

Can you explain the solution more ? why do you divide 14/5 ?

Kudos [?]: [0], given: 4

Math Expert
Joined: 02 Aug 2009
Posts: 5210

Kudos [?]: 5840 [0], given: 117

14! is equal to which of the following? [#permalink]

### Show Tags

20 Apr 2016, 07:52
ghofran wrote:
chetan2u wrote:
Bunuel wrote:
14! is equal to which of the following?

A. 87,178,291,200
B. 88,180,293,207
C. 89,181,294,209
D. 90,000,000,003
E. 91,114,114,114

since 14! is PRODUCT of all numbers till 14, it should end in 0s in units and tens place.. as lower integer value of [] in $$[\frac{14}{5}] + [\frac{14}{5^2}]= 2$$
ONLY A has two 0s in end..
A

Can you explain the solution more ? why do you divide 14/5 ?

hi,
this is the method to find number of 5 in 14!..
since 14! contains 1*2*3..*5*..*9*10*11..14, 14/5=2.8 -- lower integer is 2--you can see it has two 5 in its product- 5 and 10..
so what you are doing by dividing is you are finding the multiple of 5 till 14..
the moment it is 15!.. our answer is 15/5 =3 so 5,10 and 15...

say it goes up to 25!..
here we have 25/5 + 25/5^2+ 25/5^3.. = 5+1+0=6..
the 6 are ONE each in 5,10,15,20 and TWO in 25..

very important concept in FACTORIALS..
Please let me know if there is some query
_________________

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

Kudos [?]: 5840 [0], given: 117

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3097

Kudos [?]: 1114 [1], given: 327

Location: India
GPA: 3.5
14! is equal to which of the following? [#permalink]

### Show Tags

20 Apr 2016, 07:59
1
KUDOS
Bunuel wrote:
14! is equal to which of the following?

A. 87,178,291,200
B. 88,180,293,207
C. 89,181,294,209
D. 90,000,000,003
E. 91,114,114,114

This problem can be solved at a glance, no need of calculation.

14! is divisible by 5 and hence the units digit will be 0

Among the given options only (A) follows.
_________________

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 )

Kudos [?]: 1114 [1], given: 327

Manager
Status: single
Joined: 19 Jan 2015
Posts: 95

Kudos [?]: 15 [0], given: 1170

Location: India
GPA: 3.2
WE: Sales (Pharmaceuticals and Biotech)
Re: 14! is equal to which of the following? [#permalink]

### Show Tags

20 Apr 2016, 08:46
after 4!, every factorial last digit ends in 0.
5!=120
6!=720.

so only option A last digit ends with 0.
So option A is correct.

Kudos [?]: 15 [0], given: 1170

Retired Moderator
Joined: 12 Aug 2015
Posts: 2213

Kudos [?]: 869 [0], given: 602

Re: 14! is equal to which of the following? [#permalink]

### Show Tags

20 Apr 2016, 09:54
Abhishek009 wrote:
Bunuel wrote:
14! is equal to which of the following?

A. 87,178,291,200
B. 88,180,293,207
C. 89,181,294,209
D. 90,000,000,003
E. 91,114,114,114

This problem can be solved at a glance, no need of calculation.

14! is divisible by 5 and hence the units digit will be 0

Among the given options only (A) follows.

Disagree
The way to solve by only a glance is that it is divisible by 5 and 2 both(you wrote it is divisible by 5)
E.G 25 is divisible by 5 and it ends in 5 too

Small technical error .
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 869 [0], given: 602

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3097

Kudos [?]: 1114 [0], given: 327

Location: India
GPA: 3.5
14! is equal to which of the following? [#permalink]

### Show Tags

20 Apr 2016, 10:18
stonecold wrote:
Abhishek009 wrote:
Bunuel wrote:
14! is equal to which of the following?

A. 87,178,291,200
B. 88,180,293,207
C. 89,181,294,209
D. 90,000,000,003
E. 91,114,114,114

This problem can be solved at a glance, no need of calculation.

14! is divisible by 5 and hence the units digit will be 0

Among the given options only (A) follows.

Disagree
The way to solve by only a glance is that it is divisible by 5 and 2 both(you wrote it is divisible by 5)
E.G 25 is divisible by 5 and it ends in 5 too

Small technical error .

I agree U are dividing by 2 but consider this -

5! = 5*4*3*2*1 =>5^1*3^1*2^3

Check there are 3 two's that doesn't mean there will be 3 zeros in 5!

Remember this short little form { Something I learnt during my CAT days }

Quote:
The number of trailing zeroe's in a factorial is the highest power of 5

I am just working around the same form to answer the question quickly....

Check this formula to any factorial - 10,15 ,20....... ( U will get it )

Further for this problem a quick glance at the options U will notice only option (A) has a trailing 0, so U need to find if the factorial is divisible by 5 or not.....

Quote:
E.G 25 is divisible by 5 and it ends in 5 too

No of 5s in 25! is -

25/5 = 5
5/5 =1

Total no of 5's in 25! is 6 ( 5+ 1)

No of 2s in 25! is -

25/2 = 12
12/2 = 6
6/2 = 3
3/2 = 1

Total no of 2's in 25! is 22 ( 12+6+3+1)

In 25 ! (No of 5's < No of 2's)

So, 25 ! will have 6 zero's in the end, though no of 2's in 25! is more than no of 5's.

Hope I am clear...
_________________

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 )

Kudos [?]: 1114 [0], given: 327

Director
Joined: 24 Nov 2015
Posts: 586

Kudos [?]: 40 [0], given: 231

Location: United States (LA)
Re: 14! is equal to which of the following? [#permalink]

### Show Tags

12 Sep 2017, 12:31
After 4! any factorial number must end in unit's digit as 0
we don't need to actually calculate the value of 14!
So the answer is straightforward option A

Kudos [?]: 40 [0], given: 231

Re: 14! is equal to which of the following?   [#permalink] 12 Sep 2017, 12:31
Display posts from previous: Sort by