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

 It is currently 17 Jul 2018, 14:08

### 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

# If (10!)/(2y) is an odd integer, what is y?

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 863
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
If (10!)/(2y) is an odd integer, what is y? [#permalink]

### Show Tags

03 Oct 2015, 02:47
3
00:00

Difficulty:

25% (medium)

Question Stats:

69% (00:51) correct 31% (01:14) wrong based on 134 sessions

### HideShow timer Statistics

If $$\frac{10!}{2^y}$$ is an odd integer, what is y?

A. 5
B. 6
C. 7
D. 8
E. 10

_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Current Student
Joined: 20 Mar 2014
Posts: 2641
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If (10!)/(2y) is an odd integer, what is y? [#permalink]

### Show Tags

03 Oct 2015, 03:30
reto wrote:
If (10!)/(2y) is an odd integer, what is y?

A. 5
B. 6
C. 7
D. 8
E. 10

reto, check the question.

10!/16 will still give you an even integer. 10! has 2^8 in it and for obtaining an odd integer when you divide 10! by another integer, you need to cancel out all 8 2s.
Retired Moderator
Joined: 29 Apr 2015
Posts: 863
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Re: If (10!)/(2y) is an odd integer, what is y? [#permalink]

### Show Tags

03 Oct 2015, 03:51
Engr2012 wrote:
reto wrote:
If (10!)/(2y) is an odd integer, what is y?

A. 5
B. 6
C. 7
D. 8
E. 10

reto, check the question.

10!/16 will still give you an even integer. 10! has 2^8 in it and for obtaining an odd integer when you divide 10! by another integer, you need to cancel out all 8 2s.

Thanks it's done. You are very attentive!
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

SVP
Joined: 08 Jul 2010
Posts: 2119
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: If (10!)/(2y) is an odd integer, what is y? [#permalink]

### Show Tags

03 Oct 2015, 04:34
1
reto wrote:
If $$\frac{10!}{2^y}$$ is an odd integer, what is y?

A. 5
B. 6
C. 7
D. 8
E. 10

10! = 1*2*3*4*5*6*7*8*9*10

For calculating the power of 2 in 10!

$$2*4*6*8*10 have 2^1*2^2*2^1*2^3*2^1 = 2^8$$

i.e. $$10! = 2^8*Odd Numbers$$

Hence, 10!/2^8 will be an Odd Integer

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Intern
Joined: 01 Nov 2015
Posts: 37
Location: India
Concentration: Marketing, Entrepreneurship
WE: Engineering (Computer Software)
Re: If (10!)/(2y) is an odd integer, what is y? [#permalink]

### Show Tags

11 Dec 2015, 19:11
A odd number is one that does not have 2 as its one of the prime factor

10! has a total of 8 factors of 2

So, we need to remove all these 8 factors to make the number odd

If we remove < 8 2 factors, the number will be even, and > 8 => number will not be an integer

Ans. D
Manager
Joined: 01 Jan 2016
Posts: 57
GPA: 3.75
WE: Engineering (Energy and Utilities)
Re: If (10!)/(2y) is an odd integer, what is y? [#permalink]

### Show Tags

26 Aug 2017, 08:44
The formula for finding the number of powers of a prime number p, in the n! is
n/p+n/p^2+n/p^3 ... till p^x≤n (https://gmatclub.com/forum/math-number- ... 88376.html)

Applying formula, p=2,n=10, x=3(since 2^3<10 but 2^4>10)
so, 10/2+10/4+10/8=5+2+1=8
So since 10! has 8 powers of 2, to make it odd, 2 in denominator needs to be raised to 8.
Option D
_________________

If you like it, give kudos. Thanks

The price of success is hard work, dedication to the job at hand, and the determination that whether we win or lose, we have applied the best of ourselves to the task at hand.
~Vince Lombardi

Re: If (10!)/(2y) is an odd integer, what is y?   [#permalink] 26 Aug 2017, 08:44
Display posts from previous: Sort by

# Events & Promotions

 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®.