BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Number Properties

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 304
Joined: Wed Jan 27, 2010 8:35 amFollowed by: 3 members
Location: International Space Station
Thanked: 11 times
by Aman verma » Tue Aug 09, 2011 8:57 am
Q: If 2^n can exactly divide P! such that the quotient is an odd positive integer , then the value of n which is NOT possible is:

I. 43

II. 44

III.45


a) I only

b) II only

c) III only

d) I and III both

e) I, II and III
800. Arjun's-Bird-Eye
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 2789
Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members
Location: Chennai, India
Thanked: 206 times
GMAT Score:640

by GmatKiss » Tue Aug 09, 2011 9:40 am
i feel some info is missing on P, not sure though!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 20
Joined: Thu Feb 17, 2011 9:13 am
Thanked: 1 times

by sharmishtha_goel » Tue Aug 09, 2011 11:13 am
IMO E.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 304
Joined: Wed Jan 27, 2010 8:35 amFollowed by: 3 members
Location: International Space Station
Thanked: 11 times

by Aman verma » Tue Aug 09, 2011 11:17 am
sharmishtha_goel wrote:IMO E.
How ?
800. Arjun's-Bird-Eye
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 20
Joined: Thu Feb 17, 2011 9:13 am
Thanked: 1 times

by sharmishtha_goel » Tue Aug 09, 2011 11:42 am
Aman verma wrote:
sharmishtha_goel wrote:IMO E.
How ?

for 50! , n = 47
48! , n = 46
47! , n = 42
46! , n = 42


If we take the factorial of a number greater than 51 n > 47
For a number less than 46 , n < 42
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 2789
Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members
Location: Chennai, India
Thanked: 206 times
GMAT Score:640

by GmatKiss » Tue Aug 09, 2011 12:56 pm
Not able to follow, can u pls explain in detail
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 304
Joined: Wed Jan 27, 2010 8:35 amFollowed by: 3 members
Location: International Space Station
Thanked: 11 times

by Aman verma » Thu Aug 11, 2011 4:31 am
GmatKiss wrote:Not able to follow, can u pls explain in detail
Now the highest power of 2 that can exactly divide 50! is 47, hence n=47,
Similarly the highest power of 2 that can exactly divide 49! & 48! is 46,
the the highest power of 2 that can exactly divide 47! & 46! is 42
Now if we take the factorial of a number greater than 51, then n > 47
For a number less than 46 ,then n < 42.Hence OA[spoiler]e)[/spoiler]

I will appreciate if anybody could suggest a better approach.
800. Arjun's-Bird-Eye
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 2789
Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members
Location: Chennai, India
Thanked: 206 times
GMAT Score:640

by GmatKiss » Thu Aug 11, 2011 5:17 am
How p is considered to be 50, 49 and so on!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Junior | Next Rank: 30 Posts
Posts: 20
Joined: Thu Feb 17, 2011 9:13 am
Thanked: 1 times

by sharmishtha_goel » Thu Aug 11, 2011 6:17 am
Aman verma wrote:
GmatKiss wrote:Not able to follow, can u pls explain in detail
Now the highest power of 2 that can exactly divide 50! is 47, hence n=47,
Similarly the highest power of 2 that can exactly divide 49! & 48! is 46,
the the highest power of 2 that can exactly divide 47! & 46! is 42
Now if we take the factorial of a number greater than 51, then n > 47
For a number less than 46 ,then n < 42.Hence OA[spoiler]e)[/spoiler]

I will appreciate if anybody could suggest a better approach.

HI,

This approach is the simplest :) ....i will elaborate so that you can understand the logic behind it.

10! = 1.2.3.4.5.6.7.8.9.10
To calculate the highest power of 2 that can divide 10! , first count the number or even numbers.
10/2 = 5 , i.e. 2^5 completely divides 10!
Notice that of the 5 even numbers ( 2 4 6 8 10) 4 and 8 have more than 1 power of 2.
To calculate the highest power of 2^2 i.e 4
10 / 4 = 2 (quotient only)
To calculate the highest power of 2^3 i.e 8
10 / 8 = 1 .
Adding up 5 + 2 + 1 = 8 i.e. 2^8 divides 10! completely giving you an odd quotient or you can say that the highest power of 2 in factorial 10 is 8 .
cross check : 1.2.3.4.5.6.7.8.9.10
1.2.3.2^2.5.2.3.7.2^3.9.2.5
1.2^(1+2+1+3+1).3.5.3.7.9.5
1.2^8.3.5.3.7.9.5

Hope that helps.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1