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

It is currently 16 Oct 2018, 11:45

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 n*(n + 2)! = n!*(n + 1)!, then n could be which of the following

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49915
If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following  [#permalink]

Show Tags

New post 20 Mar 2018, 01:04
1
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

77% (02:00) correct 23% (02:16) wrong based on 77 sessions

HideShow timer Statistics

Retired Moderator
avatar
G
Joined: 26 Nov 2012
Posts: 593
Premium Member
Re: If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following  [#permalink]

Show Tags

New post 20 Mar 2018, 01:43
Bunuel wrote:
If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following values?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


By substituting the values, we can get C

4 * 6! = 4! * 5!

4 * 6 * 5! = 4! * 5!

Eliminate 5! on both sides.

24 = 24.

Hence C.
examPAL Representative
User avatar
G
Joined: 07 Dec 2017
Posts: 707
Re: If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following  [#permalink]

Show Tags

New post 20 Mar 2018, 01:52
1
Bunuel wrote:
If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following values?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


In addition to the substitution-based, Alternative approach shown above, we'll also show the complete, Precise calculation.

Since (n+2)! = (n+2)(n+1)!, we'll cancel out (n+1)! on both sides to get n(n+2) = n!
Canceling out n then gives n+2 = (n-1)!
Then for n = 1 this is 3 = 1 which is false.
For n = 2 this is 4 = 1 which is false.
For n = 3 this is 5 = 2 which is false.
For n = 4 this is 6 = 6 which is true.

(C) is our answer.
_________________

Image
Sign up for 7-day free trial
Image

I am a CR Expert - Ask Me ANYTHING about CR
I am a DS Expert - Ask Me ANYTHING about DS


Watch free GMAT tutorials in Math, Verbal, IR, and AWA.

GMAT test takers: Watch now the GMAC interview with the people who write the GMAT test!
We discussed the chances of improving a GMAT score; how important the first questions on the test are; what to do if you don’t have enough time to complete a whole section; and more.

You can watch all the action from the interview here.

PS Forum Moderator
User avatar
P
Joined: 16 Sep 2016
Posts: 311
GMAT 1: 740 Q50 V40
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following  [#permalink]

Show Tags

New post 20 Mar 2018, 02:05
Bunuel wrote:
If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following values?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


Instead of putting in values into the complicated equation provided, we can first simplify a bit.

n*(n + 2)! = n!*(n + 1)!
n*(n+2)*(n+1)! = (n-1)!*n*(n+1)! ...( we can expand using the definition of n!)
n*(n+2)*(n+1)! = (n-1)!*n*(n+1)! ...( Cancelling the common terms in LHS & RHS)
(n+2) = (n-1)!

When we put values starting n=1,2,3,4...

We find this equation holds true for n=4.

(4 + 2) = 6 = ( 4-1 )!

Hence C.

Best,
Gladi
Intern
Intern
avatar
B
Joined: 04 Dec 2017
Posts: 14
CAT Tests
Re: If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following  [#permalink]

Show Tags

New post 20 Mar 2018, 06:30
Bunuel wrote:
If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following values?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


n * (n+2) * (n+1)! = n * (n-1)! * (n+1)!

=> (n+2) = (n-1)! ........Eq (A)

Eq (A) satisfied by Option (C): 4
Manager
Manager
User avatar
B
Joined: 28 Jan 2018
Posts: 54
Location: Netherlands
Concentration: Finance
GMAT 1: 710 Q50 V36
GPA: 3
Re: If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following  [#permalink]

Show Tags

New post 20 Mar 2018, 10:15
Bunuel wrote:
If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following values?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


n*(n + 2)! = n!*(n+1)!, or (n+2) = (n-1)!

Plug in the value, only 4 fit: (4+2) = (4-1)! = 6

=> Answer (C)
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following  [#permalink]

Show Tags

New post 21 Mar 2018, 16:15
Bunuel wrote:
If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following values?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6



We can re-express (n + 2)! as (n + 2)*(n + 1)! Similarly, we can re-express n! as (n)*(n - 1)!

Using those re-expressions, we can simplify the equation as:
n*(n + 2)! = n!*(n + 1)!

n*(n + 2)(n + 1)! = n*(n - 1)!*(n + 1)!

Dividing both sides by n*(n + 1)!, we have:

n + 2 = (n - 1)!

We can see that, in general, (n - 1)! will be much larger than (n + 2). Therefore, the equation can only be true for a small value of n. Let’s consider the answer choices now.

(A) 2

2 + 2 = (2 - 1)! ?

4 = 1! ?

4 = 1 ? → No

(B) 3

3 + 2 = (3 - 1)! ?

5 = 2! ?

5 = 2 ? → No

(C) 4

4 + 2 = (4 - 1)! ?

6 = 3! ?

6 = 6 ? → Yes

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Director
Director
User avatar
P
Joined: 13 Mar 2017
Posts: 622
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following  [#permalink]

Show Tags

New post 09 Apr 2018, 21:57
Bunuel wrote:
If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following values?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


n*(n + 2)! = n!*(n + 1)!
(n + 2)! /(n + 1)! = n!/n
n+2 = (n-1)!

lets start checking values
(A) 2
4 = 1....... Incorrect
(B) 3
5 = 2!............Incorrect
(C) 4
6 = 3! ............... Correct

Answer C
_________________

CAT 2017 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2063
If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following  [#permalink]

Show Tags

New post 10 Apr 2018, 00:01

Solution



Given:
    • We are given that n*(n+2)! = n! * (n+1)!

To find:
    • We need to find the option that satisfies n*(n+2)! = n! * (n+1)!

Approach and Working:

    By applying n! = n*(n-1)!, n*(n+2)! = n! * (n+1)! can be written as n*(n+2) *(n+1)! = n! * (n+1)!
    • By cancelling (n+1)! from both the sides, we get n*(n+2) = n!

      • For n=2, 2*4≠2!
      • For n=3, 3*5 ≠3!
      • For n=4, 4*6= 4!=24, hence, the value of n is 4.

Hence, the correct answer is option C.
Answer: C
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

GMAT Club Bot
If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following &nbs [#permalink] 10 Apr 2018, 00:01
Display posts from previous: Sort by

If n*(n + 2)! = n!*(n + 1)!, then n could be which of the following

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.