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

 It is currently 16 Jul 2018, 11:38

### 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 (n+2)!= n!(an^2+bn+c), then abc=?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5836
GMAT 1: 760 Q51 V42
GPA: 3.82
If (n+2)!= n!(an^2+bn+c), then abc=? [#permalink]

### Show Tags

12 Mar 2018, 01:04
00:00

Difficulty:

5% (low)

Question Stats:

90% (00:42) correct 10% (00:58) wrong based on 42 sessions

### HideShow timer Statistics

[GMAT math practice question]

If $$(n+2)!= n!(an^2+bn+c),$$ then $$abc=?$$

$$A. 2$$
$$B. 3$$
$$C. 4$$
$$D. 6$$
$$E. 8$$

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Joined: 22 May 2017 Posts: 117 Re: If (n+2)!= n!(an^2+bn+c), then abc=? [#permalink] ### Show Tags 12 Mar 2018, 01:24 1 (n+2)(n+1)n!= n! (an2+bn+c) (n+2)(n+1) = (an2+bn+c) n2 + 3n +2 = (an2+bn+c) abc = 1*3*2 =6 Posted from my mobile device _________________ Kudos please if explanation helped ------------------------------------------------------------------------------------------------- Don't stop when you are tired , stop when you are DONE . Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5836 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If (n+2)!= n!(an^2+bn+c), then abc=? [#permalink] ### Show Tags 14 Mar 2018, 00:24 => $$(n+2)! = (n+2)(n+1)n! = (n^2 + 3n + 2)n!$$ So, $$a = 1, b = 3$$, and $$c = 2$$. Thus, $$abc = 6.$$ Therefore, D is the answer. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

CEO
Joined: 12 Sep 2015
Posts: 2630
If (n+2)!= n!(an^2+bn+c), then abc=? [#permalink]

### Show Tags

14 Mar 2018, 09:08
Top Contributor
1
MathRevolution wrote:
[GMAT math practice question]

If $$(n+2)!= n!(an^2+bn+c),$$ then $$abc=?$$

$$A. 2$$
$$B. 3$$
$$C. 4$$
$$D. 6$$
$$E. 8$$

First recognize that (n + 2)! = (n + 2)(n + 1)(n)(n - 1)(n - 2)(n - 3)....(3)(2)(1)
= (n + 2)(n + 1)(n!)
= (n!)(n + 2)(n + 1)

The question tells us that (n + 2)! = n!(an² + bn + c)
So, we can write: (n!)(n + 2)(n + 1) = n!(an² + bn + c)
Divide both sides by n! to get: (n + 2)(n + 1) = an² + bn + c
Use FOIL to expand left side: n² + 3n + 2 = an² + bn + c
In other words: 1n² + 3n + 2 = an² + bn + c

So, a = 1, b = 3 and c = 2
This means abc = (1)(3)(2) = 6

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – Founder of gmatprepnow.com

VP
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1114
Location: India
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Re: If (n+2)!= n!(an^2+bn+c), then abc=? [#permalink]

### Show Tags

16 Mar 2018, 23:56
MathRevolution wrote:
[GMAT math practice question]

If $$(n+2)!= n!(an^2+bn+c),$$ then $$abc=?$$

$$A. 2$$
$$B. 3$$
$$C. 4$$
$$D. 6$$
$$E. 8$$

It can be written as:

$$\frac{(n + 2) (n + 1) (n)!}{n!}$$ $$=$$ $$(an^2+bn+c)$$

$$(n + 2) (n + 1)$$= $$(an^2+bn+c)$$

$$n^2 + 3n + 2 =$$ $$(an^2+bn+c)$$

Therefore, $$a = 1, b = 3, c = 2$$

(D)
_________________

"Do not watch clock; Do what it does. KEEP GOING."

Re: If (n+2)!= n!(an^2+bn+c), then abc=?   [#permalink] 16 Mar 2018, 23:56
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®.