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

 It is currently 15 Aug 2018, 11:52

### 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

# The expression n! is defined as the product of the integers from 1 thr

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47918
The expression n! is defined as the product of the integers from 1 thr  [#permalink]

### Show Tags

30 Jul 2018, 21:52
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:17) correct 21% (01:13) wrong based on 70 sessions

### HideShow timer Statistics

The expression n! is defined as the product of the integers from 1 through n. If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to p/q?

A. 99!
B. 199!
C. 199!/99!
D. 299!/99!
E. 299!/199!

NEW question from GMAT® Quantitative Review 2019

(PS01656)

_________________
Intern
Joined: 01 Jan 2018
Posts: 15
Re: The expression n! is defined as the product of the integers from 1 thr  [#permalink]

### Show Tags

30 Jul 2018, 21:59
200 through 299 will cancel out leaving 100 through 199.
It can be written as 199!/99!.
C should be the ans.

Sent from my Redmi Note 3 using GMAT Club Forum mobile app
Manager
Joined: 22 Feb 2018
Posts: 246
Re: The expression n! is defined as the product of the integers from 1 thr  [#permalink]

### Show Tags

30 Jul 2018, 22:15
1
Bunuel wrote:
The expression n! is defined as the product of the integers from 1 through n. If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to p/q?

A. 99!
B. 199!
C. 199!/99!
D. 299!/99!
E. 299!/199!

NEW question from GMAT® Quantitative Review 2019

(PS01656)

OA:C

$$p =\frac{{299!}}{{99!}}$$

$$q =\frac{{299!}}{{199!}}$$

$$\frac{p}{q}=\frac{\frac{{299!}}{{99!}}}{\frac{{299!}}{{199!}}}$$

$$\frac{p}{q}=\frac{{299!}}{{99!}}*\frac{{199!}}{{299!}}=\frac{{199!}}{{99!}}$$
_________________

Good, good Let the kudos flow through you

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3161
Location: United States (CA)
Re: The expression n! is defined as the product of the integers from 1 thr  [#permalink]

### Show Tags

03 Aug 2018, 15:01
Bunuel wrote:
The expression n! is defined as the product of the integers from 1 through n. If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to p/q?

A. 99!
B. 199!
C. 199!/99!
D. 299!/99!
E. 299!/199!

The quotient p/q is the product of the integers from 100 to 199, inclusive, since the product of the integers from 200 to 299, inclusive, appears in both p and q and thus it gets canceled out.

We can consider the product of the integers from 100 to 199, inclusive, as the product of the integers from 1 to 199, inclusive, divided by the product of the integers from 1 to 99, inclusive. That is,

p/q = the product of the integers from 100 to 199, inclusive = 199!/99!

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Senior Manager
Status: Asst. Manager
Joined: 01 Oct 2017
Posts: 473
Location: India
Concentration: Operations, Entrepreneurship
GPA: 4
WE: Supply Chain Management (Energy and Utilities)
Re: The expression n! is defined as the product of the integers from 1 thr  [#permalink]

### Show Tags

05 Aug 2018, 05:37
Bunuel wrote:
The expression n! is defined as the product of the integers from 1 through n. If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to p/q?

A. 99!
B. 199!
C. 199!/99!
D. 299!/99!
E. 299!/199!

NEW question from GMAT® Quantitative Review 2019

(PS01656)

Given,
p=100*101*102*.......................*298*299 and
q=200*201*202*.......................*298*299
Thus, $$\frac{p}{q}$$=$$\frac{101*102*103*.......................*298*299}{200*201*202*.......................*298*299}$$=100*101*102*--------------*198*199=$$\frac{1*2*3*.................*198*199}{1*2*3*...............*98*99}$$=$$\frac{199!}{99!}$$

Ans. (C)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Re: The expression n! is defined as the product of the integers from 1 thr &nbs [#permalink] 05 Aug 2018, 05:37
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®.