Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 21 Oct 2016, 22:28

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# GMAT Diagnostic Test Question 9

Author Message
Founder
Affiliations: AS - Gold, HH-Diamond
Joined: 04 Dec 2002
Posts: 14093
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
Followers: 3594

Kudos [?]: 21672 [0], given: 4394

GMAT Diagnostic Test Question 9 [#permalink]

### Show Tags

28 Sep 2013, 21:14
Expert's post
22
This post was
BOOKMARKED
GMAT Diagnostic Test Question 9
Field: Arithmetic
Difficulty: 650

Which of the following is a factor of 18!+1?

A. 15
B. 17
C. 19
D. 33
E. 39
_________________

Founder of GMAT Club

US News 2008 - 2017 Rankings progression - New!
Just starting out with GMAT? Start here...
Need GMAT Book Recommendations? Best GMAT Books

Co-author of the GMAT Club tests

GMAT Club Premium Membership - big benefits and savings

Founder
Affiliations: AS - Gold, HH-Diamond
Joined: 04 Dec 2002
Posts: 14093
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
Followers: 3594

Kudos [?]: 21672 [5] , given: 4394

Re: GMAT Diagnostic Test Question 9 [#permalink]

### Show Tags

28 Sep 2013, 21:14
5
KUDOS
Expert's post
6
This post was
BOOKMARKED
18! and 18!+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Now, since we can factor out each 15, 17, 33=3*11, and 39=3*13 out of 18!, then 15, 17, 33 and 39 ARE factors of 18! and are NOT factors of 18!+1. Therefore only 19 could be a factor of 18!+1.

_________________

Founder of GMAT Club

US News 2008 - 2017 Rankings progression - New!
Just starting out with GMAT? Start here...
Need GMAT Book Recommendations? Best GMAT Books

Co-author of the GMAT Club tests

GMAT Club Premium Membership - big benefits and savings

Intern
Joined: 05 Oct 2013
Posts: 21
Followers: 0

Kudos [?]: 6 [1] , given: 0

Re: GMAT Diagnostic Test Question 9 [#permalink]

### Show Tags

21 Oct 2013, 11:11
1
KUDOS
bb wrote:
GMAT Diagnostic Test Question 9
Field: Arithmetic
Difficulty: 650

Which of the following is a factor of 18!+1?

A. 15
B. 17
C. 19
D. 33
E. 39

Solution 1: Because 19 is a prime, applying Wilson's theorem, we have 19 is a factor of (19-1)! + 1 = 18! +1.
Solution 2: We have 15 = 3*5, 33= 3*11, 39 = 3*13. Therefor, 15, 17, 33, 39 are factors of 18! = 1 * 2 *3 * 4 * 5 * ... * 17 * 18. Because 18! +1 and 18! are co-prime, 15, 17,33 and 39 is not a factor of 18! + 1. The answer must be C (19).
Intern
Joined: 19 Jul 2013
Posts: 23
Location: United States
GMAT 1: 340 Q27 V12
GPA: 3.33
Followers: 0

Kudos [?]: 6 [0], given: 9

Re: GMAT Diagnostic Test Question 9 [#permalink]

### Show Tags

29 Dec 2013, 15:25
bb wrote:
18! and 18!+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Now, since we can factor out each 15, 17, 33=3*11, and 39=3*13 out of 18!, then 15, 17, 33 and 39 ARE factors of 18! and are NOT factors of 18!+1. Therefore only 19 could be a factor of 18!+1.

I Find it difficult to understand the explaination..is there any other way to solve this question...
Math Expert
Joined: 02 Sep 2009
Posts: 35242
Followers: 6619

Kudos [?]: 85346 [1] , given: 10236

Re: GMAT Diagnostic Test Question 9 [#permalink]

### Show Tags

30 Dec 2013, 01:39
1
KUDOS
Expert's post
6
This post was
BOOKMARKED
lindt123 wrote:
bb wrote:
18! and 18!+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Now, since we can factor out each 15, 17, 33=3*11, and 39=3*13 out of 18!, then 15, 17, 33 and 39 ARE factors of 18! and are NOT factors of 18!+1. Therefore only 19 could be a factor of 18!+1.

I Find it difficult to understand the explaination..is there any other way to solve this question...

Frankly, solution provided is the easiest from my point of view.

We have that each 15, 17, 33, and 39 IS a factor of 18!, thus NOT a factor of 18!+1. Therefore, only 19 can be a factor of 18!+1. Since one of the options must be correct and we know that A, B, D and E are not, then C must be correct.

Does this make sense?

Check similar questions to practice:
if-a-and-b-are-odd-integers-a-b-represents-the-product-of-144714.html
is-x-1-a-factor-of-100740.html
if-x-and-y-are-positive-integers-what-is-the-gcf-of-x-and-y-144190.html
what-is-the-greatest-common-factor-of-positive-integers-a-126637.html
what-is-the-greatest-common-factor-of-x-and-y-109273.html
what-is-the-greatest-common-divisor-of-positive-integers-m-129802.html
x-and-y-are-positive-integers-such-that-x-8y-12-what-is-the-126743.html
gcd-of-a-b-126427.html
if-a-and-b-are-positive-integers-divisible-by-6-is-6-the-100324.html
if-a-and-b-are-positive-itegers-what-is-the-value-of-a-b-135199.html
is-x-1-a-factor-of-100740.html
find-the-number-that-divides-103251.html
if-n-is-the-least-of-3-consecutive-positive-integers-and-128102.html
if-both-x-and-y-are-positive-integers-that-are-divisible-by-119658.html
what-is-the-greatest-common-divisor-of-positive-integers-m-129802.html
for-every-positive-even-integer-n-the-function-h-n-is-defi-82314.html
if-a-b-and-c-are-positive-integers-with-a-b-c-85644.html
x-is-the-product-of-all-even-numbers-from-2-to-50-inclusive-156545.html
for-every-positive-even-integer-n-the-function-h-n-is-126691.html
for-every-positive-even-integer-n-the-function-h-n-149722.html
if-n-is-a-positive-integer-greater-than-1-then-p-n-represe-144553.html
if-x-y-and-z-are-3-different-prime-numbers-which-of-the-153338.html

Hope this helps.
_________________
Intern
Joined: 19 Jul 2013
Posts: 23
Location: United States
GMAT 1: 340 Q27 V12
GPA: 3.33
Followers: 0

Kudos [?]: 6 [0], given: 9

Re: GMAT Diagnostic Test Question 9 [#permalink]

### Show Tags

05 Jan 2014, 18:17
Bunuel wrote:
lindt123 wrote:
bb wrote:
18! and 18!+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Now, since we can factor out each 15, 17, 33=3*11, and 39=3*13 out of 18!, then 15, 17, 33 and 39 ARE factors of 18! and are NOT factors of 18!+1. Therefore only 19 could be a factor of 18!+1.

I Find it difficult to understand the explaination..is there any other way to solve this question...

Frankly, solution provided is the easiest from my point of view.

We have that each 15, 17, 33, and 39 IS a factor of 18!, thus NOT a factor of 18!+1. Therefore, only 19 can be a factor of 18!+1. Since one of the options must be correct and we know that A, B, D and E are not, then C must be correct.

Does this make sense?

Check similar questions to practice:
if-a-and-b-are-odd-integers-a-b-represents-the-product-of-144714.html
is-x-1-a-factor-of-100740.html
if-x-and-y-are-positive-integers-what-is-the-gcf-of-x-and-y-144190.html
what-is-the-greatest-common-factor-of-positive-integers-a-126637.html
what-is-the-greatest-common-factor-of-x-and-y-109273.html
what-is-the-greatest-common-divisor-of-positive-integers-m-129802.html
x-and-y-are-positive-integers-such-that-x-8y-12-what-is-the-126743.html
gcd-of-a-b-126427.html
if-a-and-b-are-positive-integers-divisible-by-6-is-6-the-100324.html
if-a-and-b-are-positive-itegers-what-is-the-value-of-a-b-135199.html
is-x-1-a-factor-of-100740.html
find-the-number-that-divides-103251.html
if-n-is-the-least-of-3-consecutive-positive-integers-and-128102.html
if-both-x-and-y-are-positive-integers-that-are-divisible-by-119658.html
what-is-the-greatest-common-divisor-of-positive-integers-m-129802.html
for-every-positive-even-integer-n-the-function-h-n-is-defi-82314.html
if-a-b-and-c-are-positive-integers-with-a-b-c-85644.html
x-is-the-product-of-all-even-numbers-from-2-to-50-inclusive-156545.html
for-every-positive-even-integer-n-the-function-h-n-is-126691.html
for-every-positive-even-integer-n-the-function-h-n-149722.html
if-n-is-a-positive-integer-greater-than-1-then-p-n-represe-144553.html
if-x-y-and-z-are-3-different-prime-numbers-which-of-the-153338.html

Hope this helps.

Thanx a lot Bunuel...was able to understand better this time..
Intern
Status: Learning
Joined: 07 Aug 2011
Posts: 43
Location: India
Schools: WBUT - Class of 2011
GMAT Date: 01-06-2014
GPA: 2.6
WE: Research (Education)
Followers: 1

Kudos [?]: 34 [2] , given: 10

Re: GMAT Diagnostic Test Question 9 [#permalink]

### Show Tags

20 Aug 2014, 01:59
2
KUDOS
How 17 is a factor of 18!+1 or 18!?

17 is a prime no. I agree with 15= 5*3, 33=11*3, 39=13*3

Bunuel wrote:
lindt123 wrote:
bb wrote:
18! and 18!+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Now, since we can factor out each 15, 17, 33=3*11, and 39=3*13 out of 18!, then 15, 17, 33 and 39 ARE factors of 18! and are NOT factors of 18!+1. Therefore only 19 could be a factor of 18!+1.

I Find it difficult to understand the explaination..is there any other way to solve this question...

Frankly, solution provided is the easiest from my point of view.

We have that each 15, 17, 33, and 39 IS a factor of 18!, thus NOT a factor of 18!+1. Therefore, only 19 can be a factor of 18!+1. Since one of the options must be correct and we know that A, B, D and E are not, then C must be correct.

Does this make sense?

Check similar questions to practice:
if-a-and-b-are-odd-integers-a-b-represents-the-product-of-144714.html
is-x-1-a-factor-of-100740.html
if-x-and-y-are-positive-integers-what-is-the-gcf-of-x-and-y-144190.html
what-is-the-greatest-common-factor-of-positive-integers-a-126637.html
what-is-the-greatest-common-factor-of-x-and-y-109273.html
what-is-the-greatest-common-divisor-of-positive-integers-m-129802.html
x-and-y-are-positive-integers-such-that-x-8y-12-what-is-the-126743.html
gcd-of-a-b-126427.html
if-a-and-b-are-positive-integers-divisible-by-6-is-6-the-100324.html
if-a-and-b-are-positive-itegers-what-is-the-value-of-a-b-135199.html
is-x-1-a-factor-of-100740.html
find-the-number-that-divides-103251.html
if-n-is-the-least-of-3-consecutive-positive-integers-and-128102.html
if-both-x-and-y-are-positive-integers-that-are-divisible-by-119658.html
what-is-the-greatest-common-divisor-of-positive-integers-m-129802.html
for-every-positive-even-integer-n-the-function-h-n-is-defi-82314.html
if-a-b-and-c-are-positive-integers-with-a-b-c-85644.html
x-is-the-product-of-all-even-numbers-from-2-to-50-inclusive-156545.html
for-every-positive-even-integer-n-the-function-h-n-is-126691.html
for-every-positive-even-integer-n-the-function-h-n-149722.html
if-n-is-a-positive-integer-greater-than-1-then-p-n-represe-144553.html
if-x-y-and-z-are-3-different-prime-numbers-which-of-the-153338.html

Hope this helps.

_________________

If you like my post give me kudos.

Arindam Sur

Math Expert
Joined: 02 Sep 2009
Posts: 35242
Followers: 6619

Kudos [?]: 85346 [0], given: 10236

Re: GMAT Diagnostic Test Question 9 [#permalink]

### Show Tags

20 Aug 2014, 02:47
arindamsur wrote:
How 17 is a factor of 18!+1 or 18!?

17 is a prime no. I agree with 15= 5*3, 33=11*3, 39=13*3

Bunuel wrote:
lindt123 wrote:

I Find it difficult to understand the explaination..is there any other way to solve this question...

Frankly, solution provided is the easiest from my point of view.

We have that each 15, 17, 33, and 39 IS a factor of 18!, thus NOT a factor of 18!+1. Therefore, only 19 can be a factor of 18!+1. Since one of the options must be correct and we know that A, B, D and E are not, then C must be correct.

Does this make sense?

Check similar questions to practice:
if-a-and-b-are-odd-integers-a-b-represents-the-product-of-144714.html
is-x-1-a-factor-of-100740.html
if-x-and-y-are-positive-integers-what-is-the-gcf-of-x-and-y-144190.html
what-is-the-greatest-common-factor-of-positive-integers-a-126637.html
what-is-the-greatest-common-factor-of-x-and-y-109273.html
what-is-the-greatest-common-divisor-of-positive-integers-m-129802.html
x-and-y-are-positive-integers-such-that-x-8y-12-what-is-the-126743.html
gcd-of-a-b-126427.html
if-a-and-b-are-positive-integers-divisible-by-6-is-6-the-100324.html
if-a-and-b-are-positive-itegers-what-is-the-value-of-a-b-135199.html
is-x-1-a-factor-of-100740.html
find-the-number-that-divides-103251.html
if-n-is-the-least-of-3-consecutive-positive-integers-and-128102.html
if-both-x-and-y-are-positive-integers-that-are-divisible-by-119658.html
what-is-the-greatest-common-divisor-of-positive-integers-m-129802.html
for-every-positive-even-integer-n-the-function-h-n-is-defi-82314.html
if-a-b-and-c-are-positive-integers-with-a-b-c-85644.html
x-is-the-product-of-all-even-numbers-from-2-to-50-inclusive-156545.html
for-every-positive-even-integer-n-the-function-h-n-is-126691.html
for-every-positive-even-integer-n-the-function-h-n-149722.html
if-n-is-a-positive-integer-greater-than-1-then-p-n-represe-144553.html
if-x-y-and-z-are-3-different-prime-numbers-which-of-the-153338.html

Hope this helps.

Please rad carefully: each 15, 17, 33, and 39 IS a factor of 18!, thus NOT a factor of 18!+1.

17 is a factor of 18! because 18! contains 17 as a multiple: 18! = 1*2*3*...*17*18.
_________________
Intern
Status: Learning
Joined: 07 Aug 2011
Posts: 43
Location: India
Schools: WBUT - Class of 2011
GMAT Date: 01-06-2014
GPA: 2.6
WE: Research (Education)
Followers: 1

Kudos [?]: 34 [0], given: 10

Re: GMAT Diagnostic Test Question 9 [#permalink]

### Show Tags

20 Aug 2014, 03:20
Thank you Bunuel sir for open my eyes.
_________________

If you like my post give me kudos.

Arindam Sur

Re: GMAT Diagnostic Test Question 9   [#permalink] 20 Aug 2014, 03:20
Similar topics Replies Last post
Similar
Topics:
37 GMAT Diagnostic Test Question 5 26 06 Jun 2009, 21:07
16 GMAT Diagnostic Test Question 4 37 06 Jun 2009, 21:06
22 GMAT Diagnostic Test Question 3 33 06 Jun 2009, 19:33
9 GMAT Diagnostic Test Question 2 26 06 Jun 2009, 19:03
36 GMAT Diagnostic Test Question 1 30 05 Jun 2009, 22:30
Display posts from previous: Sort by

# GMAT Diagnostic Test Question 9

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO 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®.