NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 19:10 It is currently 24 Apr 2024, 19:10
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

For any integer p, *p is equal to the product of all the int

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
gmatpapa
Senior Manager
Senior Manager
Joined: 31 Oct 2010
Status:Up again.
Posts: 418
Own Kudos [?]: 2217 [66]
Given Kudos: 75
Concentration: Strategy, Operations
Schools: Ivey '16 (A) Carlson '17 (A) McCombs '17 (A) W.P. Carey '17 (M$)
GMAT 1: 740 Q49 V42
GMAT 2: 710 Q48 V40
Send PM
For any integer p, *p is equal to the product of all the int [#permalink] New post   Updated on: 30 Sep 2013, 05:23
6
Kudos
60
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

61% (01:38) correct 39% (01:53) wrong based on 1075 sessions
Hide Show timer Statistics
For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *7 + 3 and *7 + 7, inclusive?

(A) None
(B) One
(C) Two
(D) Three
(E) Four
ShowHide Answer
Official Answer
A

Originally posted by gmatpapa on 19 Apr 2011, 05:33.
Last edited by Bunuel on 30 Sep 2013, 05:23, edited 1 time in total.
Renamed the topic and edited the question.
Most Helpful Reply
User avatar
gmatpapa
Senior Manager
Senior Manager
Joined: 31 Oct 2010
Status:Up again.
Posts: 418
Own Kudos [?]: 2217 [75]
Given Kudos: 75
Concentration: Strategy, Operations
Schools: Ivey '16 (A) Carlson '17 (A) McCombs '17 (A) W.P. Carey '17 (M$)
GMAT 1: 740 Q49 V42
GMAT 2: 710 Q48 V40
Send PM
Re: Prime numbers/ Divisibility [#permalink] New post   19 Apr 2011, 07:38
44
Kudos
31
Bookmarks
Baten80 wrote:
7!+3 to 7!+4
so 5043 to 5047 [5043, 5044, 5045, 5046 and 5047]
there is no prime numbers.
Ans. A
What others easy way?


The quick way is to realize that if a factor(or any of its multiples) is added to a multiple of that factor, the result will be divisible by that factor. For example: 3 is a factor of 9. If 3 is added to 9, the result will be divisible by 3. Is 5 is added to 25, the result will be divisible by 5.

Coming to the problem. You see, 7! will be divisible by all numbers from 1 through 7. In other words, all integers from 1 to 7 are factors of 7! So, if any number between 1 to 7 is added to 7!, the result will be divisible by the number that is added (if 3 is added to 7!, result will be divisible by 3. If four is added, the result will be divisible by 4 and so on..) Essentially, the numbers between 7!+3 and 7!+7, inclusive will be: 7!+3, 7!+4, 7!+5, 7!+6, 7!+7. All these numbers will be divisible by one or the other number between 3 to 7, hence making all of them non-prime.

Answer A.
User avatar
fluke
Retired Moderator
Joined: 20 Dec 2010
Posts: 1114
Own Kudos [?]: 4702 [18]
Given Kudos: 376
Send PM
Re: Prime numbers/ Divisibility [#permalink] New post   19 Apr 2011, 07:39
10
Kudos
8
Bookmarks
gmatpapa wrote:
For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *7 + 3 and *7 + 7, inclusive?


(A) None

(B) One

(C) Two

(D) Three

(E) Four


Q: How many prime numbers between 7!+3 and 7!+7

7!+3=7*6*5*4*3*2*1+3=3(7*6*5*4*2+1). Not prime.
7!+4=7*6*5*4*3*2*1+4=4(7*6*5*3*2+1). Not prime.
7!+5=7*6*5*4*3*2*1+5=5(7*6*4*3*2+1). Not prime.
7!+6=7*6*5*4*3*2*1+6=6(7*5*4*3*2+1). Not prime.
7!+7=7*6*5*4*3*2*1+7=7(6*5*4*3*2+1). Not prime.

We can infer:
No primes between "n!+2 AND n!+n".
General Discussion
User avatar
P
MHIKER
Director
Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 972
Own Kudos [?]: 4927 [2]
Given Kudos: 690
Concentration: Accounting
Send PM
Re: Prime numbers/ Divisibility [#permalink] New post   19 Apr 2011, 07:19
2
Bookmarks
7!+3 to 7!+4
so 5043 to 5047 [5043, 5044, 5045, 5046 and 5047]
there is no prime numbers.
Ans. A
What others easy way?
User avatar
gmatpapa
Senior Manager
Senior Manager
Joined: 31 Oct 2010
Status:Up again.
Posts: 418
Own Kudos [?]: 2217 [0]
Given Kudos: 75
Concentration: Strategy, Operations
Schools: Ivey '16 (A) Carlson '17 (A) McCombs '17 (A) W.P. Carey '17 (M$)
GMAT 1: 740 Q49 V42
GMAT 2: 710 Q48 V40
Send PM
Re: Prime numbers/ Divisibility [#permalink] New post   19 Apr 2011, 12:03
Here's a similar problem:

ds-is-x-x-1-a-prime-number-61428.html
User avatar
B
subhashghosh
Retired Moderator
Joined: 16 Nov 2010
Posts: 909
Own Kudos [?]: 1172 [0]
Given Kudos: 43
Location: United States (IN)
Concentration: Strategy, Technology
Send PM
Reviews Badge
Re: Prime numbers/ Divisibility [#permalink] New post   19 Apr 2011, 21:03
7! = 720 * 7 = 5040

# in question = 5043, 5044, 5045, 5046, 5047

none of these are prime

Answer - A
User avatar
mniyer
Intern
Intern
Joined: 06 Apr 2011
Posts: 24
Own Kudos [?]: 170 [0]
Given Kudos: 4
Send PM
GMAT ToolKit User
Re: Prime numbers/ Divisibility [#permalink] New post   20 Apr 2011, 19:25
gmatpapa wrote:
For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *7 + 3 and *7 + 7, inclusive?


(A) None

(B) One

(C) Two

(D) Three

(E) Four


Here's my thinking (pundits please correct me if I'm wrong):
Generally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *7 would be divisible by all numbers from 1 to 7.

=> *7+3 would give me a number which is a multiple of 3 and therefore divisible (since *7 is divisible by 3)
In fact adding any "prime" number between 1 to 7 to *7 will definitely be divisible.

So the answer is none (A)!

Supposing if the question had asked for prime numbers between *7 + 3 and *7 + 11 then the answer would be 1. For *7 +3 and *7 + 13, it is 2 and so on...
User avatar
varunmaheshwari
Manager
Manager
Joined: 25 Aug 2008
Posts: 100
Own Kudos [?]: 294 [1]
Given Kudos: 5
Location: India
WE 1: 3.75 IT
WE 2: 1.0 IT
Send PM
Re: Prime numbers/ Divisibility [#permalink] New post   21 Apr 2011, 04:43
7! = 7*6*5*4*3*2*1 = 42* 120 = 5040
Numbers in question = 5043, 5044, 5045, 5046, 5047

None of these are prime as they are divisible by the numbers present in 7!

Answer is A
User avatar
amit2k9
Director
Director
Joined: 08 May 2009
Status:There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Posts: 552
Own Kudos [?]: 589 [0]
Given Kudos: 10
Send PM
Re: Prime numbers/ Divisibility [#permalink] New post   30 Apr 2011, 22:17
7! + 1<a< 7 are all non prime numbers.
Hence A.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618824 [2]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: For any integer p, *p is equal to the product of all the int [#permalink] New post   30 Sep 2013, 05:25
1
Kudos
1
Bookmarks
Expert Reply
gmatpapa wrote:
For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *7 + 3 and *7 + 7, inclusive?

(A) None
(B) One
(C) Two
(D) Three
(E) Four


Similar questions to practice:
for-any-integer-m-greater-than-1-m-denotes-the-product-of-148722.html
for-any-integer-n-greater-than-1-n-denotes-the-product-of-131701.html
let-p-be-the-product-of-the-positive-integers-between-1-and-132329.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
does-the-integer-k-have-a-factor-p-such-that-1-p-k-126735.html
if-x-is-an-integer-does-x-have-a-factor-n-such-that-100670.html
avatar
sanket1991
Manager
Manager
Joined: 14 Sep 2014
Posts: 74
Own Kudos [?]: 95 [0]
Given Kudos: 51
WE:Engineering (Consulting)
Send PM
Re: For any integer p, *p is equal to the product of all the int [#permalink] New post   07 Jan 2015, 09:04
*p is nothing but p!

for any a>=5 *a will end with 0
so +3 will give xxx3
and +7 will give xxx7
between 3 and 7 there is only 5 which cant be a prime number.
so ans None
avatar
PareshGmat
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1562
Own Kudos [?]: 7208 [0]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: For any integer p, *p is equal to the product of all the int [#permalink] New post   07 Jan 2015, 20:47
gmatpapa wrote:
Baten80 wrote:
7!+3 to 7!+4
so 5043 to 5047 [5043, 5044, 5045, 5046 and 5047]
there is no prime numbers.
Ans. A
What others easy way?


The quick way is to realize that if a factor(or any of its multiples) is added to a multiple of that factor, the result will be divisible by that factor. For example: 3 is a factor of 9. If 3 is added to 9, the result will be divisible by 3. Is 5 is added to 25, the result will be divisible by 5.

Coming to the problem. You see, 7! will be divisible by all numbers from 1 through 7. In other words, all integers from 1 to 7 are factors of 7! So, if any number between 1 to 7 is added to 7!, the result will be divisible by the number that is added (if 3 is added to 7!, result will be divisible by 3. If four is added, the result will be divisible by 4 and so on..) Essentially, the numbers between 7!+3 and 7!+7, inclusive will be: 7!+3, 7!+4, 7!+5, 7!+6, 7!+7. All these numbers will be divisible by one or the other number between 3 to 7, hence making all of them non-prime.

Answer A.


Agree to this.... there is no need to "actually calculate" the factorial & sum up.

The factorial part (7!) has factors of all numbers stated from 3 to 7, inclusive. So they are indeed not prime
User avatar
B
sivaspurthy
Intern
Intern
Joined: 07 Nov 2012
Status:Pursuit of happyness
Posts: 17
Own Kudos [?]: 6 [0]
Given Kudos: 837
Location: India
Concentration: General Management, Leadership
Schools: Stanford '18 INSEAD Jan '17 HBS '18
GMAT Date: 04-24-2013
WE:General Management (Energy and Utilities)
Send PM
Re: For any integer p, *p is equal to the product of all the int [#permalink] New post   05 Mar 2016, 07:20
hi
is *p equal to p!??? becoz the question says the product of the integers between 1 and p and hence it does not include p. just a doubt...

siva
User avatar
G
ENGRTOMBA2018
SVP
SVP
Joined: 20 Mar 2014
Posts: 2362
Own Kudos [?]: 3626 [1]
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Send PM
GMAT ToolKit User Reviews Badge
For any integer p, *p is equal to the product of all the int [#permalink] New post   05 Mar 2016, 08:13
1
Kudos
sivaspurthy wrote:
hi
is *p equal to p!??? becoz the question says the product of the integers between 1 and p and hence it does not include p. just a doubt...

siva


No, the question mentions that "*p is equal to the product of all the integers between 1 and p, inclusive" and hence *p =1*2*3...p = p!

Hope this helps.

P.S.: nice display pic! 2003 world cup I think.
User avatar
D
stonecold
Alum
Joined: 12 Aug 2015
Posts: 2282
Own Kudos [?]: 3127 [0]
Given Kudos: 893
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Send PM
GMAT ToolKit User
Re: For any integer p, *p is equal to the product of all the int [#permalink] New post   14 Mar 2016, 05:48
Using the rule => multiple + multiple = multiple
we can say that 7!+4,7!+5,7!+6 are all non primes.
hence A
avatar
aekukula
Intern
Intern
Joined: 07 Mar 2016
Posts: 14
Own Kudos [?]: 12 [0]
Given Kudos: 3
Location: Indonesia
Schools: Haas '19 (A$) Anderson '19 Marshall '19 Tepper '19 IE '20 Foster '19 (A$) Darden '19 (II) McCombs '19 (II) Duke '19 (A$)
GPA: 3.06
Send PM
Re: For any integer p, *p is equal to the product of all the int [#permalink] New post   23 Apr 2016, 01:57
gmatpapa wrote:
Baten80 wrote:
7!+3 to 7!+4
so 5043 to 5047 [5043, 5044, 5045, 5046 and 5047]
there is no prime numbers.
Ans. A
What others easy way?


The quick way is to realize that if a factor(or any of its multiples) is added to a multiple of that factor, the result will be divisible by that factor. For example: 3 is a factor of 9. If 3 is added to 9, the result will be divisible by 3. Is 5 is added to 25, the result will be divisible by 5.

Coming to the problem. You see, 7! will be divisible by all numbers from 1 through 7. In other words, all integers from 1 to 7 are factors of 7! So, if any number between 1 to 7 is added to 7!, the result will be divisible by the number that is added (if 3 is added to 7!, result will be divisible by 3. If four is added, the result will be divisible by 4 and so on..) Essentially, the numbers between 7!+3 and 7!+7, inclusive will be: 7!+3, 7!+4, 7!+5, 7!+6, 7!+7. All these numbers will be divisible by one or the other number between 3 to 7, hence making all of them non-prime.

Answer A.


Great Explanation!

let me add it up of my own explanation...

so the list is
(7!+3), (7!+ 4), (7! + 5), (7! + 6), (7! + 7)

Notice that 7! = 7 x 6 x 5 x 4 x 3 x 2 (there is 5 and 2 in there so the Unit Digit must be 0)

is one of (7!+ 4), (7! + 5), (7! + 6) a prime number ?

just focus on the unit digit ! a prime number is a number that is divisible only by 1 and its own number,

unit digit of (7!+ 4) is 4 (since unit digit of 7! is 0), so therefore it is divisible by 2 (because it is even) = NOT A PRIME NUMBER
unit digit of (7! + 5) is 5, so therefore it is divisible by 5 = NOT A PRIME NUMBER
unit digit of (7! + 6) is 6, so therefore it is divisible by 2 (because it is even) = NOT A PRIME NUMBER

There you have it !
avatar
S
SVP482
Intern
Intern
Joined: 06 Nov 2016
Posts: 22
Own Kudos [?]: 21 [0]
Given Kudos: 2
Send PM
Re: For any integer p, *p is equal to the product of all the int [#permalink] New post   21 Feb 2017, 06:17
gmatpapa wrote:
For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *7 + 3 and *7 + 7, inclusive?

(A) None
(B) One
(C) Two
(D) Three
(E) Four



Here is how I did it.

If we interpret *p to be multiple of all prime numbers instead of all numbers, it might be a touch easy.

*7 + 3 = 1 * 2 * 3 * 5 * 7 + 3 = 213
*7 + 7 = 1 * 2 * 3 * 5 * 7 + 7 = 217

214, 215 and 216 as we know are not prime.
avatar
B
bobthebuilder14
Intern
Intern
Joined: 17 Mar 2013
Posts: 43
Own Kudos [?]: 6 [0]
Given Kudos: 146
Location: India
Schools: Owen '21 (A$) Foster '21 (A$)
GMAT 1: 710 Q47 V41
GPA: 3
Send PM
Re: For any integer p, *p is equal to the product of all the int [#permalink] New post   01 Apr 2017, 00:37
Hello Bunuel,

The "Similar problems" links are of great help. Is there any place where I can find a problem of a certain type and then similar problems so that I can practice all variations of that concept/problem type?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618824 [0]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: For any integer p, *p is equal to the product of all the int [#permalink] New post   01 Apr 2017, 05:57
Expert Reply
makshinde wrote:
Hello Bunuel,

The "Similar problems" links are of great help. Is there any place where I can find a problem of a certain type and then similar problems so that I can practice all variations of that concept/problem type?


You can check categorised questions in our questions bank: https://gmatclub.com/forum/viewforumtags.php
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32657
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: For any integer p, *p is equal to the product of all the int [#permalink] New post   07 Nov 2023, 01:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: For any integer p, *p is equal to the product of all the int [#permalink]
07 Nov 2023, 01:24
Moderators:
Bunuel
Math Expert
92900 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions