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

It is currently 15 Nov 2018, 16:00

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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • GMATbuster's Weekly GMAT Quant Quiz # 9

     November 17, 2018

     November 17, 2018

     09:00 AM PST

     11:00 AM PST

    Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

x# is defined for every positive even integer x as the product of all

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

Hide Tags

Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 846
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User Premium Member
x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 06 Sep 2015, 09:28
3
6
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

55% (01:39) correct 45% (01:22) wrong based on 347 sessions

HideShow timer Statistics

x# is defined for every positive even integer x as the product of all even integers from 2 to x. What is the smallest possible prime factor of (x#+7)?

A. 2
B. 3
C. 5
D. 7
E. 11

_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Intern
Intern
avatar
Joined: 16 Aug 2015
Posts: 21
x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post Updated on: 06 Sep 2015, 16:41
1
We can resolve this problem by picking some smart numbers.

First of all, x# is an even number, accordingly x#+7 is odd, so the answer cannot be 2 even if it's tempting at the first sight !
Now we can proceed by taking some numbers, if we consider


X=4, then x#+7= 15 = 3 x 5. we got it, 3 is the smallest prime factor that we can obtain.

Originally posted by issamL on 06 Sep 2015, 13:28.
Last edited by issamL on 06 Sep 2015, 16:41, edited 1 time in total.
Manager
Manager
User avatar
Joined: 14 Mar 2014
Posts: 147
GMAT 1: 710 Q50 V34
Re: x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 06 Sep 2015, 16:23
1
IMO: B

Since smallest possible prime factor is required.
Let x = 2 then --> 2# = 2
x#+7 ==> 2#+7 = 2+7 = 9 = 3*3.
Thus 3 is the smallest possible Prime Factor

2 cannot be the possible prime factor because --> x# is always even since it is product of even numbers
Even +7 = Odd. Hence 2 cannot be prime factor of this result.
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos
¯\_(ツ)_/¯ :-)

Current Student
avatar
B
Joined: 07 Jan 2015
Posts: 82
Location: Thailand
GMAT 1: 540 Q41 V23
GMAT 2: 570 Q44 V24
GMAT 3: 550 Q44 V21
GMAT 4: 660 Q48 V33
GPA: 3.31
WE: Science (Other)
Re: x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 14 Sep 2015, 20:32
issamL wrote:
We can resolve this problem by picking some smart numbers.

First of all, x# is an even number, accordingly x#+7 is odd, so the answer cannot be 2 even if it's tempting at the first sight !
Now we can proceed by taking some numbers, if we consider


X=4, then x#+7= 15 = 3 x 5. we got it, 3 is the smallest prime factor that we can obtain.


If x=4, should x#+7 be 31?
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8531
Location: Pune, India
Re: x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 14 Sep 2015, 22:34
1
Aves wrote:
issamL wrote:
We can resolve this problem by picking some smart numbers.

First of all, x# is an even number, accordingly x#+7 is odd, so the answer cannot be 2 even if it's tempting at the first sight !
Now we can proceed by taking some numbers, if we consider


X=4, then x#+7= 15 = 3 x 5. we got it, 3 is the smallest prime factor that we can obtain.


If x=4, should x#+7 be 31?


No. # is a user defined operator i.e. the question defines for what # stand.

x# = 2*4*..*x

So if x = 2, x# = 2
If x = 4, x# = 2*4 = 8
If x = 6, x# = 2*4*6 = 48
and so on...

So x# + 7 when x = 4 will be 8 + 7 = 15 because when x is 4, x# is 8.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Current Student
avatar
B
Joined: 07 Jan 2015
Posts: 82
Location: Thailand
GMAT 1: 540 Q41 V23
GMAT 2: 570 Q44 V24
GMAT 3: 550 Q44 V21
GMAT 4: 660 Q48 V33
GPA: 3.31
WE: Science (Other)
Re: x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 14 Sep 2015, 22:45
VeritasPrepKarishma wrote:
Aves wrote:
issamL wrote:
We can resolve this problem by picking some smart numbers.

First of all, x# is an even number, accordingly x#+7 is odd, so the answer cannot be 2 even if it's tempting at the first sight !
Now we can proceed by taking some numbers, if we consider


X=4, then x#+7= 15 = 3 x 5. we got it, 3 is the smallest prime factor that we can obtain.


If x=4, should x#+7 be 31?


No. # is a user defined operator i.e. the question defines for what # stand.

x# = 2*4*..*x

So if x = 2, x# = 2
If x = 4, x# = 2*4 = 8
If x = 6, x# = 2*4*6 = 48
and so on...

So x# + 7 when x = 4 will be 8 + 7 = 15 because when x is 4, x# is 8.


Oh, it was only the product of all even integers not all integers.

I made a silly mistake.
Intern
Intern
avatar
S
Joined: 01 Sep 2016
Posts: 7
Re: x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 18 Dec 2016, 19:50
When x is taken as 6,X#+7 will be 55.
In this case ,the smallest prime factor will be 5 right?
Senior Manager
Senior Manager
avatar
B
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 19 Dec 2016, 01:57
1
reto wrote:
x# is defined for every positive even integer x as the product of all even integers from 2 to x. What is the smallest possible prime factor of (x#+7)?

A. 2
B. 3
C. 5
D. 7
E. 11


We have

\(2*4*6*8*10* … * x = 2^{\frac{x}{2}}*1*2*3*4*5* … * \frac{x}{2} = 2^{\frac{x}{2}}*(\frac{x}{2})!\)

If we need this expression to be an integer, min value that \(x\) can take is \(2\).

\(x# + 7 = 2^1*1! + 7 = 9 = 3^2\)

Min prime factor is \(3\)

Answer B
Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 689
Premium Member
Re: x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 03 Apr 2017, 22:58
x# is the product of all even nos. from 2 to x. Thus the answer would be an even no.

x#+7= Even +Odd= Odd

Therefore the smallest possible prime factor would be 3 and not 2 because the final answer is ODD and not even.
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Intern
Intern
User avatar
B
Joined: 07 Dec 2016
Posts: 41
Reviews Badge
Re: x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 10 Apr 2017, 04:43
Yes it will have to be odd and thus 3 is the small prime factor
_________________

Cheers!
If u like my post..... payback in Kudos!! :beer

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 689
Premium Member
Re: x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 13 Apr 2017, 08:35
VeritasPrepKarishma wrote:
Aves wrote:
issamL wrote:
We can resolve this problem by picking some smart numbers.

First of all, x# is an even number, accordingly x#+7 is odd, so the answer cannot be 2 even if it's tempting at the first sight !
Now we can proceed by taking some numbers, if we consider


X=4, then x#+7= 15 = 3 x 5. we got it, 3 is the smallest prime factor that we can obtain.


If x=4, should x#+7 be 31?


No. # is a user defined operator i.e. the question defines for what # stand.

x# = 2*4*..*x

So if x = 2, x# = 2
If x = 4, x# = 2*4 = 8
If x = 6, x# = 2*4*6 = 48
and so on...

So x# + 7 when x = 4 will be 8 + 7 = 15 because when x is 4, x# is 8.


But karishma (48+7= 55) which is not divisible by 3.
So it is not true in all cases.
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8531
Location: Pune, India
Re: x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 13 Apr 2017, 21:59
Shiv2016 wrote:

But karishma (48+7= 55) which is not divisible by 3.
So it is not true in all cases.


We need the smallest "possible" prime factor which CAN be a factor of a number of the form x# + 7.

There are some prime factors which CANNOT be factors of a number of this form. One such prime factor is 2 because numbers of the form x# + 7 will always be odd.

The next smallest prime factor is 3. Since there is a number of the form x# + 7 for which 3 is a factor (it needn't be a factor of EVERY such number), 3 is the smallest such prime factor.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 689
Premium Member
Re: x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 13 Apr 2017, 22:36
VeritasPrepKarishma wrote:
Shiv2016 wrote:

But karishma (48+7= 55) which is not divisible by 3.
So it is not true in all cases.


We need the smallest "possible" prime factor which CAN be a factor of a number of the form x# + 7.

There are some prime factors which CANNOT be factors of a number of this form. One such prime factor is 2 because numbers of the form x# + 7 will always be odd.

The next smallest prime factor is 3. Since there is a number of the form x# + 7 for which 3 is a factor (it needn't be a factor of EVERY such number), 3 is the smallest such prime factor.



Okay. Got it. Thanks!! :)
Intern
Intern
avatar
B
Joined: 13 Feb 2018
Posts: 11
Re: x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 15 Jul 2018, 03:46
Any conceptual approach to solving this problem?
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8531
Location: Pune, India
Re: x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 16 Jul 2018, 03:00
1
agarwalaayush2007 wrote:
Any conceptual approach to solving this problem?



x# is defined for every positive even integer x as the product of all even integers from 2 to x.
implies
2# = 2
4# = 2*4 = 8
6# = 2*4*6 = 48
and so on...

What is the smallest possible prime factor of (x#+7)?
2# + 7 will be 9
4# + 7 will be 15
6# + 7 will be 55
and so on...

Note that x# will always be even so if you add 7 to it, it will become odd. So 2 will never be a factor of x# + 7.
Next we see that 3 CAN be a factor of x# + 7 (9 and 15 have 3 as a factor) so the smallest such prime number must be 3.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Intern
avatar
B
Joined: 13 Feb 2018
Posts: 11
Re: x# is defined for every positive even integer x as the product of all  [#permalink]

Show Tags

New post 17 Jul 2018, 06:08
KarishmaB wrote:
agarwalaayush2007 wrote:
Any conceptual approach to solving this problem?



x# is defined for every positive even integer x as the product of all even integers from 2 to x.
implies
2# = 2
4# = 2*4 = 8
6# = 2*4*6 = 48
and so on...

What is the smallest possible prime factor of (x#+7)?
2# + 7 will be 9
4# + 7 will be 15
6# + 7 will be 55
and so on...

Note that x# will always be even so if you add 7 to it, it will become odd. So 2 will never be a factor of x# + 7.
Next we see that 3 CAN be a factor of x# + 7 (9 and 15 have 3 as a factor) so the smallest such prime number must be 3.


Thank you Karishma. Great help!
GMAT Club Bot
Re: x# is defined for every positive even integer x as the product of all &nbs [#permalink] 17 Jul 2018, 06:08
Display posts from previous: Sort by

x# is defined for every positive even integer x as the product of all

  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®.