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

It is currently 21 Apr 2019, 21:44

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

f(x)=x^2−1 For which of the following values of x is f(x) divisible by

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54401
f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

Show Tags

New post 29 Aug 2017, 23:53
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

63% (02:01) correct 37% (02:00) wrong based on 112 sessions

HideShow timer Statistics

Most Helpful Community Reply
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

Show Tags

New post 30 Aug 2017, 00:22
2
4
The expression f(x)=x^2−1 = (x+1)(x-1)
Evaluating answer options
A. 1812 : f(x) = (1813)(1811)
B. 2721 : f(x) = (2722)(2720)
C. 3118 : f(x) = (3119)(3117)
D. 4245 : f(x) = (4244)(4246)
E. 5653 : f(x) = (5652)(5654)

Of the answer options, we can reject Options A and C straightaway,
as they are not divisible by 2.

Careful evaluation of the other answer options :
Option B = Both 2722 and 2720 are divisible by 2 but not by 3
Option D = Both 4244 and 4246 are divisible by 2 but not by 3.
But, in Option E, 5652 is divisble by 2 and 5654 is divisible by 3.
Hence Option E is our answer!

_________________
You've got what it takes, but it will take everything you've got
General Discussion
Current Student
User avatar
P
Joined: 18 Aug 2016
Posts: 619
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Reviews Badge
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

Show Tags

New post 30 Aug 2017, 00:05
1
Bunuel wrote:
f(x)=x^2−1. For which of the following values of x is f(x) divisible by 6?

A. 1812
B. 2721
C. 3118
D. 4245
E. 5653


Divisible by 6 = Divisible by 2 & Divisible by 3

none of the numbers should be divisible by 3 as they have to follow x^2-1 divisible by 3
only A, C & E left as the sum of their digits is not divisible by 3
B & D are out
now check the last digit of A , C and E
2^2-1 = 3 which is not divisible by 2 ...A out
8^2-1 = 3 which is not divisible by 2 ...C out
3^2-1 = 8 divisible by 2 and the answer

E
_________________
We must try to achieve the best within us


Thanks
Luckisnoexcuse
Manager
Manager
User avatar
G
Joined: 27 Dec 2016
Posts: 232
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
Reviews Badge
f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

Show Tags

New post 30 Aug 2017, 00:15
Bunuel wrote:
f(x)=x^2−1. For which of the following values of x is f(x) divisible by 6?

A. 1812
B. 2721
C. 3118
D. 4245
E. 5653


A number is divisible by 6 when the sum of all of the digit is divisible by 3 and the number itself is EVEN.

Try to plugin value X and evaluate its UNIT DIGIT :
A. 1812 -> \((1812^2)-1\) --> the result is ODD, not the answer.
B. 2721 --> \((2721^2)-1\) --> the result is EVEN, can be the answer.
C. 3118 --> \((3118^2)-1\) --> the result is ODD, not the answer.
D. 4245 --> \((4245^2)-1\) --> the result is EVEN, can be the answer.
E. 5653 --> \((5653^2)-1\) --> the result is EVEN, can be the answer.

As we can see, only B, D and E left.
At this point, I chose to calculate E : \((4245^2)-1\) = 18020024, which sum all of the digits is not divisible by 3. E cannot be the answer.

stuck between B and E.
_________________
There's an app for that - Steve Jobs.
Manager
Manager
User avatar
G
Joined: 27 Dec 2016
Posts: 232
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
Reviews Badge
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

Show Tags

New post 30 Aug 2017, 00:21
Luckisnoexcuse wrote:
Bunuel wrote:
f(x)=x^2−1. For which of the following values of x is f(x) divisible by 6?

A. 1812
B. 2721
C. 3118
D. 4245
E. 5653


Divisible by 6 = Divisible by 2 & Divisible by 3

none of the numbers should be divisible by 3 as they have to follow x^2-1 divisible by 3
only A, C & E left as the sum of their digits is not divisible by 3
B & D are out
now check the last digit of A , C and E
2^2-1 = 3 which is not divisible by 2 ...A out
8^2-1 = 3 which is not divisible by 2 ...C out
3^2-1 = 8 divisible by 2 and the answer

E


Could you please elaborate more the one that I highlighted?
_________________
There's an app for that - Steve Jobs.
Manager
Manager
User avatar
B
Joined: 19 Jul 2017
Posts: 85
Location: India
Concentration: General Management, Strategy
GPA: 3.5
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

Show Tags

New post 30 Aug 2017, 02:11
For a number to be divisible by 6 , check if its divisible by 2,3.

From the given, first filter the numbers that are divisible by 3 as x^2 -1 will definitely be not divible by 3;

This leaves us with A, C , E. Now the square of the last digit and subtract 1. The last digit should be even to be divisble by 6.


A. 1812 -- 2^2-1 =3 not evn
B. 2721 -- Eliminate since divisible by 3.
C. 3118 -- 8^8-1=63 not even
D. 4245 -- Eliminate divisible by 3
E. 5653 -- 8; even

Ans:E
Manager
Manager
User avatar
B
Joined: 19 Jul 2017
Posts: 85
Location: India
Concentration: General Management, Strategy
GPA: 3.5
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

Show Tags

New post 30 Aug 2017, 02:12
pushpitkc wrote:
The expression f(x)=x^2−1 = (x+1)(x-1)
Evaluating answer options
A. 1812 : f(x) = (1813)(1811)
B. 2721 : f(x) = (2722)(2720)
C. 3118 : f(x) = (3119)(3117)
D. 4245 : f(x) = (4244)(4246)
E. 5653 : f(x) = (5654)(5655)

Of the answer options, we can reject Options A and C straightaway,
as they are not divisible by 2.

Carefully evaluation the other answer options :
Option B = Both 2722 and 2720 are divisible by 2 but not by 3
Option D = Both 4244 and 4246 are divisible by 2 but not by 3.
But, in Option E, 5655 is divisble by 2 and 5654 is divisible by 3.
Hence Option E is our answer!


Nice explaination pushpitkc
Intern
Intern
avatar
B
Joined: 23 Jul 2017
Posts: 3
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

Show Tags

New post 31 Aug 2017, 14:02
septwibowo wrote:
Luckisnoexcuse wrote:
Bunuel wrote:
f(x)=x^2−1. For which of the following values of x is f(x) divisible by 6?

A. 1812
B. 2721
C. 3118
D. 4245
E. 5653


Divisible by 6 = Divisible by 2 & Divisible by 3

none of the numbers should be divisible by 3 as they have to follow x^2-1 divisible by 3
only A, C & E left as the sum of their digits is not divisible by 3
B & D are out
now check the last digit of A , C and E
2^2-1 = 3 which is not divisible by 2 ...A out
8^2-1 = 3 which is not divisible by 2 ...C out
3^2-1 = 8 divisible by 2 and the answer

E


Could you please elaborate more the one that I highlighted?


If a number that is divisible by 3 is squared, the result is also divisible by 3. So looking at the answer choices, the answer choice cannot itself be divisible by 3 since we will end up subtracting 1 after we square it because after we subtract 1 the result will no longer be divisible by 3.
Intern
Intern
avatar
B
Joined: 09 Feb 2013
Posts: 24
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

Show Tags

New post 04 Sep 2017, 04:57
pushpitkc wrote:
The expression f(x)=x^2−1 = (x+1)(x-1)
Evaluating answer options
A. 1812 : f(x) = (1813)(1811)
B. 2721 : f(x) = (2722)(2720)
C. 3118 : f(x) = (3119)(3117)
D. 4245 : f(x) = (4244)(4246)
E. 5653 : f(x) = (5654)(5655)

Of the answer options, we can reject Options A and C straightaway,
as they are not divisible by 2.

Careful evaluation of the other answer options :
Option B = Both 2722 and 2720 are divisible by 2 but not by 3
Option D = Both 4244 and 4246 are divisible by 2 but not by 3.
But, in Option E, 5655 is divisble by 2 and 5654 is divisible by 3.
Hence Option E is our answer!


E. 5653 : f(x) = (5654)(5655)

Should be :
E. 5653 : f(x) = (5654)(5652)

5652 is divisible by 2 as well as 3.

Regards
Kshitij
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7575
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

Show Tags

New post 04 Sep 2017, 07:26
1
Bunuel wrote:
f(x)=x^2−1. For which of the following values of x is f(x) divisible by 6?

A. 1812
B. 2721
C. 3118
D. 4245
E. 5653



HI..

as also mentioned above \(x^2-1 = (x-1)(x+1)\)...
this should tell us that ANS will be a number that is NOT div by 3 and 2
A and C are div by 2 so eliminate
B and D are div by 3, so eliminate
ans E

Reason:-
1) if x is EVEN, both the number above it and below it will be odd so their product will be ODD and not div by 2
2) If x is div by 3, the number above and below it will not be div by 3

_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 10578
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

Show Tags

New post 21 Mar 2019, 05:18
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
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by   [#permalink] 21 Mar 2019, 05:18
Display posts from previous: Sort by

f(x)=x^2−1 For which of the following values of x is f(x) divisible by

  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®.