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

 It is currently 16 Jul 2018, 03:57

### 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

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47015
f(x)=x^2−1 For which of the following values of x is f(x) divisible by [#permalink]

### Show Tags

29 Aug 2017, 23:53
00:00

Difficulty:

55% (hard)

Question Stats:

62% (01:17) correct 38% (01:09) wrong based on 118 sessions

### HideShow timer Statistics

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

_________________
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2933
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

30 Aug 2017, 00:22
2
4
The expression f(x)=x^2−1 = (x+1)(x-1)
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
Director
Joined: 18 Aug 2016
Posts: 631
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by [#permalink]

### Show Tags

30 Aug 2017, 00:05
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
Joined: 27 Dec 2016
Posts: 231
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
f(x)=x^2−1 For which of the following values of x is f(x) divisible by [#permalink]

### Show Tags

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
Joined: 27 Dec 2016
Posts: 231
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by [#permalink]

### Show Tags

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
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

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
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

30 Aug 2017, 02:12
pushpitkc wrote:
The expression f(x)=x^2−1 = (x+1)(x-1)
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
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

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
Joined: 09 Feb 2013
Posts: 26
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by [#permalink]

### Show Tags

04 Sep 2017, 04:57
pushpitkc wrote:
The expression f(x)=x^2−1 = (x+1)(x-1)
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
Joined: 02 Aug 2009
Posts: 6202
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by [#permalink]

### Show Tags

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

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by   [#permalink] 04 Sep 2017, 07:26
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®.