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Math Expert V
Joined: 02 Sep 2009
Posts: 59725
f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 63% (02:00) correct 37% (02:00) wrong based on 138 sessions

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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

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

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3
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!

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Current Student P
Joined: 18 Aug 2016
Posts: 593
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]

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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
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Luckisnoexcuse
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Concentration: Marketing, Social Entrepreneurship
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f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

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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.
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Concentration: Marketing, Social Entrepreneurship
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Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

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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?
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Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

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

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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
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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]

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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.
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Joined: 09 Feb 2013
Posts: 22
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

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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 V
Joined: 02 Aug 2009
Posts: 8320
Re: f(x)=x^2−1 For which of the following values of x is f(x) divisible by  [#permalink]

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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

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

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