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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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29 Aug 2017, 23:05

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

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

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29 Aug 2017, 23:15

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.

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

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29 Aug 2017, 23:21

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?
_________________

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

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29 Aug 2017, 23:22

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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!

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

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30 Aug 2017, 01:11

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

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

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30 Aug 2017, 01:12

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!

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

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31 Aug 2017, 13:02

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.

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

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04 Sep 2017, 03:57

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!

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 _________________