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# For all integers i, f(i) = i(i-1). What is the value of f(x)?

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Director
Joined: 08 Jun 2013
Posts: 515
Location: India
GMAT 1: 200 Q1 V1
GPA: 3.82
WE: Engineering (Other)
For all integers i, f(i) = i(i-1). What is the value of f(x)?  [#permalink]

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03 Aug 2018, 08:12
2
00:00

Difficulty:

85% (hard)

Question Stats:

43% (01:47) correct 57% (01:45) wrong based on 68 sessions

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For all integers i, f(i) = i(i-1). What is the value of f(x)?

(1) f(x)=x
(2) f(x-1) = (x-2)

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Math Expert
Joined: 02 Sep 2009
Posts: 51185
Re: For all integers i, f(i) = i(i-1). What is the value of f(x)?  [#permalink]

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03 Aug 2018, 09:09
For all integers i, f(i) = i(i-1). What is the value of f(x)?

(1) f(x)=x.

f(x) = x(x - 1), so x(x - 1) = x --> x = 0 or x = 2.

If x = 0, then f(x) = 0 but if x = 2, then f(x) = 2. Not sufficient.

(2) f(x-1) = (x-2).

f(x - 1) = (x - 1)(x - 1 - 1), so (x - 1)(x - 1 - 1) = (x - 2) --> x = 2.

If x = 2, then f(x) = f(2) = 2(2 - 1) = 2. Sufficient.

Hope it's clear.
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Joined: 03 Apr 2018
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Re: For all integers i, f(i) = i(i-1). What is the value of f(x)?  [#permalink]

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06 Aug 2018, 12:03
Bunuel wrote:
For all integers i, f(i) = i(i-1). What is the value of f(x)?

(1) f(x)=x.

f(x) = x(x - 1), so x(x - 1) = x --> x = 0 or x = 2.

If x = 0, then f(x) = 0 but if x = 2, then f(x) = 2. Not sufficient.

(2) f(x-1) = (x-2).

f(x - 1) = (x - 1)(x - 1 - 1), so (x - 1)(x - 1 - 1) = (x - 2) --> x = 2.

If x = 2, then f(x) = f(2) = 2(2 - 1) = 2. Sufficient.

Hope it's clear.

for statement 1 , I did x(x-1)=x, so x^2-x=x => x^2=2x =>x=2 .... i am not able to understand how x can be 0 going by this
Director
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Joined: 01 Oct 2017
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WE: Supply Chain Management (Energy and Utilities)
Re: For all integers i, f(i) = i(i-1). What is the value of f(x)?  [#permalink]

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06 Aug 2018, 12:11
Bunuel wrote:
For all integers i, f(i) = i(i-1). What is the value of f(x)?

(1) f(x)=x.

f(x) = x(x - 1), so x(x - 1) = x --> x = 0 or x = 2.

If x = 0, then f(x) = 0 but if x = 2, then f(x) = 2. Not sufficient.

(2) f(x-1) = (x-2).

f(x - 1) = (x - 1)(x - 1 - 1), so (x - 1)(x - 1 - 1) = (x - 2) --> x = 2.

If x = 2, then f(x) = f(2) = 2(2 - 1) = 2. Sufficient.

Hope it's clear.

for statement 1 , I did x(x-1)=x, so x^2-x=x => x^2=2x =>x=2 .... i am not able to understand how x can be 0 going by this

$$x^2=2x$$
Or, $$x^2-2x=0$$
Or, x(x-2)=0
Or, x=0 or x-2=0

So, x=0, 2

P.S.:- When you see variables in both sides of linear equations or inequalities, never cancel the common variable terms instead drag them to one side and factorize.
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Regards,

PKN

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Posts: 384
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GMAT 1: 630 Q44 V33
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WE: Marketing (Telecommunications)
For all integers i, f(i) = i(i-1). What is the value of f(x)?  [#permalink]

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06 Aug 2018, 12:25

x^2=2x => x^2-2x=0 => x(x-2)=0 => x=0 OR (x-2)=0 => x=0 OR x=2
For all integers i, f(i) = i(i-1). What is the value of f(x)? &nbs [#permalink] 06 Aug 2018, 12:25
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