If x^2=x+1, then x^3=?

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 am; Followed by:2 members

If x^2=x+1, then x^3=?

by Gmat_mission » Mon Apr 23, 2018 12:27 am

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$$If\ \ \ x^2=x+1,\ \ then\ \ \ x^3=?$$ A. 3x+2
B. 3x-2
C. 2x+1
D. 2x-3
E. 3x+4

[spoiler]OA=C[/spoiler].

How can I find the correct answer? I couldn't solve this PS question. May someone helps me? Please.

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Source: Beat The GMAT — Problem Solving | Mon Apr 23, 2018 12:27 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Mon Apr 23, 2018 12:44 am

Gmat_mission wrote:$$If\ \ \ x^2=x+1,\ \ then\ \ \ x^3=?$$ A. 3x+2
B. 3x-2
C. 2x+1
D. 2x-3
E. 3x+4

[spoiler]OA=C[/spoiler].

How can I find the correct answer? I couldn't solve this PS question. May someone helps me? Please.

We have x^2 = x + 1 ---(1)

Multyplying the equation with x, we get

x^3 = x^2 + x ---(2),

Replacing the value of x^2 in equation (2), we get

x^3 = (x + 1) + x = 2x +1

The correct answer: C

Hope this helps!

-Jay
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Manhattan Review GMAT Prep

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Mon Apr 23, 2018 5:09 am

Gmat_mission wrote:$$If\ \ \ x^2=x+1,\ \ then\ \ \ x^3=?$$ A. 3x+2
B. 3x-2
C. 2x+1
D. 2x-3
E. 3x+4

GIVEN: xÂ² = x + 1
We want to determine the value of xÂ³
So, let's take the given equation and multiply both sides by x to get: (x)(xÂ²) = (x)(x + 1)
Simplify: xÂ³ = xÂ² + x
Check the answer choices. . . . . xÂ² + x is not there!
At this points, we need to use the given information to create equivalent equations

Since we're told that xÂ² = x + 1.
So, take xÂ³= xÂ² + x and replace xÂ² with x + 1 to get: xÂ³ = (x + 1) + x
Simplify: xÂ³ = 2x + 1
Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members