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 amFollowed by: 2 members

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.

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 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; 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: x² = x + 1
We want to determine the value of x³
So, let's take the given equation and multiply both sides by x to get: (x)(x²) = (x)(x + 1)
Simplify: x³ = x² + x
Check the answer choices. . . . . x² + x is not there!
At this points, we need to use the given information to create equivalent equations

Since we're told that x² = x + 1.
So, take x³= x² + x and replace x² with x + 1 to get: x³ = (x + 1) + x
Simplify: x³ = 2x + 1
Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Apr 24, 2018 10:43 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

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

Answer: C

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