GMAT Club Olympics 2024 (Day 9): If n^4 + n^2 = 1, then which of the

Question

If  n^4 + n^2 = 1 , then which of the following must equal to  n^6 ?

A.  n^2 - 1

B.  n^2 + 1

C.  2n^2

D.  2n^2 - 1

E.  2n^2 + 1

Bunuel · Accepted Answer

GMAT Club Official Explanation:

n^6 = n^4*n^2

Since given that  n^4 = 1 - n^2 , then:

n^6 = n^4*n^2 =

= (1 - n^2)n^2 =

= n^2 - n^4 =

= n^2 - (1 - n^2) =

=2n^2 - 1

Answer: D.

jack5397 · Answer

IMO - D

n^4+n^2 = 1 ----- eq.1

multiply both sides by n^2

n^6+n^4 = n^2

Substitute the value of n^4 from eq.1

n^6 + (1-n^2) = n^2

n^6 = 2n^2-1

Option D

Milkyway_28 · Answer

A straightforward way to solve this is to equate  n^6  to the answer choices and see if they equal  n^4 + n^2 = 1

Intuitively, the lower options looked more suitable than the top ones so I started from the bottom and worked my way up.

2n^2 + 1=n^6

n^6 - 2n^2 = 1

n^2(n^4 - 2) = 1

Here I rearranged  n^4 + n^2 = 1  to  n^4 = 1 - n^2 ​​​​​​​ and plugged in  n^4

n^2(1 - n^2 - 2) = 1  
​​​​​​​
 - n^2 - n^4 = 1  or  n^2 + n^4 = - 1  Doesn't work

We try again with the next value

2n^2 - 1=n^6

n^6 - 2n^2 = - 1

n^2(n^4 - 2) = - 1

n^2(1 - n^2 - 2) = - 1

- n^2 - n^4 = - 1  or  n^2 + n^4 = 1  which works

The answer is D

pianogirl · Answer

n^4+n^2=1 => n^6 + n^4 = n^2 => n^6 = n^2 +n^2 - n^2 - n^4 = 2*n^2-1

The right answer is  D

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

GMAT Club Olympics 2024 (Day 9): If n^4 + n^2 = 1, then which of the

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

GMAT Club Olympics 2024 (Day 9): If n^4 + n^2 = 1, then which of the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards