If p^2 is an integer and (p^6-p^4-q-1)^(1/2) = 10 what is the value of

Question

If  p^2  is an integer and  \sqrt{p^6-p^4-q-1}=10  what is the value of  p^2 ?

(1)  p^2=\sqrt{p^2+20}

(2)  q=\sqrt{q+2}

ReedArnoldMPREP · Answer

Think there's a typo here. The square root in the stem doesn't have an '=.'

But statement one shows me that 'p^2' is 5, I believe.

Not sure how realistic this question is.

Bunuel · Answer

______________________
Fixed the typo. Thank you!

chetan2u · Answer

(1)  p^2=\sqrt{p^2+20} 
Square both sides..
 p^4=p^2+20............p^4-p^2-20=0.........(p^2-5)(p^2+4)=0 
As  p^2  is a square root it has to be a positive integer. Also, If  p^2 = -4 , then p will be an imaginary number.
Thus  p^2=5 
Sufficient

(2)  q=\sqrt{q+2} 
Square both sides..
 q^2=q+2......q^2-q-2=0....(q+1)(q-2)=0 
q can be 2 or -1, but again q can be positive so 2.
Putting 2 in the equation  \sqrt{p^6-p^4-q-1}=10  does not give p^2 as 5. So, I believe the statement should be 
  q=-\sqrt{q+2}  
So q is negative, and so q=-1.
Put this value in  \sqrt{p^6-p^4-q-1}=10 
 \sqrt{p^6-p^4-(-1)-1}=10 
 \sqrt{p^6-p^4}=10 
 p^6-p^4=100 
Three possible values of p^2, but only integer value is 5, and other two are imaginary values.
Sufficient

D

Please check statement II for typo.

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.

If p^2 is an integer and (p^6-p^4-q-1)^(1/2) = 10 what is the value of

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 Data Sufficiency (DS) Questions

If p^2 is an integer and (p^6-p^4-q-1)^(1/2) = 10 what is the value of

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