If p and q are nonnegative integers, is √x an integer?

Question

(1)  \frac{x}{5^p*2^q}=k , where k is an integer.
(2) p and q are even integers.

Balajikarthick1990 · Answer

I will go with E....

st 2 --no info abt x

st 1: p=0 q=0 i took x=1 and x=2 in one case root(x) is int and in other no...

Combining same case applied.

Omar31Peru · Answer

Hi Bunuel,

St 1 not sufficient
St 2 Not Sufficient
Both 1 and 2 , Is this the solution ?

p , q= 2 5^2 * 2 ^2 = 100 ; so x= 100 or 1000 Ok
p= 4 ; q =2 ---- 1250 , so x = 1250 or 2500 not sufficient. Is this method correct to get the answer E?

adiagr · Answer

Option (2) should give us a hint.

Statement (1) 
say p = (1/2) and q = (1/2)
 \frac{x}{5^p2^q} . Then if x =  (5^{0.5})*(2^{0.5}) 
we get k= 1.

So condition of statement 1 is satisfied . It can be seen that  √x is not an integer

Now say p = 2 and q = 2
 \frac{x}{5^p2^q} . Then if x =  (5^2)*(2^2) 
we get k= 1.

So condition of statement 1 is satisfied . It can be seen that in this situation  √x  is  an integer

So statement 1 is not sufficient.

Statement 2 says nothing about x hence not sufficient

Combining Statement 1 and 2.

when x =  (5^2)*(2^2) ; p=2, q=2

We know that, √x is an integer

Suppose

x = 2 *  (5^2)*(2^2) ; p=2, q=2

then both statement 1 and 2 are satisfied.

In this case: √x is not an integer.

E is the answer.

gauravsaggis1 · Answer

so,
p & q>=0.
 
for sqrt X to be integer, x must be a square.
1) can not be said anything about k,p and q. so insufficient
2) mentions nothing about the relation among x,p and q. so insufficient.
1)+2). p and q are square but k is still unknown. so, insufficient.

Omar31Peru · Answer

Thanks for your help¡¡

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 and q are nonnegative integers, is √x an integer?

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