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¡¡

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

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

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