New Set: Number Properties!!!

I read on gmat club that the value of square root of x is considered positive value only (We consider + or - for absolute values only). So, in statement 2 why are we considering square root of x square as +1 or -1?

Both the square root sign (\(\sqrt{}\)) and absolute value cannot give negative result.

The value of \(\sqrt{x^2}\) is still positive for both 1 and -1:

\(\sqrt{x^2}=\sqrt{1^2}=\sqrt{1}=1\);
\(\sqrt{x^2}=\sqrt{(-1)^2}=\sqrt{1}=1\).

Hi Bunnel,

could you please tell how the list of 10 terms will look like with product of any two term resulting to terminating decimal ? can we have all the numbers in list as 1/2 ?

1) can my list look like : 1/2,1/2, 1/2.... as per me this also satisfy the statement 2 and median is equal to 0.5 or can list have all the term as 1/5 , in that median will be 0.2?




8. List A consist of 10 terms, each of which is a reciprocal of a prime number, is the median of the list less than 1/5?

(2) The product of any two terms of the list is a terminating decimal. This statement implies that the list must consists of 1/2 or/and 1/5. Thus the median could be 1/2, 1/5 or (1/5+1/2)/2=7/20. None of the possible values is less than 1/5. Sufficient.

For (2) the set could be any combination of 1/2's and 1//5:
{1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2}
{1/5, 1/5, 1/5, 1/5, 1/5, 1/5, 1/5, 1/5, 1/5, 1/5}
{1/5, 1/5, 1/5, 1/5, 1/5, 1/2, 1/2, 1/2, 1/2, 1/2}
...

The median could be 1/2, 1/5 or (1/5+1/2)/2=7/20. None of the possible values is less than 1/5. So, we have a NO answer to the question. Sufficient.

Hey Bunuel,

Had a doubt here. For case 2, since the question stem says that "\(2\sqrt{x^2}\) is a prime number" the answer to that has been to be a positive number+2 right ? So out of the two cases +1 and -1, we can't take the value -1 . So Case 2 is sufficient right? Please correct me if I am wrong.

Both 1 and -1 worrk there.

\(2\sqrt{x^2}=2\sqrt{1^2}=2\sqrt{1}=2\);
\(2\sqrt{x^2}=2\sqrt{(-1)^2}=2\sqrt{1}=2\).

But sqrt(1) can be both +1 or -1 right? and here since it says 2 is prime, it has to be a positive value.

No. This has already been addressed in this thread couple of times.

\(\sqrt{...}\) is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign (\(\sqrt{...}\)) always means non-negative square root. Check this post: https://gmatclub.com/forum/new-set-numb ... l#p2434955

 

­The question says x and y are consecutive perfect squares, not that x and y are squares of consecutive numbers. Is it right to assume that they are squares of consecutive numbers? 

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x and y being consecutive perfect squares implies that they are squares of consecutive integers. For example, 9 and 16 are consecutive perfect squares, and they are squares of consecutive integers 3 and 4, respectively.