Is y > 0?

Imo C

Statement 1 xy<√x2y2 is not sufficient as we can have negative values of x as well as y because this is only possible if one of the values is negative.
Statement 2 is also not sufficient as it does not tell us anything about y, but is does tell us the value of x is negative.
Taking together we have sufficient information to answer the question.

Bunuel Something doesn't make sense to me in this question. please help

Statement 1: The general rule states that radical a multiple by radical a = a. So in our case radical xy multiple by radical xy = xy. Other general rule states that x multiple by x = x in a square. So in our case radical xy multiple by radical xy = radical of x in square multiple by y in square (both variables should be under the radical). When we combine those two rules it seems that both sides of the inequality suppose to be equal - radical xy multiple by radical xy in each side. but for some reason it is not correct as the statement state clearly that the left side of the inequality is small than the right side of it.

Similar problem i faced with statement 2 - if we raise both sides of the inequality by a square it seems that both sides suppose to be equal - x in a square in each side. But according the statement it is not true.

Thanks in advance!

\(y > 0\)?

(1) \(xy < \sqrt{x^2y^2}\)

This statement tells us two things:

1. x is negative and y is positive OR
2. y is negative and x is positive

Hence, (1) =====> NOT SUFFICIENT

(2) \(\sqrt{x^2}>x\)[/quote]

This statement tells us that

x is negative

However, we cannot say anything about y

Hence, (2) =====> NOT SUFFICIENT

Combining (1) & (2)

x is negative (From (2)

As we know that x is negative from (1) we can see that y has to take a positive value in order for (1) to be true

Hence, y > 0 can be answered

Hence, Answer is C

Hi Mate,

Which Bunnel replies to you, let me share what helps me sort through the inequalities, and such questions in general.

The question you should always ask yourself is, when will a product of 2 numbers, be less than the square root, of its squares?

If you take 2 numbers, it will help you visualise better.
Take x = -4 and y = 4, their product will be -16.
If you square both the numbers, you get 16*16 = 256 (a positive number)
And now if you take the square root, you get 16 (positive number)
=> -16 < 16

In essence, a product of 2 numbers can only be less that the product of it's square, and then a square root only if one of the numbers is a negative number.

hope this helps.

Hello oryahalom,

Looks like your question was already answered by akshayk, however in case that is not clear, just remember one thing, whenever you are working with inequalities NEGATIVE values play an important role, and that is the reason inequalities is very tricky.

Lets solve your query with an example:

We can write:
\(2^2 = 4\) OR
\(-2^2 = 4\)

So, in case you have a variable, \(x^2 = 4\), you cannot assume that \(x\) will always take a positive value, as shown above, \(x\) can either be \(+2\) or \(-2\)

Similarly, now when you take a root:

\(\sqrt{4} = +/-2\)

Hope this clarifies, if you please let me know.