If xy > 0, is (xy)^2<√xy ?

Yes, you can square both sides her as both are +ive..

Hi chetan2u ! Can you explain the other method where we square the stem?

Given: xy>0
So both positive or both negative.

Approaching to check if answer is C or E:
Let's look at Statement 2 first:

x-16+16>-16+16
x>0

So we know x is positive.
We know y has to be positive now.

Statement 1:
4/x>7y.

We know x is positive. So y has to be positive.
4/1>7y
4>7y
4/7>y

Let's take y as 1/4 and x as 1

\((xy)^2<\sqrt{xy}\)
(1/4)^2<1/2

Sufficient.

Given that xy > 0 ---- x and y have the same sign x < 0 & y < 0 OR x>0 and y>0

Statement 1:
4/x > 7y -------> 4/x – 7y > 0 ----------- (4-7xy) / x > 0
Now we don’t know the sign of x hence we can not multiply both sides by x
If x > 0 then xy < 0.57 -------- 0 < xy < 0.57 ---------- it will give YES as an answer to the question
If x < 0 the xy > 0.57 ------- xy > 0.57---------- now this can give YES or NO as an answer to the question
INSUFFICIENT

Statement 2:
X – 16 > -16 ----------- x > 0 ------ if x>0 then y>0 since we know that xy>0
But we don’t know where the values of xy together lie
If 0< xy < 1 then we get YES to the question
If xy > 1 then we can NO to the question
INSUFFICIENT

Statement 1+ 2
By combining these we know that x>0 and y>0 and xy>0
The only case that will work is xy < 0.57 --------- hence we can get a conclusive answer
SUFFICIENT

Answer – C

Both sides of the inequality in the question stem are positive.
Implication:
We can safely square both sides, with the following result:
Is \((xy)^4 < xy\) ?
The answer will be YES only if 0<xy<1.
Question stem, rephrased:
Is 0<xy<1?

Statement 1:
Case 1: x and y are both negative
Multplying both sides by x and flipping the inequality, we get:
4 < 7xy
4/7 < xy
If xy=0.9, then the answer to the rephrased question stem is YES.
If xy=1, then the answer to the rephrased question stem is NO.
INSUFFICIENT.

Statement 2:
Adding 16 to both sides, we get:
x>0
No information about y.
INSUFFICIENT.

Statements combined:
Since x is positive, multiplying both sides of Statement 1 by x yields the following:
4 > 7xy
4/7 > xy
Since xy>0 and xy < 4/7, we know that 0<x<1.
Thus, the answer to the rephrased qustion stem is YES.
SUFFICIENT.