|xy| > x^2y^2 ?

[guerrero]

|xy| > x^2y^2 ?

(1) 0 < x^2 < 1/4

(2) 0 < y^2 < 1/9

Source : GMATPREP

I am struggling to deduce the question . Any one can elaborate ? Thanks!

OA C

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Hi guerrero,

This DS question is perfect for TESTing values, especially since we are told NOTHING about X and Y to begin....

We're asked if |XY| > (X^2)(Y^2)? This is a Yes/No question.

Fact 1: 0 < X^2 < 1/4

This tells us that -1/2 < X < 1/2
If X = 0, then it doesn't matter what Y is, and the answer to the question is NO
If X = .1 and Y = 1, then the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: 0 < Y^2 < 1/9

This tells us that -1/3 < Y < 1/3
We can use the exact same "pattern" from Fact 1 here in Fact 2 (we'll just flip-flop the X and Y values)
If Y = 0, then it doesn't matter what the X is, and the answer to the question is NO
If Y = .1 and X = 1, then the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined we know:
-1/2 < X < 1/2
-1/3 < Y < 1/3

Number Property knowledge comes in handy here.
|XY| will be a positive fraction.
(X^2)(Y^2) will be a SMALLER positive fraction because we're squaring two fractions and multiplying them.

The answer to the question is ALWAYS YES.
Together SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[lunarpower]

A student called my attention to this thread.

Fact 1: 0 < X^2 < 1/4
If
This tells us that -1/2 < X < 1/2
If X = 0, then it doesn't matter what Y is, and the answer to the question is NO
If X = .1 and Y = 1, then the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: 0 < Y^2 < 1/9

This tells us that -1/3 < Y < 1/3
We can use the exact same "pattern" from Fact 1 here in Fact 2 (we'll just flip-flop the X and Y values)
If Y = 0, then it doesn't matter what the X is, and the answer to the question is NO
If Y = .1 and X = 1, then the answer to the question is YES
Fact 2 is INSUFFICIENT

Rich -- I agree that testing cases is the best way to go here, but, careful with the due diligence. We know that 0 < x^2 < 1/4. So x = 0 is not an allowed value; the allowed values are everything between -1/2 and +1/2, except 0.
For y it's pretty much the same deal, with 1/3 substituted for 1/2.

[lunarpower]

So, when you test cases, it has to be a little more interesting. Basically, in statement 1 you have to pick a value of y that's greater than 1/|x| (or less than -1/|x|), and vice versa for statement 2.
E.g., in statement 1, if x = 1/3, then you have to pick y > 3 or < -3.
(If you don't see why, try it! You'll notice what happens if x = 1/3 and y = 3. From there, you can discern pretty quickly why y has to be bigger.)

Also, with the two statements together, if you don't IMMEDIATELY see the number properties at work, just start testing values.
Once you try a couple of values that fit both statements together, it will become abundantly clear what is going on, even if you didn't think about "fraction properties" to begin with.

[mevicks]

|xy| > x^2y^2 ?

(1) 0 < x^2 < 1/4

(2) 0 < y^2 < 1/9

Q: Is |xy| > x²y² ?
Square both sides:

Is x²y² > (x²y²)² ?

St1: Gives no information about y, INSUFFICIENT
St2: Gives no information about x, INSUFFICIENT

St1+St2:

Let x² = y² = (1/10)
(1/10) is less than both (1/4) and (1/9) & greater than 0

So the target question becomes Is (1/100) > (1/100)² ?
The answer is YES, and we can test other values to prove that this is always true for fractions(Basically a square of a fraction is smaller than the fraction itself)

Answer C

Regards,
Vivek