If I've tested it correctly, answer choice A

Mechmeera wrote:Source: Veritas Prep

Is (y-10)² > (x+10)²?

1. -y>x+5
2. x>y

(y-10)² > (x+10)² ?

y²+ 100 - 20y > x² + 100 + 20x ?

y² - x² - 20y - 20x > 0 ?

(y+x)(y-x) - 20(y+x) > 0 ?

(y+x)(y - x - 20) > 0 ?

The left side will be greater than 0 if the factor in red and the factor in blue have the SAME SIGN.
Question stem, rephrased:
Do y+x and y-x-20 have the same sign?

Statement 2: -y > x+5
-5 > y+x
y+x < -5.
Thus, the factor in red is negative.
No information about the factor in blue.
INSUFFICIENT.

Statement 2: x>y
0 > y-x
y-x < 0.
Thus, the factor in blue is negative.
No information about the factor in red.
INSUFFICIENT.

Statements combined:
Since the factor in red and the factor in blue are both negative, SUFFICIENT.

The correct answer is C.

Since both (y - 10) and (x + 10) are squared, this question can be reduced to the following.

Is |y - 10| > |x + 10|?

Statement 1: -y > x + 5

One way to go from here is to plug in some numbers.

Try y = -6 and x = 0.

|-6 - 10| > |0 + 10| Yes.

Try y = 2 and x = -100 (Plugging in numbers with large absolute values often makes things very clear.)

|2 - 10| < |-100 + 10| No.

Insufficient.

Statement 2: x > y

We already got answer Yes with x = 0 and y = -6.

Try x = 100 and y = 0

|0 - 10| < |100 + 10| No.

Insufficient.

Statements Combined:

Given -y > x + 5 and x > y we can add the two inequalities to get the following.

-y + x > x + y + 5

-5 > 2y

y < -5/2

So y must be negative.

If y is negative and -y > x + 5, then |y| > x + 5 and |y - 10| = |y| + 10

So if x is positive, then we get |y| + 10 > x + 5 + 10 Yes.

Given that y < x, if x is negative then |y| > |x| and |y - 10| > |x + 10| Yes.

Sufficient.

The correct answer is C.

That's a pretty long route to the answer though. So here is a, somewhat, more efficient alternative.

Is (y − 10)² > (x + 10)²?

Is (y − 10)² - (x + 10)² > 0

Now we have a difference of squares that can be factored.

Is (y - 10 + x + 10)(y - 10 - x - 10) > 0?

Is (y + x)(y - x - 20) > 0?

For the expression to be true, both factors on the left must have the same sign.

Statement 1: - y = x + 5

x + y = -5

The first factor is negative.

For the second factor, use y = -x - 5

Substitute to get (y - x - 20) = (y + y - 15)

The value of (y + y - 15) could be positive or negative depending on the value of y.

Insufficient.

Statement 2: x > y

If x > y, then (y - x - 20) < 0

However (y + x) could be positive or negative.

Statements combined:

Statement 1 means (y + x) < 0.

Statement 2 means (y - x - 20) < 0

So both factors are negative and (y + x)(y - x - 20) > 0.

Sufficient.

The correct answer is C.