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Is (y–10)2>(x+10)2?
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Source: Beat The GMAT — Data Sufficiency |
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GMATGuruNY
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(y-10)² > (x+10)² ?Mechmeera wrote:Source: Veritas Prep
Is (y-10)² > (x+10)²?
1. -y>x+5
2. x>y
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.
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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.
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.
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Contact me at [email protected] for a free consultation.
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Hi diegocml,
Since you didn't show your work, it's unclear whether you actually solved the question correctly or not (since the answer you've listed is incorrect). If you show your work, then we can figure out what mistakes (if any) you made.
GMAT assassins aren't born, they're made,
Rich
Since you didn't show your work, it's unclear whether you actually solved the question correctly or not (since the answer you've listed is incorrect). If you show your work, then we can figure out what mistakes (if any) you made.
GMAT assassins aren't born, they're made,
Rich
