BrentGMATPrepNow wrote:
Is x < -1?
(1) (x - 5)² > (1 - x)²
(2) (2 - x)² < (4 + x)²
No takers?
Here's my solution...
Target question: Is x < -1? Statement 1: (x - 5)² > (1 - x)² Note: I created this question to see if anyone falls for the trap of taking the square root of both sides to get: x - 5 > 1 - x
If you fall for this trap, you will incorrectly conclude that x > 3, when, in actuality, we should get x < 3
Key concept: If k is a negative value, and we square it, and then take the square root, we get a positive value.
For example, if x = -5, then x² = (-5)² = 25, which means √x = √25 = 5, which is not the same value we started with. Here's how we should tackle the question....
Given: (x - 5)² > (1 - x)²
Expand and simplify both sides to get: x² - 10x + 25 > 1 - 2x + x²
Subtract x² from both sides: -10x + 25 > 1 - 2x
Add 10x to both sides: 25 > 1 + 8x
Subtract 1 from both sides: 24 > 8x
Divide both sides by 8 to get: 3 > x
So, x could equal 2 in which case the answer to the target question is
NO, x is not less than -1Alternatively, x could equal -3 in which case the answer to the target question is
YES, x is less than -1Since we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: (2 - x)² < (4 + x)²Expand and simplify both sides to get: 4 - 4x + x² < 16 + 8x + x²
Subtract x² from both sides to get: 4 - 4x < 16 + 8x
Add 4x to both sides: 4 < 16 + 12x
Subtract 16 from both sides: -12 < 12x
Divide both sides by 12 to get: -1 < x
So, the answer to the target question is
NO, x is not less than -1Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B