Is x < -1?

(1) (x - 5)² > (1 - x)²

(2) (2 - x)² < (4 + x)²

Answer: B

Source: www.gmatprepnow.com

## Is x < -1?

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### GMAT/MBA Expert

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No takers?[email protected] wrote: ↑Mon Jun 27, 2022 10:52 amIs x < -1?

(1) (x - 5)² > (1 - x)²

(2) (2 - x)² < (4 + x)²

Answer: B

Source: www.gmatprepnow.com

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 -1

Alternatively, x could equal -3 in which case the answer to the target question is YES, x is less than -1

Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

**Statement 2: (2 - x)² < (4 + x)²**

Expand 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 -1

Since we can answer the target question with certainty, statement 2 is SUFFICIENT

**Answer: B**