Data Sufficiency

Hi practhi18oct,

Yes, your approach is correct. This DS question has a clever "design element" to it - the entire prompt revolves around X and it's relationship to the number 3 (less than 3, equal to 3, greater than 3). Recognizing the built-in patterns that the GMAT writers place into their questions can make answering those questions a whole lot easier.

In other DS prompts, you might have to do a bit more work and consider other possibilities (e.g. X as a positive or negative fraction), but you nailed it here. As you continue to practice DS questions, it's important to be thorough - there are always obvious possibilities, but the measure of your success with be in spotting and evaluating the LESS OBVIOUS possibilities.

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

Is √[(x - 3)²] = 3 - x ?

1. x ≠ 3
2. -x|x| > 0

Target question: Is √[(x - 3)²] = 3 - x ?

This question is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

To begin, notice that we have two nice rules:
- If k > 0, then √(k²) = k
- If k < 0, then √(k²) = -k

Now observe that (3-x) = -(x-3)

Given the above information, under what conditions will √[(x-3)²] = 3-x?
In other words, under what conditions will √[(x-3)²] = -(x-3)?
This will occur IF x-3 is NEGATIVE.

So, we can now rephrase the target question as: Is (x-3) negative?
Or we can write: Is x-3 < 0?

. . . or better yet: Is x < 3?

Now that we've REPHRASED the target question in much simpler terms, we can check the statements.

Statement 1: x ≠ 3
This does not give us a definitive answer to the REPHRASED target question (Is x < 3? )
As such, statement 1 is NOT SUFFICIENT

Statement 2: -x|x| > 0
First notice that this implies that x does not equal zero.
Next, notice that, if x does not equal zero, then |x| will always be positive.
So, -x|x| > 0 is the same as saying (-x)(positive) > 0
In other words, the product (-x)(positive) results in a positive number.
This tells us that (-x) must be positive, which means x must be negative.
If x is negative, then x is definitely less than 3.
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent