MathRevolution wrote:

[GMAT math practice question]

Is \(n<0\)?

\(1) n-1<0\)

\(2) |3-n| > |n+5|\)

This is a different approach to statement 2:

Statement 2: |3-n| really just means 'the distance between 3 and n on a number line'.

For example, if n = 2, then |3-n| = |3-2| = |1| = 1. The distance between 3 and 2 on a number line is 1.

If n = 10, then |3-n| = |3-10| = |-7| = 7. And likewise, the distance between 3 and 10 on a number line is 7.

This is just a fact about

absolute values of differences.

Similarly, |n + 5| can be read as |n - (-5)|. That makes it the absolute value of a difference. So, you can read this one as 'the distance between n and -5 on a number line'.

That means you can fully translate statement 2 like this:

The distance between n and 3 on a number line, is greater than the distance between n and -5 on a number line.Or in other words,

n is closer to -5 than it is to 3.What does that tell you about n? In other words, which numbers are closer to -5 than to 3? Jot down a number line on your paper and start figuring it out.

The numbers to the right of 3 will all be closer to 3, so those don't work:

Now look at the numbers in between -5 and 3:

All of the ones that are closer to -5, are negative numbers.

We can conclude that if a number is closer to -5 than it is to 3, it's definitely got to be a negative number.

That makes statement 2

sufficient.

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