Tough Modulus Questions--Data Suficiency

[Abhimanyu Sood]

Here are three Mod Questions from IMS GMAT...

1 ) In the number line,is R between S and T ?
a.) |r-s|<|r-t|
b.)|r-s|>|s-t|

2.) In the number line,is s between r and T ?
a.)|r-s|<|r-t|
b.)|r-s|<|s-t|


3.) In the number line,is s between r and T ?
a.)|r-t|>|r-s|
b.)|r-t|>|t-s|

My answers are

1.b
2.e
3.c

Please let me know if someone has different answers....

[Guest]

I got

1.b, 2 e and 3.c

Pathik

[StaceyKoprince]

Sorry we haven't gotten back to you for so long - we've been swamped!

Please make sure to read (and follow!) the forum guidelines. Only one problem should be posted in each thread. I'll answer your first one here; if you'd like us to address the others, please repost them in their own threads.

I got the same thing - B.

[Guest]

Stacey, could you explain how you arrived at your answer for number one (or how you'd do any of the three problems)? Double absolute value problems are a bit confusing to me b/c there are three scenarios to try, right?

Thanks

[rfernandez]

Can't speak for how Stacey did it, but I suggest approaching these problems graphically. I look only at the first problem.

The key is to understand that |a - b| means "the distance between a and b on the number line." Try a bunch of values for a and b, varying their signs, and you'll see that this "distance" interpretation is accurate. For example, if a = -7 and b = 2, the distance between these numbers is 9 units. Also, |a - b| = |-7 - 2| = |-9| = 9

1 ) In the number line,is R between S and T ?
(1) |r - s| < |r - t|
(2) |r - s| > |s - t|

Rephrase (1): The distance between r and s is less than the distance between r and t. Draw a number line, and place r and s on it. Now, you want to place t on the number line such that t's distance from r is greater than s's distance from r. That leaves two possibilities:
----------r-----s--t------
-t--------r-----s---------

This is insufficient information, therefore. r MAY be between s and t, it need not be.

Rephrase (2): The distance between r and s is greater than the distance between s and t. Draw a number line, and place r and s on it. Now, you want to place t on the number line such that t's distance from s is less than s's distance from r. That leaves two possibilities:
-------r--------s--t------
-------r-----t--s---------

In either case, the answer to the question is "No." Sufficient. The answer is B.