AS # 32

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oquiella: Master | Next Rank: 500 Posts; Posts: 164; Joined: Tue May 12, 2015 9:06 am; Thanked: 3 times

by oquiella » Sat Oct 24, 2015 3:18 pm

32. Is |a-3| < 2?
(1) |a| > 2
(2) |a-1| < 3

EXPLAIN IN STEPS

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Source: Beat The GMAT — Data Sufficiency | Sat Oct 24, 2015 3:18 pm

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

by MartyMurray » Sat Oct 24, 2015 4:57 pm

You could solve this algebraically, but it might be faster and easier to just use some picked numbers along with logic.

For each of the statements if there is a way to make |a-3| less than and also greater than or equal to 2, then the statement is insufficient.

Statement 1 gives us a set of numbers to work with, all those greater than 2 and less than -2.

If we plug 3 into the original statement, we get |3-3| = |0| < 2.

If we plug -3 into the original statement, we get |-3-3| = |-6| > 2.

So Statement 1 is insufficient.

Statement 2 gives us another set of numbers, all those within 3 units of 1.

3 works again, and once again gives us |0| < 2.

-1 works, and plugged into the original statement -1 gives us |-1-3| = |-4| > 2.

So Statement 2 is insufficient.

Let's try combining the statements.

Given Statement 1, a cannot be 0 and if a is negative, it has to be less than -2.

Given Statement 2, if a is negative, it has to be greater than -2.

So no negative values of a are possible.

Given Statement 1, if a is positive, it has to be greater than 2.

Given Statement 2, a has to be be within 3 units of 1, meaning a < 4.

So with the statements combined the only possible values of a are 2 < a < 4.

Let's test the end points.

Plugging 4 into the original equation gives us |4-3| = |1| < 2

Plugging 2 into the original equation gives us |2-3| = |-1| < 2

Any a between 4 and 2 will give us a-3 between 1 and -1.

So combined the statements are sufficient and the answer is C.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Oct 25, 2015 2:45 am

oquiella wrote:32. Is |a-3| < 2?
(1) |a| > 2
(2) |a-1| < 3

|x-y| = the DISTANCE between x and y.
|x| = the distance between x and 0.

|a-3| < 2?
In words:
Is the distance between a and 3 less than 2?
Put another way:
On the number line, is a within the red portion below?
.....1<-----3----->5.....

Question stem, rephrased:
On the number line, is a between 1 and 5?

Statement 1: |a| > 2
In words:
The distance between a and 0 is is greater than 2.
Put another way:
On the number line, a is within one of the two blue portions below:
<----- -2.....0.....2 ----->
If a=3, then a is between 1 and 5 on the number line.
If a=-3, then a is NOT between 1 and 5 on the number line.
INSUFFICIENT.

Statement 2: |a-1| < 3
In words:
The distance between a and 1 less than 3.
Put another way:
On the number line, a is within the green portion below:
.....-2<-----1----->4.....
If a=3, then a is between 1 and 5 on the number line.
If a=0, then a is NOT between 1 and 5 on the number line.
INSUFFICIENT.

Statements combined:
<----- -2.....0....2 ----->
.............-2<---1--->4.....
The colored ranges overlap between 2 and 4.
Implication:
To satisfy both statements, a must be within the red range below:
......2<----->4......
Thus, a must be between 1 and 5 on the number line.
SUFFICIENT.

The correct answer is C.

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