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Source: — Data Sufficiency |

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by lunarpower » Wed Jul 27, 2011 3:47 am
jainrahul1985 wrote:If y >= 0, what is the value of x?
1. |x - 3| >= y
2. |x - 3| <= - y

OA B
nicely explained by a student on our mgmat forum here:
https://www.manhattangmat.com/forums/post9165.html#p9165
Ron has been teaching various standardized tests for 20 years.

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by Anurag@Gurome » Wed Jul 27, 2011 3:52 am
jainrahul1985 wrote:If y >= 0, what is the value of x?
1. |x - 3| >= y
2. |x - 3| <= - y
Statement 1: |x - 3| ≥ y ≥ 0
Hence, for any non-negative value of y, x can have different values. For example, if y = 2, then |x - 3| ≥ 2. So x can be 5 or 6 or -1 etc.

Not sufficient

Statement 2: |x - 3| ≤ -y ≤ 0
Now |x - 3| can never be negative. Thus to satisfy the above relation |x - 3| has to be equal to zero. Hence, x = 3

Sufficient

The correct answer is B.
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by jainrahul1985 » Wed Jul 27, 2011 3:57 am
Hi Ron ,
I was able to understand/solve statement 1
(1) |x-3| >= y, where y>=0

case 1:
x-3 >= 0
x >= 3

case 2:
x-3 <= -0
x <= 3. INSUFFICIENT.

I could not understand/solve statement 2 . Please suggest
lunarpower wrote:
jainrahul1985 wrote:If y >= 0, what is the value of x?
1. |x - 3| >= y
2. |x - 3| <= - y

OA B
nicely explained by a student on our mgmat forum here:
https://www.manhattangmat.com/forums/post9165.html#p9165
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by krishp84 » Wed Jul 27, 2011 8:37 am
jainrahul1985 wrote:If y >= 0, what is the value of x?
1. |x - 3| >= y
2. |x - 3| <= - y

OA B
As per stem, y >= 0

|x - 3| can be positive or 0
1) |x - 3| >= y
y can take any value positive value greater than 0, so x will have multiple values
(1) not sufficient

2) |x - 3| <= - y
- y should be positive or 0 because it is greater than equal to |x-3|
This can happen only when y is negative or 0
As per question stem y is positive or 0
So common value only 0 and it will be equal to |x-3| because it is absolute value
|x-3| = 0
(2) is sufficient

MA : B
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by lunarpower » Fri Jul 29, 2011 2:14 am
jainrahul1985 wrote:I could not understand/solve statement 2 . Please suggest
the idea is this:
* the left-hand side is an absolute value, which must be either 0 or positive.
* the right-hand side is (-y) where y is 0 or positive, so it must be 0 or negative.
therefore, the only way for the inequality to be true is for both sides to be 0.
hence, x = 3 and y = 0.
this is the only possibility, so, sufficient.

if you still don't get this, try plugging in *other* values of y -- you'll quickly see why none of them will work except y = 0.
Ron has been teaching various standardized tests for 20 years.

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