Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: what is the value of x? [#permalink]
09 Jan 2010, 13:45

4

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

If y\geq{0}, what is the value of x?

(1) |x - 3|\geq{y}

(2) |x - 3|\leq{-y}

(1) Given y is non negative value and |x - 3|\geq{y}, so |x - 3| is more than some non negative value, (we could say the same ourselves as absolute value in our case (|x - 3|) is never negative). So we can not determine single numerical value of x. Not sufficient.

Or another way: to check |x - 3|\geq{y}\geq{0} is sufficient or not just plug numbers: A. x=5, y=1>0, and B. x=8, y=2>0: you'll see that both fits in |x - 3|>=y, y\geq{0}.

Or another way: |x - 3|\geq{y} means that:

x - 3\geq{y}\geq{0} when x-3>0 --> x>3

OR (not and) -x+3\geq{y}\geq{0} when x-3<0 --> x<3

Generally speaking |x - 3|\geq{y}\geq{0} means that |x - 3|, an absolute value, is not negative. So, there's no way you'll get a unique value for x. INSUFFICIENT.

(2) |x-3|\leq{-y}, y\geq{0} --> 0\leq{-y}, equation says that |x-3| less or equals to zero, but |x-3| never negative (|x-3|\geq{0}), so only solution is if |x-3|=0=y --> x-3=0 --> x=3. SUFFICIENT

In other words: -y is zero or less, and the absolute value (|x-3|) must be at zero or below this value. But absolute value (in this case |x-3|) can not be less than zero, so it must be 0.

stmt1: |x-3| >= y in case y>= 0 if we consider y = 0, |x-3| >= 0 but y can be 0, 1,2,3 anything so insufficient.

stmt2: |x-3| <= -y since y >= 0 => -y <= 0 so we can say |x-3| <= -y <= 0 but |x-3| has to be positive which is only possible if y = 0 and |x-3| = 0 only one condition suffice this if x=3, hence sufficient. so B is the answer _________________

Re: Simple inequality [#permalink]
18 Jun 2010, 23:37

Expert's post

gmatbull wrote:

If y >= 0, what is the value of x ?

(1) |x - 3| >= y (2) |x - 3| <= -y

I know that the value of an abs expression cannot be less than 0. so does that imply that x is 0 units from 3?

As y is some non-negative value (0, 7, 1.4, ...) then -y is some non-positive value (0, -9, -5.6, ...). Statement 2 says that |x-3|\leq{-y} (|x-3|\leq{non-positive}) - absolute value is less than or equal to some non-positive value, BUT absolute value can not be negative, least value of it is zero, thus |x-3|={0}=y --> x=3.

Re: Simple inequality [#permalink]
19 Jun 2010, 00:17

Bunuel wrote:

gmatbull wrote:

If y >= 0, what is the value of x ?

(1) |x - 3| >= y (2) |x - 3| <= -y

I know that the value of an abs expression cannot be less than 0. so does that imply that x is 0 units from 3?

As y is some non-negative value (0, 7, 1.4, ...) then -y is some non-positive value (0, -9, -5.6, ...). Statement 2 says that |x-3|\leq{-y} (|x-3|\leq{non-positive}) - absolute value is less than or equal to some non-positive value, BUT absolute value can not be negative, least value of it is zero, thus |x-3|={0}=y --> x=3.

Refer for the full solution to my previous post.

Hope it's clear.

I trust your explanations - very clear. Thanks _________________

KUDOS me if you feel my contribution has helped you.

Re: what is the value of x? [#permalink]
08 Oct 2010, 15:00

Graphical Solution

We know y>=0. We need to know x.

(1) y<=|x-3|

The inequality represents the regino between the x-axis and the blue line. Knowing y>=0 is not enough to know x

(2)-y>=|x-3| OR y<=-|x-3|

The inequality represents the region below the blue line. We know y>=0, this can only represent the point where, the blue line meets the x-axis or x=3. Sufficient

Re: what is the value of x? [#permalink]
14 Mar 2011, 02:57

Expert's post

vjsharma25 wrote:

Bunuel wrote:

(2) |x-3|\leq{-y}, y\geq{0} --> [highlight]0\leq{-y}[/highlight], equation says that |x-3| less or equals to zero, but |x-3| never negative (|x-3|\geq{0}), so only solution is if |x-3|=0=y --> x-3=0 --> x=3. SUFFICIENT It should be [highlight]0\geq{-y}[/highlight] in my opinion

No, it should be as it is.

(2) |x-3|\leq{-y} --> now, as LHS is absolute value, which is always non-negative, then we have that -y is more than or equal to some non-negative value: 0\leq{-y} --> y\leq{0}. As also is given that y\geq{0} then y=0 --> |x-3|\leq{0} --> absolute value can not be negative, so |x-3|=0 --> x=3. _________________

Re: what is the value of x? [#permalink]
14 Mar 2011, 03:05

Bunuel wrote:

vjsharma25 wrote:

Bunuel wrote:

(2) |x-3|\leq{-y}, y\geq{0}-->[highlight]0\leq{-y}[/highlight], equation says that |x-3| less or equals to zero, but |x-3| never negative (|x-3|\geq{0}), so only solution is if |x-3|=0=y --> x-3=0 --> x=3. SUFFICIENT It should be [highlight]0\geq{-y}[/highlight] in my opinion

No, it should be as it is.

(2) |x-3|\leq{-y} --> now, as LHS is absolute value, which is always non-negative, then we have that -y is more than or equal to some non-negative value: 0\leq{-y} --> y\leq{0}. As also is given that y\geq{0} then y=0 --> |x-3|\leq{0} --> absolute value can not be negative, so |x-3|=0 --> x=3.

Does this symbol ---> means "implies that"?. Because I interpreted it that way in the statement. Rest of the explanation is clear to me.

Re: what is the value of x? [#permalink]
19 Jun 2011, 08:15

1

This post received KUDOS

Ahhhhh i hate absolute value questions. Gets me every time! _________________

******************************************************************* ~ PickyTooth - Eat Like a Local Foodie // www.pickytooth.com ~ *******************************************************************

Re: If y>=0, What is the value of x? (1) |x-3|>=y (2) |x-3|<=-y [#permalink]
12 Jan 2014, 06:38

1

This post received KUDOS

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________