Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 26 Sep 2016, 07:50

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 21 Feb 2009
Posts: 108
Followers: 1

Kudos [?]: 65 [4] , given: 4

If y >= 0, what is the value of x? [#permalink]

### Show Tags

03 Aug 2009, 15:00
4
KUDOS
12
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

38% (02:31) correct 62% (01:36) wrong based on 408 sessions

### HideShow timer Statistics

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

(1) |x - 3| >= y
(2) |x - 3| <= -y
[Reveal] Spoiler: OA

Attachments

Value Of X.jpg [ 64.91 KiB | Viewed 4400 times ]

Intern
Joined: 06 Aug 2009
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Value of X [#permalink]

### Show Tags

07 Aug 2009, 02:29
I choose C .

according to 1 and 2: y<=absolute value" x-3 "<=-y

and y>=0 (y is 0 or positive); that is to say -y is negative

==> only when y=0, the inequation is available. so when y=0, x=3.
Manager
Joined: 10 Jul 2009
Posts: 129
Location: Ukraine, Kyiv
Followers: 4

Kudos [?]: 128 [1] , given: 60

Re: Value of X [#permalink]

### Show Tags

09 Sep 2009, 11:59
1
KUDOS
what is the OA? Please post it. Think it is D...
_________________

Never, never, never give up

Math Expert
Joined: 02 Sep 2009
Posts: 34861
Followers: 6483

Kudos [?]: 82666 [9] , given: 10115

Re: Value of X [#permalink]

### Show Tags

09 Sep 2009, 15:52
9
KUDOS
Expert's post
1
This post was
BOOKMARKED
barakhaiev wrote:
what is the OA? Please post it. Think it is D...

y>=0
(1) |x-3|>= y, x can be any number >=3, x<=3 Not suff
2) |x-3|<=-y, y>=0, equation says that |x-3|less or equals to zero, but |x-3| never negative (|x-3|>=0), so only solution is if |x-3|=0=y --> x-3=0 --> x=3 Sufficinet

B it is.
_________________

Last edited by Bunuel on 09 Sep 2009, 17:25, edited 1 time in total.
Manager
Joined: 25 Aug 2009
Posts: 176
Followers: 1

Kudos [?]: 85 [1] , given: 12

Re: Value of X [#permalink]

### Show Tags

09 Sep 2009, 16:50
1
KUDOS
$$y >= 0$$

1.) $$|x-3| >= y$$

=> $$-y >= (x-3) >= y$$

=> $$3-y >= x >= 3+y$$

Now, if y = 0 , then, $$3 >= x >= 3$$ => x can only be 3
but, if y = 1 , then, $$2 >= x >= 4$$ => which is not possible for any value of x.

=> x can only be 3 when y = 0 ..sufficient..

2.) $$|x-3| <= -y$$

=> $$y <= (x-3) <= -y$$

=> $$3+y <= x <= 3-y$$

when y = 0 ; then, $$3 <= x <= 3$$ => x can only be 3..
when y = 1 ; then $$4 <= x <= 2$$, which is not possible for any value of x.

=> x can only be 3 when y = 0 ,, sufficient..

Hence, Ans is D.
Math Expert
Joined: 02 Sep 2009
Posts: 34861
Followers: 6483

Kudos [?]: 82666 [1] , given: 10115

Re: Value of X [#permalink]

### Show Tags

09 Sep 2009, 17:24
1
KUDOS
Expert's post
gmate2010 wrote:
$$y >= 0$$

1.) $$|x-3| >= y$$

=> $$-y >= (x-3) >= y$$

=> $$3-y >= x >= 3+y$$

Now, if y = 0 , then, $$3 >= x >= 3$$ => x can only be 3
but, if y = 1 , then, $$2 >= x >= 4$$ => which is not possible for any value of x.

=> x can only be 3 when y = 0 ..sufficient..

2.) $$|x-3| <= -y$$

=> $$y <= (x-3) <= -y$$

=> $$3+y <= x <= 3-y$$

when y = 0 ; then, $$3 <= x <= 3$$ => x can only be 3..
when y = 1 ; then $$4 <= x <= 2$$, which is not possible for any value of x.

=> x can only be 3 when y = 0 ,, sufficient..

Hence, Ans is D.

Just plug numbers for statement (1) if 6=3 y=1 |x-3|=3 > 1 or x=-2 y=2 |x-3|=5>2 not sufficient.

_________________
Manager
Joined: 04 Jan 2009
Posts: 241
Followers: 1

Kudos [?]: 11 [0], given: 0

Re: Value of X [#permalink]

### Show Tags

09 Sep 2009, 18:43
If y>=0 specified in the stem. Further mod of anything is positive.
So, 0>=y according to 1.
both y>=0 or y<=0, means y=0. So mod(x-3)>=0. Then x-3>=0 or x-3<=0
So, x>=3 or x<=3. Thus, x=3.
Same thing for 2.
So, D.
gmate2010 wrote:
$$y >= 0$$

1.) $$|x-3| >= y$$

=> $$-y >= (x-3) >= y$$

=> $$3-y >= x >= 3+y$$

Now, if y = 0 , then, $$3 >= x >= 3$$ => x can only be 3
but, if y = 1 , then, $$2 >= x >= 4$$ => which is not possible for any value of x.

=> x can only be 3 when y = 0 ..sufficient..

2.) $$|x-3| <= -y$$

=> $$y <= (x-3) <= -y$$

=> $$3+y <= x <= 3-y$$

when y = 0 ; then, $$3 <= x <= 3$$ => x can only be 3..
when y = 1 ; then $$4 <= x <= 2$$, which is not possible for any value of x.

=> x can only be 3 when y = 0 ,, sufficient..

Hence, Ans is D.

_________________

-----------------------
tusharvk

Senior Manager
Joined: 16 Apr 2009
Posts: 339
Followers: 1

Kudos [?]: 116 [0], given: 14

Re: Value of X [#permalink]

### Show Tags

09 Sep 2009, 20:03
I will go with B.
x can be anything and value of x can not be determined from A
_________________

Always tag your question

Intern
Joined: 11 Jul 2009
Posts: 15
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: Value of X [#permalink]

### Show Tags

12 Sep 2009, 08:50
My 2 cents on answer D
Rules for inequalities
1)|a| <b if - b<a<b
2)|a|>b if a<-b or a>b

apply rule 2 and derive the equation just as gmate2010 and tusharvk have done.
Math Expert
Joined: 02 Sep 2009
Posts: 34861
Followers: 6483

Kudos [?]: 82666 [2] , given: 10115

Re: Value of X [#permalink]

### Show Tags

12 Sep 2009, 10:07
2
KUDOS
Expert's post
O.K. as I see there has been kind of confusion about this question. I'm pretty sure answer is B.

I looked through the logic of people who think answer should be D and here is were they are making mistake:

(1) First of all:
To check |x - 3|>=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|>=0, y>=0. So ABSOLUTELY NO WAY (1) CAN BE SUFFICIENT.

|x - 3|>=y means that:
x - 3>=y>=0 when x-3>0 --> x>3
OR (not and)
-x+3>=y>=0 when x-3<0 --> x<3
Generally speaking |x - 3|>=y>=0 means that |x - 3|, an absolute value, is at least some positive number. So, there's no way you'll get a unique value for x. INSUFFICIENT.

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

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

So answer is B.
_________________
Manager
Joined: 10 Jul 2009
Posts: 129
Location: Ukraine, Kyiv
Followers: 4

Kudos [?]: 128 [0], given: 60

Re: Value of X [#permalink]

### Show Tags

12 Sep 2009, 11:31
Bunuel wrote:
O.K. as I see there has been kind of confusion about this question. I'm pretty sure answer is B.

I looked through the logic of people who think answer should be D and here is were they are making mistake:

(1) First of all:
To check |x - 3|>=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|>=0, y>=0. So ABSOLUTELY NO WAY (1) CAN BE SUFFICIENT.

|x - 3|>=y means that:
x - 3>=y>=0 when x-3>0 --> x>3
OR (not and)
-x+3>=y>=0 when x-3<0 --> x<3
Generally speaking |x - 3|>=y>=0 means that |x - 3|, an absolute value, is at least some positive number. So, there's no way you'll get a unique value for x. INSUFFICIENT.

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

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

So answer is B.

Got it finally! Thank you for clear explanation, Bunuel. B it is.
Of course, A is not suff...
_________________

Never, never, never give up

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11684
Followers: 527

Kudos [?]: 143 [1] , given: 0

Re: If y >= 0, what is the value of x? [#permalink]

### Show Tags

05 Feb 2014, 16:24
1
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.
_________________
Senior Manager
Joined: 10 Mar 2013
Posts: 290
GMAT 1: 620 Q44 V31
GMAT 2: 690 Q47 V37
GMAT 3: 610 Q47 V28
GMAT 4: 700 Q50 V34
GMAT 5: 700 Q49 V36
GMAT 6: 690 Q48 V35
GMAT 7: 750 Q49 V42
GMAT 8: 730 Q50 V39
Followers: 5

Kudos [?]: 91 [0], given: 2404

Re: If y >= 0, what is the value of x? [#permalink]

### Show Tags

16 Apr 2014, 20:38
Thanks for the explanation, Bunuel! What a crazy question?!
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11684
Followers: 527

Kudos [?]: 143 [0], given: 0

Re: If y >= 0, what is the value of x? [#permalink]

### Show Tags

16 May 2015, 07:55
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.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 7470
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 330

Kudos [?]: 2211 [1] , given: 162

Re: If y >= 0, what is the value of x? [#permalink]

### Show Tags

16 May 2015, 11:43
1
KUDOS
Expert's post
Hi All,

When complex-looking questions show up on Test Day, there's almost always some type of built-in pattern involved. If you can't immediate spot the pattern, then you have to put in a bit of work to prove what the pattern actually is....TESTing VALUES can help you to prove that a pattern exists.....

Here, we're told that Y >= 0. We're asked for the value of X.

Fact 1: |X-3| >= Y

IF....
Y = 0
Then |X-3| >= 0, so X can be ANY number. As Y gets bigger, certain options are eliminated, but given this 'restriction', X has an infinite number of possibilities.
Fact 1 is INSUFFICIENT

Fact 2: |X-3| <= -Y

Here, we have to be CAREFUL with the details. Notice how there's a NEGATIVE sign in front of the Y.....

IF....
Y = 0
|X-3| <= 0

Absolute values CANNOT have negative results - the result is ALWAYS 0 or a positive, so this TEST has JUST ONE solution...
X = 3

IF....
Y = 1
|X-3| <= - 1 which is NOT POSSIBLE.

From the prompt, we know that Y >= 0, so choosing a positive value for Y will NOT fit the absolute value given in Fact 2. This means that the ONLY possible value for Y is 0. By extension, there is ONLY ONE possible value for X....X = 3.
Fact 2 is SUFFICIENT

[Reveal] Spoiler:
B

GMAT assassins aren't born, they're made,
Rich
_________________

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: If y >= 0, what is the value of x?   [#permalink] 16 May 2015, 11:43
Similar topics Replies Last post
Similar
Topics:
1 If x > 0, what is the value of x ? 1 13 Dec 2015, 05:19
1 If x > y > 0, then what is the value of x^2+2xy+y2/x^2-y^2? 3 24 Jul 2015, 04:43
3 If x > 0 and y < 0, what is the value of x + y? 3 07 Sep 2013, 06:00
47 If y>=0, What is the value of x? 25 21 Jan 2012, 08:57
20 If y>=0, What is the value of x? (1) |x-3|>=y (2) |x-3|<=-y 17 09 Jan 2010, 14:17
Display posts from previous: Sort by

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

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.