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

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If y >= 0, what is the value of x? [#permalink] New post 03 Aug 2009, 14:00
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33% (02:26) correct 67% (01:42) wrong based on 142 sessions
If y >= 0, what is the value of x?

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

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Re: Value of X [#permalink] New post 07 Aug 2009, 01:29
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.
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Re: Value of X [#permalink] New post 09 Sep 2009, 10:59
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what is the OA? Please post it. Think it is D...
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Re: Value of X [#permalink] New post 09 Sep 2009, 14:52
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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.
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Last edited by Bunuel on 09 Sep 2009, 16:25, edited 1 time in total.
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Re: Value of X [#permalink] New post 09 Sep 2009, 15:50
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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.
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Re: Value of X [#permalink] New post 09 Sep 2009, 16:24
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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.

Answer B
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Re: Value of X [#permalink] New post 09 Sep 2009, 17:43
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.

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Re: Value of X [#permalink] New post 09 Sep 2009, 19:03
I will go with B.
x can be anything and value of x can not be determined from A
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Re: Value of X [#permalink] New post 12 Sep 2009, 07:50
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.
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Re: Value of X [#permalink] New post 12 Sep 2009, 09:07
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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.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Value of X [#permalink] New post 12 Sep 2009, 10:31
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...
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Re: If y >= 0, what is the value of x? [#permalink] New post 16 Apr 2014, 19:38
Thanks for the explanation, Bunuel! What a crazy question?!
Re: If y >= 0, what is the value of x?   [#permalink] 16 Apr 2014, 19:38
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