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If y>=0, What is the value of x? (1) |x-3|>=y (2) |x-3|<=-y [#permalink]
 09 Jan 2010, 14:17
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If y\geq{0}, what is the value of x? (1) |x - 3|\geq{y}(2) |x - 3|\leq{-y}
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Re: what is the value of x? [#permalink]
09 Jan 2010, 14:45
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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>3OR (not and) -x+3\geq{y}\geq{0} when x-3<0 --> x<3Generally 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. Answer: B.
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Re: Gmat Prep DS value question ! [#permalink]
21 Mar 2010, 00:54
nsp007 wrote: If y >= 0 , what is the value of x ?
1. |x-3| >= y
2. |x-3| <= -y
Can anyone pls. explain how to approach such a problem?
B stmnt1 - |x-3| >= y >=0 let y = 0 then we have |x-3| >= 0 .... x can be 0,1,2,3. hence insuff stmnt2 - |x-3| <= -y we know that |x-3| will always be +ve,so only value of y can be 0. we have |x-3| = 0 or x = 3. hence suff
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Re: Gmat Prep DS value question ! [#permalink]
21 Mar 2010, 23:11
nsp007 wrote: If y >= 0 , what is the value of x ? 1. |x-3| >= y2. |x-3| <= -yCan anyone pls. explain how to approach such a problem? OA 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
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neoreaves wrote: If y > = 0, what is the value of x?
1. |x - 3| >= y
2. |x - 3| <= - y IMO B Statement 1). |x - 3| >= y >=0 |x - 3| >= 0 , for different values of x, this is true. Statement 2). |x - 3| <= - y since |x - 3| is always >=0 , and y>=0 |x - 3| <= - y will hold true only when y is 0 => |x - 3| = 0 , only solution is x=3 hence sufficient. Thus B
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Re: Simple inequality [#permalink]
19 Jun 2010, 00:37
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.
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Re: Simple inequality [#permalink]
19 Jun 2010, 01:17
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
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Re: what is the value of x? [#permalink]
08 Oct 2010, 16:00
Graphical SolutionWe 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 Answer is (B)
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Re: what is the value of x? [#permalink]
14 Mar 2011, 03:57
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.
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Re: what is the value of x? [#permalink]
14 Mar 2011, 04:05
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.
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Re: what is the value of x? [#permalink]
14 Mar 2011, 04:16
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Re: what is the value of x? [#permalink]
14 Mar 2011, 04:42
If y>=0, what is the value of x? (1) |x-3| >= y x-3>=y x>=y+3 or x-3<=-y x<=3-y N.S. (2) -(-y)<=x-3<=-y +y<=x-3<=-y A positive y can never be less than a -ve y. It can be equal only when y=0 so; +y=x-3=-y=0 x-3=0 x=3 Sufficient. Ans: "B"
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Re: what is the value of x? [#permalink]
20 May 2011, 00:56
absolute value can never give negative results. B is possible for x = 3
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Re: what is the value of x? [#permalink]
20 May 2011, 08:38
(1) x - 3 >= 0 as y is >= 0 => x >= 3 InSufficient (2) |x-3| <= 0 as -y <= 0 but |x-3| can't be negative => x-3 = 0 => x = 3 Sufficient Answer - B
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Re: what is the value of x? [#permalink]
19 Jun 2011, 09:15
Ahhhhh i hate absolute value questions. Gets me every time!
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Re: what is the value of x?
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19 Jun 2011, 09:15
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