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If y>=0, What is the value of x? (1) x3>=y (2) x3<=y [#permalink]
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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]
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09 Jan 2010, 14:45
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 \(x3>0\) > \(x>3\) OR (not and) \(x+3\geq{y}\geq{0}\) when \(x3<0\) > \(x<3\) 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) \(x3\leq{y}\), \(y\geq{0}\) > \(0\leq{y}\), equation says that \(x3\) less or equals to zero, but \(x3\) never negative (\(x3\geq{0}\)), so only solution is if \(x3=0=y\) > \(x3=0\) > \(x=3\). SUFFICIENT In other words: \(y\) is zero or less, and the absolute value (\(x3\)) must be at zero or below this value. But absolute value (in this case \(x3\)) can not be less than zero, so it must be \(0\). Answer: B.
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Re: Gmat Prep DS value question ! [#permalink]
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21 Mar 2010, 00:54
nsp007 wrote: If \(y >= 0\) , what is the value of x ?
1. \(x3 >= y\) 2. \(x3 <= y\)
Can anyone pls. explain how to approach such a problem?
B stmnt1  x3 >= y >=0 let y = 0 then we have x3 >= 0 .... x can be 0,1,2,3. hence insuff stmnt2  x3 <= y we know that x3 will always be +ve,so only value of y can be 0. we have x3 = 0 or x = 3. hence suff



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Re: Gmat Prep DS value question ! [#permalink]
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21 Mar 2010, 23:11
nsp007 wrote: If \(y >= 0\) , what is the value of x ? 1. \(x3 >= y\) 2. \(x3 <= y\) Can anyone pls. explain how to approach such a problem? OA stmt1: x3 >= y in case y>= 0 if we consider y = 0, x3 >= 0 but y can be 0, 1,2,3 anything so insufficient. stmt2: x3 <= y since y >= 0 => y <= 0 so we can say x3 <= y <= 0 but x3 has to be positive which is only possible if y = 0 and x3 = 0 only one condition suffice this if x=3, hence sufficient. so B is the answer
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Re: value of x? [#permalink]
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08 May 2010, 10:35
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]
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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 nonnegative value (0, 7, 1.4, ...) then \(y\) is some nonpositive value (0, 9, 5.6, ...). Statement 2 says that \(x3\leq{y}\) (\(x3\leq{nonpositive}\))  absolute value is less than or equal to some nonpositive value, BUT absolute value can not be negative, least value of it is zero, thus \(x3={0}=y\) > \(x=3\). Refer for the full solution to my previous post. Hope it's clear.
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Re: what is the value of x? [#permalink]
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08 Oct 2010, 16:00
Graphical SolutionWe know y>=0. We need to know x. (1) y<=x3 The inequality represents the regino between the xaxis and the blue line. Knowing y>=0 is not enough to know x (2)y>=x3 OR y<=x3 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 xaxis or x=3. Sufficient Answer is (B)
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Re: what is the value of x? [#permalink]
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14 Mar 2011, 03:57
vjsharma25 wrote: Bunuel wrote: (2) \(x3\leq{y}\), \(y\geq{0}\) > [highlight]\(0\leq{y}\)[/highlight], equation says that \(x3\) less or equals to zero, but \(x3\) never negative (\(x3\geq{0}\)), so only solution is if \(x3=0=y\) > \(x3=0\) > \(x=3\). SUFFICIENT It should be [highlight]\(0\geq{y}\)[/highlight] in my opinion
No, it should be as it is. (2) \(x3\leq{y}\) > now, as LHS is absolute value, which is always nonnegative, then we have that \(y\) is more than or equal to some nonnegative value: \(0\leq{y}\) > \(y\leq{0}\). As also is given that \(y\geq{0}\) then \(y=0\) > \(x3\leq{0}\) > absolute value can not be negative, so \(x3=0\) > \(x=3\).
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Re: what is the value of x? [#permalink]
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14 Mar 2011, 04:05
Bunuel wrote: vjsharma25 wrote: Bunuel wrote: (2) \(x3\leq{y}\), \(y\geq{0}\) >[highlight]\(0\leq{y}\)[/highlight], equation says that \(x3\) less or equals to zero, but \(x3\) never negative (\(x3\geq{0}\)), so only solution is if \(x3=0=y\) > \(x3=0\) > \(x=3\). SUFFICIENT It should be [highlight]\(0\geq{y}\)[/highlight] in my opinion
No, it should be as it is. (2) \(x3\leq{y}\) > now, as LHS is absolute value, which is always nonnegative, then we have that \(y\) is more than or equal to some nonnegative value: \(0\leq{y}\) > \(y\leq{0}\). As also is given that \(y\geq{0}\) then \(y=0\) > \(x3\leq{0}\) > absolute value can not be negative, so \(x3=0\) > \(x=3\). 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]
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Re: what is the value of x? [#permalink]
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14 Mar 2011, 04:42
If y>=0, what is the value of x? (1) x3 >= y x3>=y x>=y+3 or x3<=y x<=3y N.S. (2) (y)<=x3<=y +y<=x3<=y A positive y can never be less than a ve y. It can be equal only when y=0 so; +y=x3=y=0 x3=0 x=3 Sufficient. Ans: "B"
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Re: what is the value of x? [#permalink]
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20 May 2011, 08:38
(1) x  3 >= 0 as y is >= 0 => x >= 3 InSufficient (2) x3 <= 0 as y <= 0 but x3 can't be negative => x3 = 0 => x = 3 Sufficient Answer  B
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Re: If y>=0, What is the value of x? (1) x3>=y (2) x3<=y [#permalink]
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16 Oct 2016, 19:49
Bunuel wrote: 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 \(x3>0\) > \(x>3\)
OR (not and) \(x+3\geq{y}\geq{0}\) when \(x3<0\) > \(x<3\)
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) \(x3\leq{y}\), \(y\geq{0}\) > \(0\leq{y}\), equation says that \(x3\) less or equals to zero, but \(x3\) never negative (\(x3\geq{0}\)), so only solution is if \(x3=0=y\) > \(x3=0\) > \(x=3\). SUFFICIENT
In other words: \(y\) is zero or less, and the absolute value (\(x3\)) must be at zero or below this value. But absolute value (in this case \(x3\)) can not be less than zero, so it must be \(0\).
Answer: B. BunuelFor A. u removed euqlity sign from the equestion. equation results in x>=3 or x<=3, Hence x could be 3. Hence A sufficies, the condition. Please tell me, where i understood it wrong.



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Re: If y>=0, What is the value of x? (1) x3>=y (2) x3<=y [#permalink]
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17 Oct 2016, 03:10
rahul202 wrote: Bunuel wrote: 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 \(x3>0\) > \(x>3\)
OR (not and) \(x+3\geq{y}\geq{0}\) when \(x3<0\) > \(x<3\)
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) \(x3\leq{y}\), \(y\geq{0}\) > \(0\leq{y}\), equation says that \(x3\) less or equals to zero, but \(x3\) never negative (\(x3\geq{0}\)), so only solution is if \(x3=0=y\) > \(x3=0\) > \(x=3\). SUFFICIENT
In other words: \(y\) is zero or less, and the absolute value (\(x3\)) must be at zero or below this value. But absolute value (in this case \(x3\)) can not be less than zero, so it must be \(0\).
Answer: B. BunuelFor A. u removed euqlity sign from the equestion. equation results in x>=3 or x<=3, Hence x could be 3. Hence A sufficies, the condition. Please tell me, where i understood it wrong. Yes, x can be 3 but how does this help to get the exact value of x? Cannot x be any other value?
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Re: If y>=0, What is the value of x? (1) x3>=y (2) x3<=y [#permalink]
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18 Oct 2016, 03:28
Bunuel wrote: (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 \(x3>0\) > \(x>3\) OR (not and) [m]x+3\geq{y}\geq{0}[/m] when \(x3<0\) > \(x<3\)
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.
Answer: B. In the highlighted part How could X be less than 3 and greater than 3 in same time??



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Re: If y>=0, What is the value of x? (1) x3>=y (2) x3<=y [#permalink]
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18 Oct 2016, 03:32
Mo2men wrote: Bunuel wrote: (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 \(x3>0\) > \(x>3\) OR (not and) [m]x+3\geq{y}\geq{0}[/m] when \(x3<0\) > \(x<3\)
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.
Answer: B. In the highlighted part How could X be less than 3 and greater than 3 in same time?? This means that from the first statement x can be any number.
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