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If y>=0, What is the value of x? (1) x3>=y (2) x3<=y
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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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If y>=0, What is the value of x? (1) x3>=y (2) x3<=y
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21 Jan 2012, 09:23
If \(y\geq{0}\), what is the value of x?(1) \(x  3\geq{y}\). As given that \(y\) is non negative value then \(x  3\) is more than (or equal to) 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) \(x3\leq{y}\). Now, as \(x3\) is never negative (\(0\leq{x3}\)) then \(0\leq{y}\) > \(y\leq{0}\) BUT stem says that \(y\geq{0}\) thus \(y=0\). \(x3\leq{0}\) > \(x3=0=y\) (as absolute value, in our case x3, can not be less than zero) > \(x3=0\) > \(x=3\). 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. Hope it helps..
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Re: value of x?
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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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If y>=0, What is the value of x? (1) x3>=y (2) x3<=y
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09 Jul 2013, 14:05
First number line: y>=0 Second: From properties of absolute value, x3>=0 is true no matter what x is. Third: (2) tells us that x3<=y. We know nothing about y other than y>=0. Therefore x3<=y only tells us that x3<=0. Fourth: Since x3<=0 AND x3>=0, we now know the exact value of x3. In the diagram it is the point on the number line that is both <=0 and >=0. The only value for which that is true is 0. So x3=0. From there you know that x3=0 and so x=3.



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Re: If y>=0, What is the value of x?
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10 Jul 2013, 13:43
If y >= 0, What is the value of x? (1) x3 >= yWe are told that x3 ≥ y but all we know is that y is a positive # greater than or equal to zero. Therefore, all we know is that x3 is greater than or equal to zero and x could be an infinite number of possibilities. (2) x3 <= y(I am having real difficulty understanding the rationale for (2) could someone explain it to me? (preferably like they would to a 5th grader ) Thanks!



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Re: If y>=0, What is the value of x?
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10 Jul 2013, 14:58
WholeLottaLove wrote: If y >= 0, What is the value of x? (1) x3 >= yWe are told that x3 ≥ y but all we know is that y is a positive # greater than or equal to zero. Therefore, all we know is that x3 is greater than or equal to zero and x could be an infinite number of possibilities. (2) x3 <= y(I am having real difficulty understanding the rationale for (2) could someone explain it to me? (preferably like they would to a 5th grader ) Thanks! Hi WholeLottaLove The important property concerning absolute value inequalities is: a <= b <> b <= a <=b [a is in the middle of b and b, inclusive] Apply to statement (2)x  3 <= y <> (y) <= (x3) <= y, <> y <= (x3) <= y We know y is 0 or positive, y is 0 or negative. Because there is not any number that is both negative and positive.Thus, there is ONLY one number that is both >= y AND <= y. That is zero. Therefore, (x3) must be zero. ==> x = 3 Hope it's clear.
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Re: If y >= 0, what is the value of x?
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16 May 2015, 11:43
Hi All, When complexlooking questions show up on Test Day, there's almost always some type of builtin 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: X3 >= Y IF.... Y = 0 Then X3 >= 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: X3 <= 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 X3 <= 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 X3 <=  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 Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: If y>=0, What is the value of x?
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06 Mar 2016, 19:57
Bunuel wrote: There is a following problem with your solution: If \(x<3\) > \((x3)\geq{y}\) > \(3y\geq{x}\); OR:If \(x\geq{3}\) > \((x3)\geq{y}\) > \(x\geq{3+y}\); But you can not combine these inequalities and write: \(3+y\leq{x}\leq{3y}\) as they are OR scenarios not AND scenarios (meaning that depending on the value of x we'll have either the first one or the second one). Also discussed here: ifygeq0whatisthevalueofx1x3geqy91640.htmlHope it helps.. Hi Bunuel, I understand the OR scenario you mentioned above. However, what if the statement reads \(x3\leq{y}\)? Then we can have \(3y\leq{x}\leq{3+y}\), can't we? So here we have the AND scenario. Is that right? And if I am correct, how can we solve the above inequalities, given that \(y\geq{0}\)? Thank you very much!



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Re: If y>=0, What is the value of x?
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06 Mar 2016, 20:51
truongynhi wrote: Bunuel wrote: There is a following problem with your solution: If \(x<3\) > \((x3)\geq{y}\) > \(3y\geq{x}\); OR:If \(x\geq{3}\) > \((x3)\geq{y}\) > \(x\geq{3+y}\); But you can not combine these inequalities and write: \(3+y\leq{x}\leq{3y}\) as they are OR scenarios not AND scenarios (meaning that depending on the value of x we'll have either the first one or the second one). Also discussed here: ifygeq0whatisthevalueofx1x3geqy91640.htmlHope it helps.. Hi Bunuel, I understand the OR scenario you mentioned above. However, what if the statement reads \(x3\leq{y}\)? Then we can have \(3y\leq{x}\leq{3+y}\), can't we? So here we have the AND scenario. Is that right? And if I am correct, how can we solve the above inequalities, given that \(y\geq{0}\)? Thank you very much! Hi, this too is OR scenario, because \(3y\leq{x}\) and \({x}\leq{3+y}\) are dependent on different set of values of x.. \(3y\leq{x}\) is when \(x<3\).. and \({x}\leq{3+y}\) is when \(x\geq{3}\).. Example of AND is when we have two eqs in x, and not dependent on each other.. say x<3.. and x+2>1..
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Re: If y>=0, What is the value of x?
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06 Mar 2016, 22:08
Hi chetan2u,
Thank you for the prompt reply. But I still have a doubt.
Take the inequation \(x^2<4\) for example. We then have \(x<2\), which means \(2<x<2\). What I understand is that x must be greater than 2 AND less than 2 for the inequalitiy to hold. So I think this is an AND scenario.
If, however, \(x^2>4\), then \(x<2\) OR \(x>2\). This is clearly an OR scenario. Here OR makes sense to me.
My inequality skill is pretty rusty. Thank you for bearing with me. I very appreciate your help!



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Re: If y>=0, What is the value of x?
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06 Mar 2016, 22:26
truongynhi wrote: Hi chetan2u,
Thank you for the prompt reply. But I still have a doubt.
Take the inequation \(x^2<4\) for example. We then have \(x<2\), which means \(2<x<2\). What I understand is that x must be greater than 2 AND less than 2 for the inequalitiy to hold. So I think this is an AND scenario.
If, however, \(x^2>4\), then \(x<2\) OR \(x>2\). This is clearly an OR scenario. Here OR makes sense to me.
My inequality skill is pretty rusty. Thank you for bearing with me. I very appreciate your help! Hi truongynhi, I am happy to help you and clear a few doubts you have..
WHAt does OR and AND mean.. 1) Take the inequation \(x^2<4\) for example. We then have \(x<2\), which means \(2<x<2\) So here too you had 2 inequalities, x<2 and x>2.. x<2 can mean x is 3 so this is a solution when we are using OR since we are not looking at both together.. But here x<2 and x>2 has a range which OVERLAPS, so this is the combined solution for two inequalities.. when you are choosing a value in this range, you are using AND, since taht value will satisfy both the inequalities..
2)If, however, \(x^2>4\), then \(x<2\) OR \(x>2\). This is clearly an OR scenario. YES, this is OR situation, because there is no overlap and hence there is no possiblity of a combined solution.. any solution will satisfy just one inequality..
Now when you have two variable as in the case of Q mentioned here.. 3+y≤x≤3−y.. you cannot take this as a solution.. WHY.. because the two inequalities you have combined have come in two different scenarios of OR while taking value of x.. there is no OVERLAP in values of x.. x<3 for one inequality and x>= 3 for other.. so don't combine the two..
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Re: If y>=0, What is the value of x?
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06 May 2019, 07:53
Apex231 wrote: If y >= 0, What is the value of x?
(1) x3 >= y (2) x3 <= y
Statement 1 is not sufficient, since if y=0, x can be anything. In Statement 2, the left side is 0 or greater, since it is an absolute value. The right side is 0 or smaller, since it is the negative of y, which is at least zero. If the left side (which is > 0) is no bigger than the right side (which is < 0), the only possibility is that they are both exactly equal to zero. And that only happens if x=3.
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Re: If y>=0, What is the value of x? (1) x3>=y (2) x3<=y
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24 Sep 2019, 09:24
ugimba wrote: If \(y\geq{0}\), what is the value of x?
(1) \(x  3\geq{y}\)
(2) \(x  3\leq{y}\) If \(y\geq{0}\), what is the value of x? (1) \(x  3\geq{y}\) \(x  3\geq{y}\geq{0}\) \(x3 \geq 0\) NOT SUFFICIENT (2) \(x  3\leq{y}\) \(x  3\leq{y} \leq 0\) \(x3 \leq 0\) x3 = 0 x = 3 SUFFICIENT IMO B
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Re: If y is greater than or equal to 0, what is the value of x?
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Re: If y is greater than or equal to 0, what is the value of x?
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