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If y >= 0, what is the value of x? [#permalink]
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03 Aug 2009, 15:00
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If y >= 0, what is the value of x? (1) x  3 >= y (2) x  3 <= y
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Re: Value of X [#permalink]
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07 Aug 2009, 02:29
I choose C .
according to 1 and 2: y<=absolute value" x3 "<=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]
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09 Sep 2009, 11:59
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what is the OA? Please post it. Think it is D...
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Re: Value of X [#permalink]
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09 Sep 2009, 15:52
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Last edited by Bunuel on 09 Sep 2009, 17:25, edited 1 time in total.



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Re: Value of X [#permalink]
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\(y >= 0\)
1.) \(x3 >= y\)
=> \(y >= (x3) >= y\)
=> \(3y >= x >= 3+y\)
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.) \(x3 <= y\)
=> \(y <= (x3) <= y\)
=> \(3+y <= x <= 3y\)
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]
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09 Sep 2009, 17:24
gmate2010 wrote: \(y >= 0\)
1.) \(x3 >= y\)
=> \(y >= (x3) >= y\)
=> \(3y >= x >= 3+y\)
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.) \(x3 <= y\)
=> \(y <= (x3) <= y\)
=> \(3+y <= x <= 3y\)
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 x3=3 > 1 or x=2 y=2 x3=5>2 not sufficient. Answer B
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Re: Value of X [#permalink]
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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(x3)>=0. Then x3>=0 or x3<=0 So, x>=3 or x<=3. Thus, x=3. Same thing for 2. So, D. gmate2010 wrote: \(y >= 0\)
1.) \(x3 >= y\)
=> \(y >= (x3) >= y\)
=> \(3y >= x >= 3+y\)
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.) \(x3 <= y\)
=> \(y <= (x3) <= y\)
=> \(3+y <= x <= 3y\)
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]
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09 Sep 2009, 20:03
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]
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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.



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Re: Value of X [#permalink]
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12 Sep 2009, 10:07
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 x3>0 > x>3 OR (not and) x+3>=y>=0 when x3<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) x3<=y, y>=0, equation says that x3less or equals to zero, but x3 never negative (x3>=0), so only solution is if x3=0=y > x3=0 > x=3 SUFFICIENT In other words: (y) is 0 or less, and the absolute value (x3) must be at (0) or below this value. But absolute value (in this case x3) can not be less than zero, so it must be 0. So answer is B.
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Re: Value of X [#permalink]
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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 x3>0 > x>3 OR (not and) x+3>=y>=0 when x3<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) x3<=y, y>=0, equation says that x3less or equals to zero, but x3 never negative (x3>=0), so only solution is if x3=0=y > x3=0 > x=3 SUFFICIENT
In other words: (y) is 0 or less, and the absolute value (x3) must be at (0) or below this value. But absolute value (in this case x3) 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]
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Re: If y >= 0, what is the value of x? [#permalink]
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16 Apr 2014, 20:38
Thanks for the explanation, Bunuel! What a crazy question?!



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