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If 0<2x+3y<50 and 50<3x+2y<0, then which of the following must be tr [#permalink]
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21 Nov 2017, 18:20
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[GMAT math practice question] If \(0<2x+3y<50\) and \(50<3x+2y<0\), then which of the following must be true? I. \(x>0\) II. \(y>0\) III. \(x<y\) A. I only B . II only C. III only D. I and III E. II, and III
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Last edited by MathRevolution on 23 Nov 2017, 13:05, edited 1 time in total.



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If 0<2x+3y<50 and 50<3x+2y<0, then which of the following must be tr [#permalink]
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22 Nov 2017, 09:50
MathRevolution wrote: [GMAT math practice question] If \(0<2x+3y<50\) and \(50<3x+2y<0\), then which of the following must be true?
I. \(x>0\) II. \(y>0\) III. \(x<y\)
A. I only B . II only C. III only D. I and III E. II and III \(0<2x+3y<50 => 2x+3y\) is positive (1) \(50<3x+2y<0 =>3x+2y\) is negative (2) notice that by adding \(xy\) to equation (1) it becomes equation (2) i.e a negative value. so \(xy<0 => x<y\). Statement III must be true\(x\) can be negative try values \(x=1\) & \(y=1\). Statement I is not always trueStatement II: As \(0<2x+3y<50\) is positive and we have already derived that \(y>x\), so if \(y\) is negative then \(x\) has to be negative which will mean that \(2x+3y<0\) which is not possible. So we can say that \(y\) must be positive. Statement II must be true.Option E
Last edited by niks18 on 23 Nov 2017, 21:28, edited 2 times in total.



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If 0<2x+3y<50 and 50<3x+2y<0, then which of the following must be tr [#permalink]
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22 Nov 2017, 19:53
=> When we add the two inequalities \(0<2x+3y<50\) and \(50<3x+2y<0\), we obtain \(50<5x+5y<50\), or \(20<2x2y< 20\). Statement I. Adding the two inequalities \(50<3x+2y<0\) and \(20<2x2y< 20\) yields \(70<x<20\). So x may not be greater than zero. Statement I may not be true. Statement II. By multiplying all sides of \(0<2x+3y<50\) by \(3\), we have \(150<6x9y< 0\). By multiplying all sides of \(50<3x+2y<0\) by \(2\), we have \(100<6x+4y< 0\). By adding the above inequalities, we have \(250<5y<0\) or \(0<y<50\). Statement II is true. Statement III. Since \(0<2x+3y<50\) is equivalent to \(50<2x3y<0\) and \(50<3x+2y<0\), adding the two inequalities yields \(100<xy<0\). This implies that \(x < y\). Statement III must be true. Therefore, the answer is E. Answer : E
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Last edited by MathRevolution on 23 Nov 2017, 13:09, edited 1 time in total.



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Re: If 0<2x+3y<50 and 50<3x+2y<0, then which of the following must be tr [#permalink]
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23 Nov 2017, 11:26
MathRevolution wrote: =>
When we add the two inequalities \(0<2x+3y<50\) and \(50<3x+2y<0\), we obtain \(50<5x+5y<50\), or \(20<2x2y< 20\).
Statement I. Adding the two inequalities \(50<3x+2y<0\) and \(20<2x2y< 20\) yields \(70<x<20\). So x may not be greater than zero. Statement I may not be true.
Statement II. Adding the two inequalities \(0<2x+3y<50\) and \(20<2x2y< 20\) yields \(20<y<70\). So y may not be greater than zero. Statement II may not be true, either.
Statement III. Since \(0<2x+3y<50\) is equivalent to \(50<2x3y<0\) and \(50<3x+2y<0\), adding the two inequalities yields \(100<xy<0\). This implies that \(x < y\). Statement III must be true.
Therefore, the answer is C.
Answer : C Hi MathRevolution, Need a clarity in Statement II. if x & y both can be negative then how will they both satisfy \(0<2x+3y<50\) and \(50<3x+2y<0\) simultaneously? Negative x & negative y will not satisfy the \(0<2x+3y<50\)



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Re: If 0<2x+3y<50 and 50<3x+2y<0, then which of the following must be tr [#permalink]
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23 Nov 2017, 13:10
niks18 wrote: MathRevolution wrote: =>
When we add the two inequalities \(0<2x+3y<50\) and \(50<3x+2y<0\), we obtain \(50<5x+5y<50\), or \(20<2x2y< 20\).
Statement I. Adding the two inequalities \(50<3x+2y<0\) and \(20<2x2y< 20\) yields \(70<x<20\). So x may not be greater than zero. Statement I may not be true.
Statement II. Adding the two inequalities \(0<2x+3y<50\) and \(20<2x2y< 20\) yields \(20<y<70\). So y may not be greater than zero. Statement II may not be true, either.
Statement III. Since \(0<2x+3y<50\) is equivalent to \(50<2x3y<0\) and \(50<3x+2y<0\), adding the two inequalities yields \(100<xy<0\). This implies that \(x < y\). Statement III must be true.
Therefore, the answer is C.
Answer : C Hi MathRevolution, Need a clarity in Statement II. if x & y both can be negative then how will they both satisfy \(0<2x+3y<50\) and \(50<3x+2y<0\) simultaneously? Negative x & negative y will not satisfy the \(0<2x+3y<50\) Yes, you are right. The solution is fixed. Please look at the above solution again.
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If 0<2x+3y<50 and 50<3x+2y<0, then which of the following must be tr [#permalink]
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23 Nov 2017, 21:23
MathRevolution wrote: niks18 wrote: MathRevolution wrote: =>
When we add the two inequalities \(0<2x+3y<50\) and \(50<3x+2y<0\), we obtain \(50<5x+5y<50\), or \(20<2x2y< 20\).
Statement I. Adding the two inequalities \(50<3x+2y<0\) and \(20<2x2y< 20\) yields \(70<x<20\). So x may not be greater than zero. Statement I may not be true.
Statement II. Adding the two inequalities \(0<2x+3y<50\) and \(20<2x2y< 20\) yields \(20<y<70\). So y may not be greater than zero. Statement II may not be true, either.
Statement III. Since \(0<2x+3y<50\) is equivalent to \(50<2x3y<0\) and \(50<3x+2y<0\), adding the two inequalities yields \(100<xy<0\). This implies that \(x < y\). Statement III must be true.
Therefore, the answer is C.
Answer : C Hi MathRevolution, Need a clarity in Statement II. if x & y both can be negative then how will they both satisfy \(0<2x+3y<50\) and \(50<3x+2y<0\) simultaneously? Negative x & negative y will not satisfy the \(0<2x+3y<50\) Yes, you are right. The solution is fixed. Please look at the above solution again. Thanks MathRevolution for the reply and clarifying



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Re: If 0<2x+3y<50 and 50<3x+2y<0, then which of the following must be tr [#permalink]
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17 Mar 2018, 10:11
MathRevolution wrote: [GMAT math practice question] If \(0<2x+3y<50\) and \(50<3x+2y<0\), then which of the following must be true?
I. \(x>0\) II. \(y>0\) III. \(x<y\)
A. I only B . II only C. III only D. I and III E. II, and III Given \(0<2x+3y<50\) and \(50<3x+2y<0\) Since => \(0<2x+3y\) and => \(3x+2y<0\) Therefore => \(3x+2y<2x+3y\) => OR \(3x2x<3y2y\) => OR \(x<y\) so satisfy III Now x,y =>both CANNOT be +ve since given \(3x+2y<0\) and =>both CANNOT be ve since given \(2x+3y>0\) Therefore =>both are OPPOSITE sign =>AND Since \(x<y\) THEREFORE \(x<0\) AND \(y>0\) so Satisfy II Option E Regards Dinesh




Re: If 0<2x+3y<50 and 50<3x+2y<0, then which of the following must be tr
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