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xz < 0? 1) x+y = x + y 2) y+z = y + z [#permalink]
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31 Oct 2017, 01:58
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[GMAT math practice question] xz < 0? 1) x+y = x + y 2) y+z = y + z
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Last edited by MathRevolution on 06 Nov 2017, 23:07, edited 3 times in total.



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Re: xz < 0? 1) x+y = x + y 2) y+z = y + z [#permalink]
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31 Oct 2017, 04:22
chetan2u wrote: MathRevolution wrote: [GMAT math practice question]
xz < 0?
1) x+y = x + y 2) y+z = y + z Hi... The OA is wrong. Pl rectify Can you please help solve this



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Re: xz < 0? 1) x+y = x + y 2) y+z = y + z [#permalink]
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31 Oct 2017, 06:35
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MathRevolution wrote: [GMAT math practice question]
xz < 0?
1) x+y = x + y 2) y+z = y + z HI rahulkashyap, OA given is A, maximum students would miss out on a crucial point and ans C but the answer should be E.xz < 0 MEANS " Is x and z of OPPOSITE sign?"1) x+y = x + yThis tells us that x and y are of SAME sign.. But what about z? Insuff 2) y+z = y + zThis tells us that z and y are of SAME sign.. But what about x? Insuff combined.. x,y and Z are of SAME sign, so xz>0.. so should be sufficient..BUT what if y is 0 1) x+y = x + y..... y = 0...... x can be POSITIVE or NEGATIVE 2) y+z = y + z..... y = 0...... z can be POSITIVE or NEGATIVE so x and z can be ANY sign InsuffE
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Re: xz < 0? 1) x+y = x + y 2) y+z = y + z [#permalink]
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31 Oct 2017, 07:40
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chetan2u wrote: MathRevolution wrote: [GMAT math practice question]
xz < 0?
1) x+y = x + y 2) y+z = y + z HI rahulkashyap, OA given is A, max would miss out on a ccrucial point and ans C but the answer should be E. xz < 0 MEANS " Is x and z of OPPOSITE sign?"1) x+y = x + yThis tells us that x and y are of SAME sign.. But what about z? Insuff 2) y+z = y + zThis tells us that z and y are of SAME sign.. But what about x? Insuff combined.. x,y and Z are of SAME sign, so xz>0.. so should be sufficient..BUT what if y is 0 1) x+y = x + y..... y = 0...... x can be POSITIVE or NEGATIVE 2) y+z = y + z..... y = 0...... z can be POSITIVE or NEGATIVE so x and z can be ANY sign InsuffE Amazing skill displayed by pointing out 'y=0' case. +1. Thanks chetan2u
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Re: xz < 0? 1) x+y = x + y 2) y+z = y + z [#permalink]
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31 Oct 2017, 12:44
MathRevolution wrote: [GMAT math practice question]
xz < 0?
1) x+y = x + y 2) y+z = y + z I got this wrong. I need to remember these problems can always be zero.
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Re: xz < 0? 1) x+y = x + y 2) y+z = y + z [#permalink]
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01 Nov 2017, 06:13
1) x+y = x + y This tells us that x and y are of SAME sign..
Can you please explain, How x and y have same signs



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Re: xz < 0? 1) x+y = x + y 2) y+z = y + z [#permalink]
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02 Nov 2017, 01:04
=> Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution. Since we have 3 variables and 0 equation, E is most likely to be the answer. Conditions 1) & 2) From the condition 1) and 2), x+y = x + y is equivalent to xy ≥ 0 and y+z = y + z is equivalent to yz ≥ 0. Then we have xy^2z ≥ 0 or xz ≥ 0. x = 1, y = 0, z = 1 implies xz = 1 > 0. x = 1, y = 0, z = 1 implies xz = 1 < 0. Both conditions together are not sufficient. The answer is E. For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Thus, E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously, there may be cases where the answer is A, B, C or D.
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Last edited by MathRevolution on 06 Nov 2017, 23:07, edited 2 times in total.



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Re: xz < 0? 1) x+y = x + y 2) y+z = y + z [#permalink]
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02 Nov 2017, 06:42
chetan2u wrote: MathRevolution wrote: [GMAT math practice question]
xz < 0?
1) x+y = x + y 2) y+z = y + z HI rahulkashyap, OA given is A, maximum students would miss out on a crucial point and ans C but the answer should be E.xz < 0 MEANS " Is x and z of OPPOSITE sign?"1) x+y = x + yThis tells us that x and y are of SAME sign.. But what about z? Insuff 2) y+z = y + zThis tells us that z and y are of SAME sign.. But what about x? Insuff combined.. x,y and Z are of SAME sign, so xz>0.. so should be sufficient..BUT what if y is 0 1) x+y = x + y..... y = 0...... x can be POSITIVE or NEGATIVE 2) y+z = y + z..... y = 0...... z can be POSITIVE or NEGATIVE so x and z can be ANY sign InsuffE For the answer to be E, even if x or z=0, that would work, correct?



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Re: xz < 0? 1) x+y = x + y 2) y+z = y + z [#permalink]
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03 Nov 2017, 20:01
MathRevolution wrote: [GMAT math practice question]
xz < 0?
1) x+y = x + y 2) y+z = y + z Statmnt 1: This is possible only when x,y = +ve or x,y = ve numer But we dont know about Z .. so insuff Statmnt 2: This is possible only when y,z = +ve or y,z = ve But we dont know X.. so insuff.. Combining above 2 statmnts.. Insufff For Ex  when x,y is +ve... y,z can be +ve or  ve.. Please give +1 Kudos if you liked my Solution..
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Re: xz < 0? 1) x+y = x + y 2) y+z = y + z [#permalink]
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03 Nov 2017, 20:24
nishantmba wrote: 1) x+y = x + y This tells us that x and y are of SAME sign..
Can you please explain, How x and y have same signs Hi nishantmbaRHS is the summation of two positive numbers i.e x+y, so LHS must be equal to this. this is only possible when both are of equal sign i.e {+,+} or {, } or x=y=0. If either of the two numbers have different sign i.e{+,}, then x+y will yield a less value and hence will not be equal to RHS



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Re: xz < 0? 1) x+y = x + y 2) y+z = y + z [#permalink]
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04 Nov 2017, 11:09
Plunkster82 wrote: MathRevolution wrote: [GMAT math practice question]
xz < 0?
1) x+y = x + y 2) y+z = y + z I got this wrong. I need to remember these problems can always be zero. Hey, Would you please share your knowledge about "these" problems? What pattern in questions are you referring to? I have got the idea but want to get extra sure from you. Thank you
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Re: xz < 0? 1) x+y = x + y 2) y+z = y + z [#permalink]
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10 Nov 2017, 09:05
TaN1213 wrote: Plunkster82 wrote: MathRevolution wrote: [GMAT math practice question]
xz < 0?
1) x+y = x + y 2) y+z = y + z I got this wrong. I need to remember these problems can always be zero. Hey, Would you please share your knowledge about "these" problems? What pattern in questions are you referring to? I have got the idea but want to get extra sure from you. Thank you The point of this question is the following property. \(x+y = x + y\) is equivalent to \(xy ≥ 0\).
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Re: xz < 0? 1) x+y = x + y 2) y+z = y + z [#permalink]
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10 Nov 2017, 09:08
niks18 wrote: nishantmba wrote: 1) x+y = x + y This tells us that x and y are of SAME sign..
Can you please explain, How x and y have same signs Hi nishantmbaRHS is the summation of two positive numbers i.e x+y, so LHS must be equal to this. this is only possible when both are of equal sign i.e {+,+} or {, } or x=y=0. If either of the two numbers have different sign i.e{+,}, then x+y will yield a less value and hence will not be equal to RHS \(x+y = x + y\) \(⇔ x+y^2 = (x + y)^2\) \(⇔ (x+y)^2 = x^2 + 2xy + y^2\) \(⇔ x^2 + 2xy + y^2 = x^2 + 2xy + y^2\) \(⇔ 2xy = 2xy\) \(⇔ xy = xy\) \(⇔ xy ≥ 0\)
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