zt < -3, z< 4 ?GHong14 wrote:
Statement 1:
z < 9
Insufficient, as z can be >=4 or <4.
Statement 2:
t<-4
=> z>3/4 -- Insufficient as, z can be >=4 or <4.
Combined :
z>3/4 and z<9 --- Still Insufficient, as z can be >=4 or <4.
E[/b]
DS6
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anshumishra
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Statement 1:
z < 9
Insufficient, as z can be >=4 or <4.
Statement 2:
t<-4
=> z>3/4 -- Insufficient as, z can be >=4 or <4.
Combined :
z>3/4 and z<9 --- Still Insufficient, as z can be >=4 or <4.
E[/b]
Thanks
Anshu
(Every mistake is a lesson learned )
Anshu
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Night reader
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zt<-3, is z<4 ? also z<-3/tGHong14 wrote:
st(1) z<9, z-z<9+3/t, 0<9+3/t, t>-1/3 Not Sufficient
st(2) t<-4, z can be anything Not Sufficient
Combined st(1&2): with z<9 no restriction what so ever Not Sufficient
answer E
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anshumishra
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Night reader wrote:zt<-3, is z<4 ? also z<-3/t --- Careful, It is easy to miss (but this is true only when t>0, when t is -ve, then z>-3/t)GHong14 wrote:
st(1) z<9, z-z<9+3/t, 0<9+3/t, t>-1/3 Not Sufficient
st(2) t<-4, z can be anything Not Sufficient
Combined st(1&2): with z<9 no restriction what so ever Not Sufficient
answer E
Thanks
Anshu
(Every mistake is a lesson learned )
Anshu
(Every mistake is a lesson learned )
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Night reader
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zt product is always to the left from -3 hence always -ve. When t is -ve, z<-3/t AND z>0 i.e. z is +ve. When t is +ve, z<-3/t AND z<0 i.e. z is -ve. Two numbers' product can be -ve only if one number is +ve and the other is -ve. Agree?anshumishra wrote:Night reader wrote:zt<-3, is z<4 ? also z<-3/t --- Careful, It is easy to miss (but this is true only when t>0, when t is -ve, then z>-3/t)GHong14 wrote:
st(1) z<9, z-z<9+3/t, 0<9+3/t, t>-1/3 Not Sufficient
st(2) t<-4, z can be anything Not Sufficient
Combined st(1&2): with z<9 no restriction what so ever Not Sufficient
answer E
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anshumishra
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zt < -3Night reader wrote:zt product is always to the left from -3 hence always -ve. When t is -ve, z<-3/t AND z>0 i.e. z is +ve. When t is +ve, z<-3/t AND z<0 i.e. z is -ve. Two numbers' product can be -ve only if one number is +ve and the other is -ve. Agree?anshumishra wrote:Night reader wrote:zt<-3, is z<4 ? also z<-3/t --- Careful, It is easy to miss (but this is true only when t>0, when t is -ve, then z>-3/t)GHong14 wrote:
st(1) z<9, z-z<9+3/t, 0<9+3/t, t>-1/3 Not Sufficient
st(2) t<-4, z can be anything Not Sufficient
Combined st(1&2): with z<9 no restriction what so ever Not Sufficient
answer E
lets say ; t=-4 and z =1 , clearly zt = -4 < -3
Let's evaluate the part in bold :
t is -ve;When t is -ve, z<-3/t AND z>0 i.e. z is +ve.
z < -3/t means z< -3/-4 => z<3/4 and z > 0 BUT in my example, I have z=1, which is not in the range (0,3/4).
I didn't evaluate the 2nd statement : When t is +ve, z<-3/t AND z<0 i.e. z is -ve.
Thanks
Anshu
(Every mistake is a lesson learned )
Anshu
(Every mistake is a lesson learned )
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Night reader
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anshumishra wrote:zt < -3Night reader wrote:zt product is always to the left from -3 hence always -ve. When t is -ve, z<-3/t AND z>0 i.e. z is +ve. When t is +ve, z<-3/t AND z<0 i.e. z is -ve. Two numbers' product can be -ve only if one number is +ve and the other is -ve. Agree?anshumishra wrote:Night reader wrote:zt<-3, is z<4 ? also z<-3/t --- Careful, It is easy to miss (but this is true only when t>0, when t is -ve, then z>-3/t)GHong14 wrote:
st(1) z<9, z-z<9+3/t, 0<9+3/t, t>-1/3 Not Sufficient
st(2) t<-4, z can be anything Not Sufficient
Combined st(1&2): with z<9 no restriction what so ever Not Sufficient
answer E
night->I think the above statement is not quite relevantlets say ; t=-4 and z =1 , clearly zt = -4 < -3
when t=-4, z<-3/(-4) AND 0<z<3/4 where z can not be 1
Let's evaluate the part in bold :t is -ve;When t is -ve, z<-3/t AND z>0 i.e. z is +ve.
z < -3/t means z< -3/-4 => z<3/4 and z > 0 BUT in my example, I have z=1, which is not in the range (0,3/4).
I didn't evaluate the 2nd statement : When t is +ve, z<-3/t AND z<0 i.e. z is -ve.
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anshumishra
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So, for any value of z in (0,3/4) where t=-4, zt > -3 (and not zt < -3).Night reader wrote:anshumishra wrote:zt < -3Night reader wrote:zt product is always to the left from -3 hence always -ve. When t is -ve, z<-3/t AND z>0 i.e. z is +ve. When t is +ve, z<-3/t AND z<0 i.e. z is -ve. Two numbers' product can be -ve only if one number is +ve and the other is -ve. Agree?anshumishra wrote:Night reader wrote:zt<-3, is z<4 ? also z<-3/t --- Careful, It is easy to miss (but this is true only when t>0, when t is -ve, then z>-3/t)GHong14 wrote:
st(1) z<9, z-z<9+3/t, 0<9+3/t, t>-1/3 Not Sufficient
st(2) t<-4, z can be anything Not Sufficient
Combined st(1&2): with z<9 no restriction what so ever Not Sufficient
answer E
night->I think the above statement is not quite relevantlets say ; t=-4 and z =1 , clearly zt = -4 < -3
when t=-4, z<-3/(-4) AND 0<z<3/4 where z can not be 1
Let's evaluate the part in bold :t is -ve;When t is -ve, z<-3/t AND z>0 i.e. z is +ve.
z < -3/t means z< -3/-4 => z<3/4 and z > 0 BUT in my example, I have z=1, which is not in the range (0,3/4).
I didn't evaluate the 2nd statement : When t is +ve, z<-3/t AND z<0 i.e. z is -ve.
When we multiply or divide an inequality by -ve value, the sign gets inverted.
Are we on the same page ?
Thanks
Anshu
(Every mistake is a lesson learned )
Anshu
(Every mistake is a lesson learned )
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Night reader
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