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Source: — Data Sufficiency |
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by anshumishra » Sat Jan 22, 2011 5:17 pm
GHong14 wrote:Image
zt < -3, z< 4 ?

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]
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Anshu

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by Night reader » Sat Jan 22, 2011 5:22 pm
GHong14 wrote:Image
zt<-3, is z<4 ? also z<-3/t
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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by anshumishra » Sat Jan 22, 2011 5:40 pm
Night reader wrote:
GHong14 wrote:Image
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)
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
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by Night reader » Sat Jan 22, 2011 6:13 pm
anshumishra wrote:
Night reader wrote:
GHong14 wrote:Image
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)
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
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?
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by anshumishra » Sat Jan 22, 2011 6:31 pm
Night reader wrote:
anshumishra wrote:
Night reader wrote:
GHong14 wrote:Image
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)
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
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?
zt < -3
lets say ; t=-4 and z =1 , clearly zt = -4 < -3

Let's evaluate the part in bold :
When t is -ve, z<-3/t AND z>0 i.e. z is +ve.
t 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

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by Night reader » Sat Jan 22, 2011 6:49 pm
anshumishra wrote:
Night reader wrote:
anshumishra wrote:
Night reader wrote:
GHong14 wrote:Image
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)
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
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?
zt < -3
night->
lets say ; t=-4 and z =1 , clearly zt = -4 < -3
I think the above statement is not quite relevant
when t=-4, z<-3/(-4) AND 0<z<3/4 where z can not be 1

Let's evaluate the part in bold :
When t is -ve, z<-3/t AND z>0 i.e. z is +ve.
t 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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by anshumishra » Sat Jan 22, 2011 6:59 pm
Night reader wrote:
anshumishra wrote:
Night reader wrote:
anshumishra wrote:
Night reader wrote:
GHong14 wrote:Image
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)
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
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?
zt < -3
night->
lets say ; t=-4 and z =1 , clearly zt = -4 < -3
I think the above statement is not quite relevant
when t=-4, z<-3/(-4) AND 0<z<3/4 where z can not be 1

Let's evaluate the part in bold :
When t is -ve, z<-3/t AND z>0 i.e. z is +ve.
t 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.
So, for any value of z in (0,3/4) where t=-4, zt > -3 (and not zt < -3).
When we multiply or divide an inequality by -ve value, the sign gets inverted.
Are we on the same page ?
Thanks
Anshu

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by Night reader » Sat Jan 22, 2011 7:05 pm
I think yes, just reversed angles
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