If zt<-3, is z<4 DS Question

[cdashw]

If zt<-3, is z<4

(1) z<9
(2) t<-4

I rationalized that this is a yes/no question. I rationalized that Stmt 1 is insufficient. But then all rational thought was lost since the answer is E.

Please explain.

[guest]

if zt < -3 then is z < 4.

It is a YES/NO question whether z < 4

Looking at it 1st statement, for the 1st inequality to be true either z is -ve or t -ve, however both cannot be negative.

1. z < 9 - Insufficient as z = 8 , t = -9 then zt < -3 , similarly z = 1 and t = -5, zt < -3 thus it is insufficient to state that z <4

2. t < -4 Insufficient since this only provides us that z > 0, but does not given any indication whether z > 4
for example t = -6, z = 2 , zt = -12
t = -5, z = 5 zt = -25

Now taking them together: z < 9 and t < -4
If one has to be negative, for the 1st statement to hold true than z is +ve between 1 and 9 and t -ive -4 to -infinity.
z = 8, t = -5 ; zt = -40
z = 3, t = -5 ; zt = -15
Thus one cannot conclusively state whether z< 4, therefore the correct answer is E.

[RonPurewal]

http://www.manhattangmat.com/forums/if-zt-3-t1773.html