Inequality problem

[ve_boss]

Are you sure that OA is E ?

You're asked to say whether z < 4.

In A) if z= 1 ( z < 4)
zt < -3 <=> t < -3 we don't know the answer as we don't know the value of t.

if z = 30 (z > 4)
zt < -3 <=> 30*t < -3 <=> t < -0.1 we don't know the answer as we don't know the value of t.
A insufficient


In B) if z= 1 (z < 4)
zt < -3 <=> t < -3 which is true because t < -4

if z = 30 (z > 4)
zt < -3 <=> 30*t < -3 <=> t < -0.1 which is true because t < -4

So we don't know whether z < 4 or not and B is insufficient.


Answer E.

[GMAT08]

Originally Posted by jayant.apte

Yep I think B should be sufficient. The OA is E but I think we should be able to take (2) and plug in values into zt < -3.

Using (2) say t = -6, then we will get z x -6 < -3 which means z < 0.5 which is less than 4. Any value of t < -4 will result in z < 4 being satisfied. Am I missing something here?

From stat 2), where t < -4, let's say t= -5. In order for zt < -3, z must be +ve (ie z>0). Given that,
any +ve number multiplied by -5 will give zt <-3. So z = 1, 2, or 3 and in this case z<4. However, z could also be 4 or 5 or 6.. etc and still satisfy both t <-4 and zt <-3. So stat 2) is insuff.

[jayant.apte]

Thanks, spotted a careless mistake on my part here. If zt < -3 and if we substitute t = -6 then we get z(-6) < -3. Dividing both sides by -6 will give us z > 0.5 and so (2) is insufficient. Therefore, answer is E

[Onir]

B cannot be the answer.

Since t<-4, let t = -5 and Z = 1
Then Zt < -3, and the answer to the asked question is "yes, Z < 4".

But, let t = -5 and z = 5
Then, Zt < -3 and the answer to the asked question is "No, Z not < 4".

So, statement B is not sufficient to answer the questions,as we get inconsistent answer.

Correct answer is E

[bmwhype]

its a clear E.

Use huge numbers, 100 and -100 and it will be clear.

[bose]

Imo E

[tarkumar]

Originally Posted by jayant.apte

Yep I think B should be sufficient. The OA is E but I think we should be able to take (2) and plug in values into zt < -3.

Using (2) say t = -6, then we will get z x -6 < -3 which means z < 0.5 which is less than 4. Any value of t < -4 will result in z < 4 being satisfied. Am I missing something here?

z x -6 < -3 => z > 3/6 dividing by -ve sign will change the inequality sign
in general t<-4 means t is negative so t = -|t|

z*-|t| < -3 => z|t| > 3 => z > 3/|t| taking |t| to be very large
approx. z > 0 and other limit will be |t| = 4 giving z > 0.75 so B alone can't be sufficient to explain if z < 4 or not

hope it helps

[Munna2002]

Yes, I thought it was B. Where's this question from?

[sanjeev_sharma]

Very good explanation fin3see

[winna.7]

Originally Posted by jayant.apte

Yep I think B should be sufficient. The OA is E but I think we should be able to take (2) and plug in values into zt < -3.

Using (2) say t = -6, then we will get z x -6 < -3 which means z < 0.5 which is less than 4. Any value of t < -4 will result in z < 4 being satisfied. Am I missing something here?

Hi ,., I think the answer should be E. One point that you have overlooked here is that :
z x -6 < -3
=> z > (-3/-6) because, when you move signs from one side to another of inequality, the inequality reverses. If -1/2 > -1, then 1/2 < 1.

=> which means z > 0.5 . we still dont know if it could be greater than 4 or not.!