Thanks

come on, man, just type in the problem when it looks like this.
it's a DS problem, so you don't even have to go to the trouble of typing the answer choices.

we have the equation zt < -3, and it wants to know whether z < 4.

(1) alone: If z < 9, then we still don't know whether z < 4. (For instance, z could be 3 [yes] or 5 [no].)
(2) alone: If t < -4, then we know that z is a positive number (because the product is negative and t is negative). you can't really divide two inequalities in any simple way, so just try plugging numbers. let t be, say, -10, and try z's that are greater than 4 and less than 4 (remember, the point here, as on all DS problems, is to prove 'MAYBE'). make sure that you don't violate the condition zt < -3.

if t = -10 and z = 1, then the condition zt < -3 is satisfied, and z is not < 4.
if t = -10 and z = 5, then the condition zt < -3 is satisfied, and z < 4.
these two results show that (2) alone is insufficient.
in fact, the same two results show that statements (1) and (2) TOGETHER are insufficient (since both of the z's selected here happen to be < 9).

answer = e

Is it wrong if I simplify the stem as below?

zt < -3

z < -3/t

and since t < -4 from Statement 2:

if t = -5 --> z < -3/-5 = 0.6 --> z < 0.6 is less than 4

if t = -10 --> z < -3/-10 = 0.3 --> z < 0.3 which is less than 4

yeah, that's wrong.

you can't divide by t unless you've ascertained whether t is positive or negative. and moreover, if t is negative, then you have to switch around the inequality sign ("<" becomes ">").
so if t < -4, then you actually have z > -3/t, not "<".

Hey Ron,

According to a lecture I saw of you (a video posted on Vimeo), you mentioned that if you are given an inequality, use that with each statement.

For example here, we would have

1) z<9 and zt<-3
2) t< -4 and zt<-3

Here's my question.

If statement 1 had read z<-2, does the method described below work?

z<4
zt<4t

4t<-3
Then for zt to be less than -3 (zt<-3), t has to be less than -3/4.

So if statement 1 reads z <-2 and statement 2 reads t is lss than -4, then C would be the answer. Correct?

It looks like you made a mistake turning z<4 into zt<4t; you cannot multiply both sides by t unless you know ahead of time that t is positive..

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Tim Sanders
Manhattan GMAT Instructor

Hey Ron,

I tried adding equations but could not arrive at a meaningful solution. Please review my approach and let me know, how to derive the solution from my apporach.

1) adding equations...
zt<-3
z<9
Zt+z<6 OR z(t+1)<6 therefore, z could be 2,3,6 or1 - Insufficient

2) adding equations...
zt<-3
t<-4
zt+t<-7 or t(z+1)<-7 therefore, z could be 1, -1, 7 or -7 - Insufficient

Combined - subtracting equations
zt+z<6
zt+t<-7
z+t<13 but we know that zt<-3

I stopped here and guessed that 'z' could have 2 values...so, went for E.
I may be wrong, could you help to guide me through the solution with my approach?

Thank you,
Vj

VJ, question. If you subtract the equations shouldn't it be "z-t<13" rather than "z+t<3"?

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Jamie Nelson
ManhattanGMAT Instructor