I think the answer should be "E"

anticipation wrote:If zt < -3, is z < 4 ?

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

zt < -3 { we judge that one has to be negative and other one has to be positive}

is z < 4 ( we rewrite this as is 0 < z < 4 { is z positive } or 0 > z { or z negative } )

(1) z < 9

It can be any value either positive or negative

insufficient

( 2 ) t < -4

t is negative , so z has to be positive

But still it can be greater or less than 4

so should plug in some values.

t = -5 , z = 6 tz = -30

t = -6 , z = 1 tz = -6

in both the tz is less than -3 and the value of z can be less than or greater than 4

so insufficient

Even by considering both the statements, condition is still the same,

so my answer is E,

Hi Ron, Mitch, Brent and other experts:

When you guys do this(number picking) it seems so easy! However, number picking is my Achilles' Heel. It is just so frustratingly difficult for me to come up with right numbers.

When I micro-analyze my thinking process while I try to come up with right values to show counter examples this is what I see: I first need to ensure z <9 and then make sure that t < -4 and then ensure that zt< -3 with the aim of getting a NO for z<4. Even though I am using 'then' after every decision, the fact is- to generate right values, you essentially need to make these 4 decisions simultaneously. I simply dont know how I can do this in 20-30 seconds without befuddling my short term memory apparatus. I am saying 20-30 secs cuz in most of the hard questions you will have to rule out st-A, st-B and A+B as it comes down to E/C. thus you will make 5-6 such decisions for every question.

When I solve such questions I am either totally flustered or take more than 4 mins. Are there efficient ways to do this and which will work for most of the hard problems (inequality, modulus, reciprocal, neg/pos and their combination) etc..in less than 2-3 mins?
Thanks!

mensanumber wrote:Hi Ron, Mitch, Brent and other experts:

When you guys do this(number picking) it seems so easy! However, number picking is my Achilles' Heel. It is just so frustratingly difficult for me to come up with right numbers.

When I micro-analyze my thinking process while I try to come up with right values to show counter examples this is what I see: I first need to ensure z <9 and then make sure that t < -4 and then ensure that zt< -3 with the aim of getting a NO for z<4. Even though I am using 'then' after every decision, the fact is- to generate right values, you essentially need to make these 4 decisions simultaneously. I simply dont know how I can do this in 20-30 seconds without befuddling my short term memory apparatus. I am saying 20-30 secs cuz in most of the hard questions you will have to rule out st-A, st-B and A+B as it comes down to E/C. thus you will make 5-6 such decisions for every question.

When I solve such questions I am either totally flustered or take more than 4 mins. Are there efficient ways to do this and which will work for most of the hard problems (inequality, modulus, reciprocal, neg/pos and their combination) etc..in less than 2-3 mins?
Thanks!

When given a threshold, test EXTREMES: one value close to the threshold, one value far from the threshold.

If zt < -3, is z < 4 ?

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

In statement 1, the threshold for z is 9.

Case 1: z=8
Since zt < -3, we get:
8t < -3
t < -3/8.
Thus, it's possible that z=8 and t=-5.
In this case, both statements are satisfied and z>4.

Case 2: z=1
Since zt < -3, we get:
(1)(t) < -3
t < -3.
Thus, it's possible that z=1 and t=-5.
In this case, both statements are satisfied and z<4.

Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.