If zt < -3, is z < 4 ? (1) z < 9 (2) t < -4

Number picking would probably be the most efficient way to attack this problem. Even when we consider both statements together we can easily find two sets of numbers which give us different answers to the question whether z<4:

If z=5 and t=-5 (zt=-25<-3) the answer is NO;
If z=1 and t=-5 (zt=-5<-3) the answer is YES.

Answer: E.
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With a) we don't now nothing about t and z could be < 4 or >=4 and < 9 so INSUF
b) we don't now nothing about z, z could be or not less than 4

Now together:
if z = 5 and t <-4 it is true that zt < -3
however if z= 3 it is also true that zt< -3
so it must be E

I hope you find useful my explanation

Vote for E

i did it this way


(A) when Z < 9

if (Z = 8 and t = -1/2)

zt < -3 = true

Z < 4 (NO)


if (Z = 2 and t = -1/2)

zt < -3 = true

Z < 4 (Yes)

Data not sufficient

----------------------------

(B) t < -4

if (Z = 8 and t = -5)

zt < -3 = true

Z < 4 (NO)


if (Z = 2 and t = -5)

zt < -3 = true

Z < 4 (Yes)

Data not sufficient

-----------------------------

(C) combine when Z < 9 and t < -4

if (Z = 8 and t = -5)

zt < -3 = true

Z < 4 (NO)


if (Z = 2 and t = -5)

zt < -3 = true

Z < 4 (Yes)

Data not sufficient

there for E

Hi Bunuel and other experts,

When you do this(number picking) it seems so simply! 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 as in most of the hard questions you will have to rule out st-A, st-B and A+B. 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!

zt < -3 implies either z>0 and t<0 or z<0 and t>0
(1) we ain't told anything abt t... Also, z can be 2 or 4 producing a Y/N cases
(2) at least we know t is <0; but we dont know whether z>4 or <4.

Both alone insufff.

Taken together, tsst: z=2, t=-5 we get zt = -10 (<-3)
Response to stem is Yes, z < 4

Also, take z=4 and t=-5 we get zt = -20 (<-3)
Response is No z is not < 4.

So, E should be OA.

i missed this question.
this test a basic point
t<-4 so we divide both side by t and change the way of equality
zt<-3
z>-3/t=-3/-4=3/4
insufficient.

\(zt<-3 \ \cap \ z<4\) \(\implies z(t+1)<1\)

\(Combining \ both \ statements:\)

\(z=8, t=-5 \implies 8(-5)<1 \implies (YES)\)

\(z=-9, t=-5 \implies -8(-5)<1 \implies (NO)\)
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Hello experts, why B is not sufficient? When substitute t=-5 and we can get z <0.6. Am I missing something?