If t ≠ 0, is r greater than zero?

Question

(1) r − t = 8
(2) −rt = 8

Shiv2016 · Answer

The answer according to me should be A.

1) r=8+t
Even if t is 1 (minimum possible value in this case), then r=9.

Sufficient.

2) -rt=8
rt= -8

Either of the two nos. is negative but we don't know which one. 
Not sufficient.

I have a doubt here. We are not given that the r and t are positive integers. Then we are just assuming in statement 1 that they are positive and thus its sufficient. Otherwise statement 1 can be insufficient if t= -ve and is less than -8 i.e. -9, -10,.........then r would be less than 0.

Bunuel  can you please clear this doubt ? When should we assume that the given variables are positive or not? Because looking at statement 1, both scenarios can be possible.

Bunuel · Answer

You should not assume that a variable is positive or integer at all.

kivalo · Answer

A) r = t+8
linear function. t can be anything, i.e. -100 or +100. Not sufficient.

B) r = -8/t
t again can be positive or negative. Not sufficient.

A + B)
I'm to lazy to plug in numbers or solve a quadratic (how would you do this?)

If you know how graph of 1/x looks like then you also should how -1/x looks like. -8/t is similar as we are only interested in sign. It goes trough II and IV quadrant only. Because r = t+8 has also to be true, we look at their intersection. They intersect only in 2nd quadrant => sufficient.

https://i63.tinypic.com/2vaiixz.png

sreenu7464 · Answer

If t ≠ 0, is r greater than zero?

(1) r − t = 8
(2) −rt = 8

statement 1 & 2 alone are not enough to solve
statement 1 -> r>t
statement 2 -> either r or t is -ve
so from both we can conclude t is -ve and r is +ve 
 so my answer would be C

matt882 · Answer

1 - not suff 2 - not suff 1&2 t= r-8 and t ≠ 0 so r ≠ 8 -r(r-8)=8 -- r(r-8)=-8 Now rather then be focus on the roots of the equation focus on sign of r: r<0 --> r(r-8) need to be positive -- > not possible r(r-8)=-8 0 r(r-8) negative --> SUFF, r is positive

JS1290 · Answer

I am getting E as an answer, could any one please explain why C is the right answer? I was able to get both of the statements insufficient but when I combined them, I was not able to get them to be sufficient. Please help!

Bunuel · Answer

When you are saying that you are getting E, you have to show your work.

If t ≠ 0, is r greater than zero?

(1) r − t = 8. Not sufficient.
(2) −rt = 8. From this it follows that r and t have different signs. Not sufficient.

(1)+(2) From (2) we know that r and t have different signs. If t is positive and r is negative, then r - t = (negative) - (positive) = negative but we are given that r - t = positive, so this case is not possible, which leaves us with negative t and positive r. Sufficient.

Answer: C.

Luckisnoexcuse · Answer

(1) insufficient .....if r is negative and t is negative and r<t then equation holds e.g. r=-3 and t=-11

Also if r is positive and t is positive and r>t then also equation holds e.g. r=11 and t=3

(2) rt=-8

holds 
when r is positive and t is negative
or 
when r is negative and t is positive
hence insufficient

combining both
only
r is positive and t is negative holds
e.g. r = 5 and t =-3

Hence answer is C

Please correct me if i am wrong

Sent from my iPhone using GMAT Club Forum

Mo2men · Answer

I think there is a typo. you mean 't'

Bunuel · Answer

Yes. Edited. Thank you.

Mo2men · Answer

If t ≠ 0, is r greater than zero?

(1) r − t = 8

r = 8 + t.....r can be anything positive or negative

Insufficient

(2) −rt = 8

rt = -8.It means r & t have different signs

Combine 1 & 2

Both equations are equal to 8, hence

−rt = r − t

t = r +rt

t = r (1 + t)

r = t / (1 + t)...here we can check quick values

t= any positive value , r = positive value..........Not viable option as it violates Fact 2

-1 < t <0 , r = negative value..........................Not viable option as it violates Fact 2

t> -1 , r = positive value................................ viable option

r > 0

sufficient

Answer: C

If t ≠ 0, is r greater than zero?

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