Last visit was: 11 Dec 2024, 12:51 It is currently 11 Dec 2024, 12:51
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Dec 2024
Posts: 97,813
Own Kudos:
685,121
 [3]
Given Kudos: 88,240
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,813
Kudos: 685,121
 [3]
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
avatar
Shiv2016
Joined: 02 Sep 2016
Last visit: 14 Aug 2024
Posts: 522
Own Kudos:
Given Kudos: 277
Posts: 522
Kudos: 202
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Dec 2024
Posts: 97,813
Own Kudos:
Given Kudos: 88,240
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,813
Kudos: 685,121
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
kivalo
Joined: 20 Sep 2016
Last visit: 08 Sep 2022
Posts: 91
Own Kudos:
Given Kudos: 207
GMAT 1: 680 Q49 V35
GPA: 3.99
GMAT 1: 680 Q49 V35
Posts: 91
Kudos: 169
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.

User avatar
sreenu7464
Joined: 19 Mar 2015
Last visit: 04 Jan 2018
Posts: 12
Own Kudos:
8
 [1]
Given Kudos: 1
Location: India
Posts: 12
Kudos: 8
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
avatar
matt882
Joined: 08 Dec 2016
Last visit: 18 Sep 2020
Posts: 25
Own Kudos:
Given Kudos: 559
Location: Italy
Schools: IESE '21
Schools: IESE '21
Posts: 25
Kudos: 36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If t ≠ 0, is r greater than zero?

(1) r − t = 8
(2) −rt = 8

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< 8 --> r(r-8) negative --> SUFF, r is positive
User avatar
JS1290
Joined: 27 Dec 2016
Last visit: 04 Nov 2019
Posts: 239
Own Kudos:
Given Kudos: 1,103
Posts: 239
Kudos: 251
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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!
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Dec 2024
Posts: 97,813
Own Kudos:
685,121
 [1]
Given Kudos: 88,240
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,813
Kudos: 685,121
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
csaluja
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!

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.
User avatar
Luckisnoexcuse
User avatar
Current Student
Joined: 18 Aug 2016
Last visit: 16 Apr 2022
Posts: 529
Own Kudos:
Given Kudos: 198
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Products:
GMAT 2: 740 Q51 V38
Posts: 529
Kudos: 622
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(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
User avatar
Mo2men
Joined: 26 Mar 2013
Last visit: 09 May 2023
Posts: 2,453
Own Kudos:
1,408
 [1]
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
Products:
Schools: Erasmus (II)
Posts: 2,453
Kudos: 1,408
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
csaluja
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!

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 s 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 s and positive r. Sufficient.

Answer: C.

I think there is a typo. you mean 't'
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Dec 2024
Posts: 97,813
Own Kudos:
Given Kudos: 88,240
Products:
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,813
Kudos: 685,121
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Mo2men
Bunuel
csaluja
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!

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 s 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 s and positive r. Sufficient.

Answer: C.

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

Yes. Edited. Thank you.
User avatar
Mo2men
Joined: 26 Mar 2013
Last visit: 09 May 2023
Posts: 2,453
Own Kudos:
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
Products:
Schools: Erasmus (II)
Posts: 2,453
Kudos: 1,408
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
Moderator:
Math Expert
97813 posts