Is r s ? (1) -r + s

Question

Is r > s ?

(1) -r + s < 0
 (2) r < | s |

Well, 1st one is clear but I have some difficulties with second statement. I guessed it's not sufficient but need clarification. Thank you!

Bunuel · Accepted Answer

Welcome to GMAT Club. Below is a solution for this problem. Is r>s ? (1) -r+s<0 --> rearrange (or add r to both parts): s either r

devinawilliam83 · Answer

Thanks but I am struggling with statement II

The statement tells us that
a) r<-s or :
s -s r r<-s? r>s?
5 -5 6 No 
-5 5 -6 Yes No

b) r<s : r cannot be greater than S

both the substatements say thar  r is not greater than s  therefor should be sufficient

Bunuel · Answer

(2) r<|s| --> either r~~s . Again: this statement tells that absolute value of s is more than r , but s itself may be more, as well as less than r . Hope it's clear.~~

thapliya · Answer

2) r < |s|
doesn't it mean that r lies between s and -s -s < r < s ... so r definitely is smaller than s ?

Bunuel · Answer

That's not correct.

(2)  r<|s|  --> either  r<s  or  r<-s  (for example  r=1  and  s=2  OR  r=1  and  s=-2 ). Not sufficient.

Madhavi1990 · Answer

Is r > s ?

(1) -r + s < 0 = I re arranged the statement, so r < s so sufficient
(2) r < | s | = here there were two cases given the modulus, so insufficient: case 1) r < s 2) -r > s

But I combined 1) + 2) where the common answer was r < s. But A is OA.
Could anyone explain the flaw in my reasoning?

nickrocks · Answer

1) -r + s < 0 
-r < -s 
Multiple both side by -1, when u do this reverse the inequality
r>s
So, it is sufficient. Once u have statement 1 as sufficient, you can eliminate option B,C,E. Only option A and D are left now.
As statement 2 is not sufficient in itself , we eliminate option D and only possible answer is A.

akshayk · Answer

According to statement 1 -> -r + s < 0 => -r < -s Multiply both by -1 <— we need to flip the sign R > S Sufficient. Statement 2 has 2 scenarios, when s <0 and when s>0 hence its insufficient. A. Hope this helps. Posted from my mobile device

pushpitkc · Answer

Statement 1 which reads -r + s < 0 
Is nothing but -r < -s(when you subtract s from both sides)
When we multiply -1 on both sides, the greater than becomes lesser than (or) lesser than becomes greater than
Therefore, the inequality becomes r>s which alone is sufficient.

These are the options in a GMAT DS question
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. 
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. 
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 
(D) EACH statement ALONE is sufficient. 
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

C comes into play only when either 1 or 2 is not enough to prove the statement.

Hope that helps!

adkikani · Answer

VeritasKarishma   GMATPrepNow   MentorTutoring   chetan2u

How about below approach for analyzing St 2:
 |s| can only be 0 or +ve. 
Since r<|s|, correspondingly r can be -ve (if s=0) or r can be 0 (if s is +ve)

But in both above cases, I got r<s. Hence I can UNIQUELY ans q stem as NO.
Where did I falter?

AndrewN · Answer

Hello,  adkikani . Thank you for tagging me. In Statement (2), what is keeping you from trying a negative value for  s ? Remember,  the absolute value of a number is a measure of its distance from 0 , which is why that value is always positive. A real-world example I give with some of my students on the concept is that if I were a skilled dancer--I am not--perhaps I could moonwalk my way to the door, but I would not say I had walked negative 8 feet to get there because I had gone backwards. Distance is a positive unit. All that Statement (2) tells us that the distance that  s  lies from 0 must be greater than the value of  r . You might pick 10,000 for  r , but  s  could be -10,001, and its absolute value, its distance from 0, would be greater than a value of 10,000. The question then becomes,  Is 10,000 greater than -10,001?  The answer would be  yes , and that creates a problem. Perhaps you are conflating the absolute value part of Statement (2) with the inequality of the  original  question, which includes no absolute value symbol.

I hope that helps. Good luck, going forward.

- Andrew

KarishmaB · Answer

Given statement 2 alone, s can easily be negative and r can easily be positive. 
e.g. 4 < |-5| satisfies statement 2 but you get the answer "yes".
Hence stmnt 2 alone is not enough.

unraveled · Answer

St. 1: r > s after rearranging. SUFFICIENT. St. 2: r < | s | Graphical solution as below: r greather than s.png We have two cases here as shown in snapshot when r>s and r

Basshead · Answer

Is r > s ?

(1) -r + s < 0

s < r. Sufficient.

(2) r < | s |

-s < r < s

We don't know if s is negative or positive. Insufficient.

Answer is A.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is r > s ? (1) -r + s < 0 (2) r < | s |

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions