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

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): \(s<r\), directly answers the question. Sufficient.

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

Basically this statement tells that absolute value of s is more than r, but s itself may be more, as well as less than r.

Answer: A.

Hope it's clear.
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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

(2) \(r<|s|\) --> either \(r<s\) OR \(r<-s\). Now, try some number to see that this statement is not sufficient: if \(r=1\) and \(s=2\) then \(r<s\) BUT if \(r=1\) and \(s=-2\) then \(r>s\).

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

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.
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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?

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.

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
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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!

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?
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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
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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.

St. 1: r > s after rearranging.
SUFFICIENT.

St. 2: r < | s |
Graphical solution as below:

We have two cases here as shown in snapshot when r>s and r<s.
INSUFFICIENT.

Answer A.
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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.
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