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# Is r = s ?

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Retired Moderator
Joined: 05 Jul 2006
Posts: 1748
Is r = s ? [#permalink]

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22 Feb 2013, 10:52
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Question Stats:

58% (01:06) correct 42% (01:00) wrong based on 306 sessions

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Is r = s ?

(1) $$-s \leq r \leq s$$
(2) $$|r|\geq s$$
[Reveal] Spoiler: OA
Retired Moderator
Joined: 05 Jul 2006
Posts: 1748

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22 Feb 2013, 10:55
2
KUDOS
yezz wrote:
Is r=s?
(1) -s<=r<=s
(2) |r|>=s

i think like this

from 1

/r/<= s....insuff

from 2

/r/>=s...insuff

both
/r/ = s.... insuff .... no info about r=s...E

Is this a right approach or not
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7875
Location: Pune, India

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22 Feb 2013, 19:27
1
KUDOS
Expert's post
yezz wrote:
yezz wrote:
Is r=s?
(1) -s<=r<=s
(2) |r|>=s

i think like this

from 1

/r/<= s....insuff

from 2

/r/>=s...insuff

both
/r/ = s.... insuff .... no info about r=s...E

Is this a right approach or not

Yes, absolutely fine.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7875 Location: Pune, India Re: Is r=s [#permalink] ### Show Tags 22 Feb 2013, 19:33 2 This post received KUDOS Expert's post yezz wrote: Is r=s? (1) -s<=r<=s (2) |r|>=s For people who look at mod from the number line perspective, you can also do this: (1) -s<=r<=s On the number line, r lies between s and -s. i.e. if s = 4, -4 <= r <= 4. (2) |r|>=s This says that r >= s or r <= -s i.e. r is to the right of s or left of -s (or the same as s or -s). If s = 4, r >= 4 or r <= -4 Together, we can say that r must be equal to either s or -s i.e. if s = 4, r = 4 or -4. We still cannot say whether r = s. Hence not sufficient. Answer (E) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Joined: 16 Jan 2013
Posts: 22

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22 Feb 2013, 20:48
yezz wrote:
Is r=s?
(1) -s<=r<=s
(2) |r|>=s

(1) -s<=r<=s not suffice
(2) |r|>=s
i.e. r >= s for positive s, or r < = -s for negative s , not sufficient

from both we get, r = s and r = -s
therefore, We cannot determine
Retired Moderator
Joined: 05 Jul 2006
Posts: 1748

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23 Feb 2013, 00:25
VeritasPrepKarishma wrote:
yezz wrote:
yezz wrote:
Is r=s?
(1) -s<=r<=s
(2) |r|>=s

i think like this

from 1

/r/<= s....insuff

from 2

/r/>=s...insuff

both
/r/ = s.... insuff .... no info about r=s...E

Is this a right approach or not

Yes, absolutely fine.

Many thanks karishma
Math Expert
Joined: 02 Sep 2009
Posts: 43361
Re: Is r = s ? [#permalink]

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23 Feb 2013, 04:19
yezz wrote:
Is r = s ?

(1) $$-s \leq r \leq s$$
(2) $$|r|\geq s$$

Discussed here: inequality-and-absolute-value-questions-from-my-collection-86939-40.html#p653870
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Non-Human User
Joined: 09 Sep 2013
Posts: 14171
Re: Is r = s ? [#permalink]

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15 May 2014, 08:52
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is r = s ? [#permalink]

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11 Jun 2015, 02:32
VeritasPrepKarishma wrote:
yezz wrote:
yezz wrote:
Is r=s?
(1) -s<=r<=s
(2) |r|>=s

i think like this

from 1

/r/<= s....insuff

from 2

/r/>=s...insuff

both
/r/ = s.... insuff .... no info about r=s...E

Is this a right approach or not

Yes, absolutely fine.

Dear Karishma:
How is he translating from:
(1) -s<=r<=s to
to:
/r/>=s
Do you have any helpful links for this topic? Im struggling heavily with it
Thank you
_________________

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Retired Moderator
Joined: 06 Jul 2014
Posts: 1270
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
Is r = s ? [#permalink]

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11 Jun 2015, 02:59
2
KUDOS
reto wrote:

Dear Karishma:
How is he translating from:
(1) -s<=r<=s to
to:
/r/>=s
Do you have any helpful links for this topic? Im struggling heavily with it
Thank you

Hello reto

What is module:
Module $$|r| = r$$ than $$r > 0$$
and $$|r| = -r$$ than $$r < 0$$
so $$|2| = 2$$ and $$|-2| = 2$$
(just for simplifying you can think about module as about dropping minus from number, but for harder tasks you should use operation described above)

We can make example from this inequality $$−s≤r≤s$$ --> $$-4 ≤ 2 ≤ 4$$ or $$-4 ≤ -2 ≤ 4$$
So this inequality will be true for $$r$$ and for $$r *-1$$

So we can change $$r$$ in this inequality on $$|r|$$ and this inequality still be true --> $$-4 ≤ |2| ≤ 4$$
And from this part we can drop left side of inequality and write it as $$|2| ≤ 4$$

That's how we transform $$-s≤r≤s$$ to $$|r|≤s$$

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Joined: 29 Apr 2015
Posts: 888
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Re: Is r = s ? [#permalink]

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11 Jun 2015, 03:11
Harley1980 wrote:
reto wrote:

Dear Karishma:
How is he translating from:
(1) -s<=r<=s to
to:
/r/>=s
Do you have any helpful links for this topic? Im struggling heavily with it
Thank you

Hello reto

What is module:
Module $$|r| = r$$ than $$r > 0$$
and $$|r| = -r$$ than $$r < 0$$
so $$|2| = 2$$ and $$|-2| = 2$$
(just for simplifying you can think about module as about dropping minus from number, but for harder tasks you should use operation described above)

We can make example from this inequality $$−s≤r≤s$$ --> $$-4 ≤ 2 ≤ 4$$ or $$-4 ≤ -2 ≤ 4$$
So this inequality will be true for $$r$$ and for $$r *-1$$

So we can change $$r$$ in this inequality on $$|r|$$ and this inequality still be true --> $$-4 ≤ |2| ≤ 4$$
And from this part we can drop left side of inequality and write it as $$|2| ≤ 4$$

That's how we transform $$-s≤r≤s$$ to $$|r|≤s$$

Hey Harley!
Good to see you here! Thanks for your explanation - i really gotta study hard for that quant stuff!
Thanks and all the best
_________________

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7875
Location: Pune, India
Re: Is r = s ? [#permalink]

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11 Jun 2015, 19:30
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
reto wrote:

Dear Karishma:
How is he translating from:
(1) -s<=r<=s to
to:
/r/>=s
Do you have any helpful links for this topic? Im struggling heavily with it
Thank you

I am guessing you have already got the logic of how -s<=r<=s translates to |r| <= s.

Keep these basic relations in mind:

|r| <= s
implies -s <= r <= s

|r| >= s
implies either r <= -s or r >= s

r, the term inside the absolute value could be anything.

|x - 4| <= 4
implies -4 <= x - 4 <= 4
Add 4 to the inequality to get:
0<= x <= 8
etc
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Get started with Veritas Prep GMAT On Demand for \$199

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Non-Human User
Joined: 09 Sep 2013
Posts: 14171
Re: Is r = s ? [#permalink]

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27 Dec 2016, 03:56
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: Is r = s ? [#permalink]

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29 Sep 2017, 01:37
yezz wrote:
Is r = s ?

(1) $$-s \leq r \leq s$$
(2) $$|r|\geq s$$

Given : Nothing
DS: r = s

Statement 1 : $$-s \leq r \leq s$$
Not sufficient
$$|r| \leq s$$

Statement 2: $$|r|\geq s$$
Not sufficient

Combined : |r| = s
r = +/- s
Not sufficient

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Re: Is r = s ?   [#permalink] 29 Sep 2017, 01:37
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