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# Is r = s ?

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Retired Moderator
Joined: 05 Jul 2006
Posts: 1731
Is r = s ?  [#permalink]

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22 Feb 2013, 11:52
3
4
00:00

Difficulty:

45% (medium)

Question Stats:

56% (01:07) correct 44% (01:02) wrong based on 330 sessions

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Is r = s ?

(1) $$-s \leq r \leq s$$
(2) $$|r|\geq s$$
Retired Moderator
Joined: 05 Jul 2006
Posts: 1731

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22 Feb 2013, 11:55
2
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: 8188
Location: Pune, India

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22 Feb 2013, 20:27
1
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

Save up to $1,000 on GMAT prep through 8/20! Learn more here > GMAT self-study has never been more personalized or more fun. Try ORION Free! Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8188 Location: Pune, India Re: Is r=s [#permalink] ### Show Tags 22 Feb 2013, 20:33 2 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 Save up to$1,000 on GMAT prep through 8/20! Learn more here >

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Intern
Joined: 16 Jan 2013
Posts: 22

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22 Feb 2013, 21:48
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: 1731

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23 Feb 2013, 01:25
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: 47978
Re: Is r = s ?  [#permalink]

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23 Feb 2013, 05:19
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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Retired Moderator
Joined: 29 Apr 2015
Posts: 862
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, 03:32
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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Location: Ukraine
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GMAT 1: 660 Q48 V33
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Is r = s ?  [#permalink]

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11 Jun 2015, 03:59
2
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 $$|r|≤s$$

_________________
Retired Moderator
Joined: 29 Apr 2015
Posts: 862
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, 04:11
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: 8188
Location: Pune, India
Re: Is r = s ?  [#permalink]

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11 Jun 2015, 20:30
1
1
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
_________________

Karishma
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Re: Is r = s ?  [#permalink]

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29 Sep 2017, 02:37
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 ? &nbs [#permalink] 29 Sep 2017, 02:37
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