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Is r = s ?

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Is r = s ?  [#permalink]

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New post 22 Feb 2013, 11:52
3
4
00:00
A
B
C
D
E

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) \(|r|\geq s\)
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Re: Is r=s  [#permalink]

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New post 22 Feb 2013, 11:55
2
yezz wrote:
Is r=s?
(1) -s<=r<=s
(2) |r|>=s


Am confused about the official answer and thought of the short answer below.

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
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Re: Is r=s  [#permalink]

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New post 22 Feb 2013, 20:27
1
yezz wrote:
yezz wrote:
Is r=s?
(1) -s<=r<=s
(2) |r|>=s


Am confused about the official answer and thought of the short answer below.

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.
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Re: Is r=s  [#permalink]

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New post 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)
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Re: Is r=s  [#permalink]

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New post 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
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Re: Is r=s  [#permalink]

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New post 23 Feb 2013, 01:25
VeritasPrepKarishma wrote:
yezz wrote:
yezz wrote:
Is r=s?
(1) -s<=r<=s
(2) |r|>=s


Am confused about the official answer and thought of the short answer below.

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
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Re: Is r = s ?  [#permalink]

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New post 23 Feb 2013, 05:19
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Re: Is r = s ?  [#permalink]

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New post 11 Jun 2015, 03:32
VeritasPrepKarishma wrote:
yezz wrote:
yezz wrote:
Is r=s?
(1) -s<=r<=s
(2) |r|>=s


Am confused about the official answer and thought of the short answer below.

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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Is r = s ?  [#permalink]

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New post 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)

And about our task:
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 \(|r|≤s\)

Theory about modules: math-absolute-value-modulus-86462.html
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Re: Is r = s ?  [#permalink]

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New post 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)

And about our task:
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 \(|r|≤s\)

Theory about modules: math-absolute-value-modulus-86462.html


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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Re: Is r = s ?  [#permalink]

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New post 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
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Re: Is r = s ?  [#permalink]

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New post 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

Answer E
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Re: Is r = s ? &nbs [#permalink] 29 Sep 2017, 02:37
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