Is r = s ? (1) -s

Question

Is r = s ?

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

yezz · Answer

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

KarishmaB · Answer

Yes, absolutely fine.

KarishmaB · Answer

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)

jbisht · Answer

(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

yezz · Answer

Many thanks karishma

Bunuel · Answer

Discussed here: inequality-and-absolute-value-questions-from-my-collection-86939-40.html#p653870

reto · Answer

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

Harley1980 · Answer

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

reto · Answer

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

KarishmaB · Answer

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

shashankism · Answer

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

MHIKER · Answer

(1)  -s \leq r \leq s  gives several values for r. So Insufficient.

(2)  According \ to \ absolute \ value \ rule   |r|\geq s  is same as  -s \leq r \leq s . So Insufficient.

Considering both options gives us the same result. So C insufficient too.

The answer is  E

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) -s <= r <= s (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