Is r = s ? (1) -s

Question

Is r = s ?

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

KarishmaB · Accepted 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)

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.

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

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

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