If |0.1x - 3| = 1, then x could be which of the following values?

Question

If  |0.1x - 3| \geq 1 , then x could be which of the following values?

I. 30
II. 40
III. 50

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

rajatchopra1994 · Answer

Explanation:

|0.1x−3|≥1

I. 30
= |0.1(30)−3|≥1
= 0 NO

II. 40
= |0.1(40)−3|≥1
= 1 Yes

III. 50
= |0.1(50)−3|≥1
= 2 Yes

IMO-D

Kinshook · Answer

Asked: If  |0.1x - 3| \geq 1 , then x could be which of the following values?

I. 30
|0.1x - 3| = |3-3| = 0 ; NO
II. 40
|0.1x - 3| = |4-3| = 1 ; YES
III. 50
|0.1x - 3| = |5-3| = 2 ; YES

IMO D

Shrey08 · Answer

|0.1x - 3| \geq 1

|\frac{x}{10} - 3| \geq 1

|\frac{(x - 30)}{10}| \geq 1

|x - 30| \geq 10

-10\geq x - 30  or  x - 30\geq 10

20\geq x   or  x\geq 40

Only "II" and "III" fall in above range

So, option D is correct

Target4bschool · Answer

Isn't this weird? 
Like how can 10<x<-10 be true?

Shrey08 · Answer

-10\geq x - 30 \geq 10 What this means is: on the number line the distance of x from point 30 is at least 10. So, what are the points which are 10 unit distance apart from 30 on the number line ? 20 and 40, which lie on either side on 30 on the number line. So, if you move towards left from 20 and towards right from 40 every point will satisfy above equation. Does it still feel weird

vikramgade · Answer

This is what it should be brother.
(I think its an careless mistake. Even I loose many points for such silly mistakes.)
  10 \geq x - 30 \geq -10

Posted from my mobile device

Target4bschool · Answer

Yes, your concept (number line- distance) is right. I was just talking about the inequality expression. 
Please correct me if I am wrong but at most places, when |x|>10, then we say that either x>10 or x<-10

Bunuel · Answer

−10 ≥ x − 30 ≥ 10 does not make sense. -10 is not more than or equal to 10.

|x − 30| ≥ 10 means x ≥ 40 OR x ≤ 20.

Shrey08 · Answer

Hi  Bunuel

Why does −10 ≥ (x − 30) ≥ 10 not make sense ?

this is infact: 20 ≥ x ≥ 40 and means the same as x ≥ 40 OR x ≤ 20.

Target4bschool · Answer

When |x| < a -aa x<-a or x>a Here, |x-30| > 10 So, x-30 > 10 or x-30 < -10 What you are saying, 10 > x-30>-10, is true when |x-30| < 10

Shrey08 · Answer

Target4bschool Bunuel Alright, I got what you are pointing at(it took me a while to see it...

) 1010. But you are saying this looks misleading because this (could) mean -10>10 is it completely wrong to write 10

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.

If |0.1x - 3| >= 1, then x could be which of the following values?

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

GMAT Problem Solving (PS) Questions