Inequality

This topic has expert replies
Moderator
Posts: 772
Joined: Wed Aug 30, 2017 6:29 pm
Followed by:6 members

Inequality

by BTGmoderatorRO » Sun Oct 08, 2017 11:28 am
If 4<(7-x)/3, which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
QA is d. what is the answer to this question and why is option C wrong

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sun Oct 08, 2017 12:11 pm
If 4 < (7-x)/3,which of the following must be true?
  • I. 5<x
    2. |x+3|>2
    3. -(x+5) is positive.

    A. II only
    B .III only
    C. I and II only
    D. II and III only
    E. I,II and III
Simplify the expression in the question stem:
4 < (7-x)/3
12 < 7-x
x < -5.
Question stem rephrased:
If x < -5, which of the following must be true?

I: x > 5
Since x is negative, it is not possible that x>5.
Eliminate C and E, which include I.

II: |x+3| > 2.
|x-(-3)| > 2
|a-b| = the DISTANCE between a and b.
Thus, |x-(-3)| > 2 implies the following:
The distance between x and -3 is greater than 2.
Since x<-5, it must be true that x is more than 2 places from -3.
Eliminate B, which does not include II.

III: -(x+5)>0
x+5 < 0
x < -5.
Eliminate A, which does not include III.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Legendary Member
Posts: 712
Joined: Fri Sep 25, 2015 4:39 am
Thanked: 14 times
Followed by:5 members

by Mo2men » Mon Oct 09, 2017 6:30 am
GMATGuruNY wrote:
If 4 < (7-x)/3,which of the following must be true?
  • I. 5<x
    2. |x+3|>2
    3. -(x+5) is positive.

    A. II only
    B .III only
    C. I and II only
    D. II and III only
    E. I,II and III
Simplify the expression in the question stem:
4 < (7-x)/3
12 < 7-x
x < -5.
Question stem rephrased:
If x < -5, which of the following must be true?

II: |x+3| > 2.
|x-(-3)| > 2
|a-b| = the DISTANCE between a and b.
Thus, |x-(-3)| > 2 implies the following:
The distance between x and -3 is greater than 2.
Since x<-5, it must be true that x is more than 2 places from -3.
Eliminate B, which does not include II.
Dear Mitch,

I solved II in another way

|x+3| > 2

x +3 > 2................x>-1
or
x +3 < -2 .............x <-5

so, x >-1 or x <-5

In your solution, you have ignored the red part, making II not must be true?

Where did I go worng here?

Master | Next Rank: 500 Posts
Posts: 186
Joined: Sat Dec 24, 2016 12:38 am
Thanked: 5 times
Followed by:3 members

by rsarashi » Mon Oct 09, 2017 9:51 am
Dear Mitch,

I solved II in another way

|x+3| > 2

x +3 > 2................x>-1
or
x +3 < -2 .............x <-5

so, x >-1 or x <-5

In your solution, you have ignored the red part, making II not must be true?

Where did I go worng here?
[/quote]


Hi GMATGuruNY ,

I also want to know the same.

If we solve this we get x>-1 or x<-5

and x<-5 is true.

Please explain.

Thanks

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Mon Oct 09, 2017 10:34 am
Roland2rule wrote:If 4<(7-x)/3, which of the following must be true?
I. 5<x
II. |x+3|>2
III. -(x+5) is positive

(A) II only
(B) III only
(C) I and II only
(D) II and III only
(E) I, II and III
First, let's deal with the given inequality.
4 < (7-x)/3
Multiply both sides by 3 to get: 12 < 7 - x
Add x to both sides: x + 12 < 7
Subtract 12 from both sides to get: x < -5

So, if x < -5, which of the following statements MUST be true?

Aside: When dealing with "MUST be true" questions, we can eliminate a statement if we can find an instance where it is not true.

I. 5 < x (MUST this be true?)
No!
If x < -5, then it could be the case that x = -7, and -7 is NOT greater than 5
So, statement I need NOT be true.

II. |x+3| > 2 (MUST this be true?)
The answer is Yes. Here's why:
IMPORTANT CONCEPT: |x - k| represents the DISTANCE between x and k on the number line.
So, for example, we can think of |4 - 7| as the distance between 4 and 7 on the number line.
Notice that |4 - 7| = |-3| = 3, and 3 is indeed the distance between 4 and 7 on the number line.

Now let's examine |x+3|
We can rewrite this as |x - (-3)|
This represents the DISTANCE between x and -3 on the number line.
So, the inequality |x-(-3)| > 2 is stating that the DISTANCE between x and -3 on the number line is GREATER THAN 2
Well, since we're told that x < -5, we can be certain that the DISTANCE between x and -3 on the number line is definitely GREATER THAN 2
[If you're not convinced, sketch a number line, and place a big dot at -3. Then choose ANY value for x such that x < -5. You'll see that the distance between x and -3 is greater than 2]
So, statement II MUST be true.

III. -(x+5) is positive
This is the same as saying -(x+5) > 0 (MUST this be true?)
The answer is Yes. Here's why:
We're told that x < -5
If we add 5 to both sides we get x+5 < 0
Now, if we multiply both sides by -1, we get -(x+5) > 0
[aside: notice that, since I multiplied both sides by a negative value, I reversed the direction of the inequality]
As we can see, statement III MUST be true.

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Oct 09, 2017 12:11 pm
Mo2men wrote:Dear Mitch,

I solved II in another way

|x+3| > 2

x +3 > 2................x>-1
or
x +3 < -2 .............x <-5

so, x >-1 or x <-5

In your solution, you have ignored the red part, making II not must be true?

Where did I go worng here?
Your solution is fine.
Prompt: x<-5.
Statement II: x<-5 or x>-1
The portion in green is like a green box that contains every value less than -5 or greater than -1.
Question stem, rephrased:
Is every value represented by the inequality in red contained within the green box implied by Statement II?
YES.
Thus, Statement II must be true.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3