## If |2x - 7| > 17, which of the following must be true?

##### This topic has expert replies
Legendary Member
Posts: 1223
Joined: 15 Feb 2020
Followed by:1 members

### If |2x - 7| > 17, which of the following must be true?

by BTGModeratorVI » Thu Aug 20, 2020 7:14 am

00:00

A

B

C

D

E

## Global Stats

If |2x - 7| > 17, which of the following must be true?

A. -5 < x < 0
B. 0 < x < 12
C. -5 < x < 12
D. x < -5 or x > 12
E. x < -12 or x > 5

Source: E-gmat

### GMAT/MBA Expert

GMAT Instructor
Posts: 16118
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

### Re: If |2x - 7| > 17, which of the following must be true?

by [email protected] » Mon Aug 24, 2020 6:47 am

00:00

A

B

C

D

E

## Global Stats

BTGModeratorVI wrote:
Thu Aug 20, 2020 7:14 am
If |2x - 7| > 17, which of the following must be true?

A. -5 < x < 0
B. 0 < x < 12
C. -5 < x < 12
D. x < -5 or x > 12
E. x < -12 or x > 5

Source: E-gmat
----ASIDE-----------------------
When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive

-----ONTO THE QUESTION----------

GIVEN: |2x - 7| > 17
Rule #2 tells us that EITHER 2x - 7 > 17 OR 2x - 7 < -17

Take: 2x - 7 > 17
Add 7 to both sides: 2x > 24
Solve: x > 12

Take: 2x - 7 < -17
Add 7 to both sides: 2x < -10
Solve: x < -5

So, either x > 12 or x < -5

Brent Hanneson - Creator of GMATPrepNow.com

### GMAT/MBA Expert

GMAT Instructor
Posts: 16118
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

### Re: If |2x - 7| > 17, which of the following must be true?

by [email protected] » Mon Aug 24, 2020 6:48 am

00:00

A

B

C

D

E

## Global Stats

BTGModeratorVI wrote:
Thu Aug 20, 2020 7:14 am
If |2x - 7| > 17, which of the following must be true?

A. -5 < x < 0
B. 0 < x < 12
C. -5 < x < 12
D. x < -5 or x > 12
E. x < -12 or x > 5

Source: E-gmat
Sometimes, the quickest solution to this kind of question involves testing the answer choices

Notice that some answer choices say that x = 1 is a solution, and some say x = 1 is NOT a solution.
So, let's test x = 1
Plug it into the original inequality to get:|2(1) - 7| > 17
Simplify to get: |-5| > 17
NOT true
So, x = 1 is NOT a solution to the inequality.
We can ELIMINATE B and C because they say that x = 1 IS a solution.

Notice that some answer choices say that x = -1 is a solution, and some say x = -1 is NOT a solution.
So, let's test x = -1
Plug it into the original inequality to get:|2(-1) - 7| > 17
Simplify to get: |-9| > 17
NOT true
So, x = -1 is NOT a solution to the inequality.
We can ELIMINATE A because it says x = -1 IS a solution.

We're down to answer choices D or E.
E says x = 6 is a solution, and D says x = 6 is NOT a solution.
So, let's test x = 6
Plug it into the original inequality to get:|2(6) - 7| > 17
Simplify to get: |5| > 17
NOT true
We can ELIMINATE E because it says x = 6 IS a solution.

NOTE: With this particular question, testing the answer choices is a slower approach. However, when solving questions of this nature, the approach is still worth considering, especially with more complex inequalities.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com

GMAT Instructor
Posts: 15537
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1903 members
GMAT Score:790

### Re: If |2x - 7| > 17, which of the following must be true?

by GMATGuruNY » Mon Aug 24, 2020 11:45 am

00:00

A

B

C

D

E

## Global Stats

BTGModeratorVI wrote:
Thu Aug 20, 2020 7:14 am
If |2x - 7| > 17, which of the following must be true?

A. -5 < x < 0
B. 0 < x < 12
C. -5 < x < 12
D. x < -5 or x > 12
E. x < -12 or x > 5
|2x - 7| > 17 is clearly satisfied if x=100.
Eliminate A, B and C, whose ranges do not include x=100.

D: x>12
E: x>5

Test a value BETWEEN 5 AND 12.
If x=10, then |2x - 7| > 17 is NOT satisfied.
Since x=10 is not a valid solution, eliminate E.

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.