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If |2x - 7| > 17, which of the following must be true?
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19 Mar 2021, 06:56
19 Mar 2021, 06:56
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Question Stats:
85% (01:07) correct
14% (01:14) wrong based on 21 sessions
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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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. -5 < x < 0
B. 0 < x < 12
C. -5 < x < 12
D. x < -5 or x > 12
E. x < -12 or x > 5
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Re: If |2x - 7| > 17, which of the following must be true?
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19 Mar 2021, 07:14
19 Mar 2021, 07:14
1
Solution:
I solved this one using the options as we have -5 & 12 in most of the options.
If x=-5,
|2x-7|>17
|2*-5-7|=|-10-7|=17
As LHS=RHS x cannot be greater than -5. Thus, it has to be less than -5
Lets say -6
then the value will of LHS>RHS
Only option D fits
IMO D
Hope this helps!
I solved this one using the options as we have -5 & 12 in most of the options.
If x=-5,
|2x-7|>17
|2*-5-7|=|-10-7|=17
As LHS=RHS x cannot be greater than -5. Thus, it has to be less than -5
Lets say -6
then the value will of LHS>RHS
Only option D fits
IMO D
Hope this helps!
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Joined: 10 Apr 2015
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Re: If |2x - 7| > 17, which of the following must be true?
[#permalink]
19 Mar 2021, 08:50
19 Mar 2021, 08:50
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Bookmarks
Carcass wrote:
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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. -5 < x < 0
B. 0 < x < 12
C. -5 < x < 12
D. x < -5 or x > 12
E. x < -12 or x > 5
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
----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
Answer: D
