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Re: If |2x - 7| > 17, which of the following must be true? [#permalink]
1
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


Sometimes, the quickest solution to this kind of question involves testing the answer choices

Scan 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.

Scan the remaining 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: |-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.

Answer: D

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
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Re: If |2x - 7| > 17, which of the following must be true? [#permalink]
The approach I use to solve Mod questions is by taking two cases,

In this example, there will be two inequalities because of the mod

2x-7<-17 & 2x-7>17
If you take an absolute of both these values, it will come out to be the same as the inequality in the question

Solving these two separately will give x<-5 or x>12.

D is the correct option
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Re: If |2x - 7| > 17, which of the following must be true? [#permalink]
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Re: If |2x - 7| > 17, which of the following must be true? [#permalink]
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