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
Answer: D
Source: Egmat
If 2x  7 > 17, which of the following must be true?
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ASIDEBTGModeratorVI wrote: ↑Thu Aug 20, 2020 7:14 amIf 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
Answer: D
Source: Egmat
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
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Sometimes, the quickest solution to this kind of question involves testing the answer choicesBTGModeratorVI wrote: ↑Thu Aug 20, 2020 7:14 amIf 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
Answer: D
Source: Egmat
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.
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2x  7 > 17 is clearly satisfied if x=100.BTGModeratorVI wrote: ↑Thu Aug 20, 2020 7:14 amIf 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
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.
The correct answer is D.
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Followed here and elsewhere by over 1900 testtakers.
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
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Student Review #3