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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If 2x + y > 1, and 5 + 4y < x, which of the following must be true
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10 Nov 2021, 12:12
10 Nov 2021, 12:12
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Question Stats:
66% (01:39) correct
33% (02:23) wrong based on 12 sessions
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If 2x + y > 1, and 5 + 4y < x, which of the following must be true?
A) x < 0
B) y < 0
C) y > 0
D) x < y
E) y < x
A) x < 0
B) y < 0
C) y > 0
D) x < y
E) y < x
If 2x + y > 1, and 5 + 4y < x, which of the following must be true
[#permalink]
10 Nov 2021, 22:20
10 Nov 2021, 22:20
1
Inequality 1 - \(2x + y > 1\) which implies \(2x > 1 - y\)
Inequality 2 - \(x > 5 + 4y\)
Since both equalities have same direction we can add them
\([2x] + [x] > [1 - y] + [5 + 4y]\)
\(3x > 6 + 3y\)
\(3(x) > 3(2 + y)\)
\(x > 2 + y\)
Which also means \(x > y\) or \(y < x\)
Hence, Answer is E
Inequality 2 - \(x > 5 + 4y\)
Since both equalities have same direction we can add them
\([2x] + [x] > [1 - y] + [5 + 4y]\)
\(3x > 6 + 3y\)
\(3(x) > 3(2 + y)\)
\(x > 2 + y\)
Which also means \(x > y\) or \(y < x\)
Hence, Answer is E
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 2x + y > 1, and 5 + 4y < x, which of the following must be true
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11 Nov 2021, 06:41
11 Nov 2021, 06:41
1
GreenlightTestPrep wrote:
If 2x + y > 1, and 5 + 4y < x, which of the following must be true?
A) x < 0
B) y < 0
C) y > 0
D) x < y
E) y < x
A) x < 0
B) y < 0
C) y > 0
D) x < y
E) y < x
When a question provides us with two inequalities, you may be able to apply a property that says the following:
If the inequality symbols of two inequalities are facing the SAME DIRECTION, then we can ADD those inequalities (for more on this, see the video below)
Given:
2x + y > 1
5 + 4y < x
Rewrite the bottom equation as follows:
2x + y > 1
x > 5 + 4y
Subtract 4y from both sides of the bottom inequality:
2x + y > 1
x - 4y > 5
ADD the inequalities to get: 3x - 3y > 6
Divide both sides of the inequality by 3 to get: x - y > 2
At this point, we can conclude that x > y (aka y < x).
Answer: E
Aside: If you're not convinced, just follow these steps:
Take: x - y > 2
Add a second inequality: x - y > 2 > 0
This means: x - y > 0
Add y to both sides to get: x > y
Answer: E
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