GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
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
[#permalink]
10 Nov 2021, 12:12
10 Nov 2021, 12:12
1
Bookmarks
00:00
Question Stats:
63% (02:41) correct
36% (02:46) wrong based on 22 sessions
Hide Show timer Statistics
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
[#permalink]
11 Nov 2021, 06:41
11 Nov 2021, 06:41
2
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
RELATED VIDEO
