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If 3x + 7 > y and x + y > 2, which if the following must be true?
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18 Mar 2021, 10:20
18 Mar 2021, 10:20
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Question Stats:
76% (01:20) correct
23% (02:37) wrong based on 43 sessions
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If 3x + 7 > y and x + y > 2, which if the following must be true?
A. x < 9
B. x < 5
C. x > -5/4
D. x < -5/4
E. x > -4/5
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. x < 9
B. x < 5
C. x > -5/4
D. x < -5/4
E. x > -4/5
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 3x + 7 > y and x + y > 2, which if the following must be true?
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18 Mar 2021, 10:33
18 Mar 2021, 10:33
1
Carcass wrote:
If 3x + 7 > y and x + y > 2, which if the following must be true?
A. x < 9
B. x < 5
C. x > -5/4
D. x < -5/4
E. x > -4/5
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. x < 9
B. x < 5
C. x > -5/4
D. x < -5/4
E. x > -4/5
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Given:
3x + 7 > y
x + y > 2
Since the two inequalities are arranged so that the inequality symbols are facing the same direction, let's ADD them together.
We get:
4x + 7 + y > y + 2
Subtract y from both sides to get: 4x + 7 > 2
Subtract 7 from both sides to get: 4x > -5
Divide both sides by 4 to get: x > -5/4
Answer: C
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 3x + 7 > y and x + y > 2, which if the following must be true?
[#permalink]
18 Mar 2021, 10:33
18 Mar 2021, 10:33
Carcass wrote:
If 3x + 7 > y and x + y > 2, which if the following must be true?
A. x < 9
B. x < 5
C. x > -5/4
D. x < -5/4
E. x > -4/5
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. x < 9
B. x < 5
C. x > -5/4
D. x < -5/4
E. x > -4/5
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Another approach:
Take: 3x + 7 > y
And rewrite as: y < 3x + 7
Take: x + y > 2
And rewrite as: 2 < x + y
Subtract x from both sides to get: 2 - x < y
COMBINE the inequalities to get: 2 - x < y < 3x + 7
From this, we can conclude that 2 - x < 3x + 7
Add x to both sides: 2 < 4x + 7
Subtract 7 from both sides: -5 < 4x
Divide both sides by 4 to get: -5/4 < x
Answer: C
Cheers,
Brent
