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6x < y + a
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30 Aug 2023, 01:13
30 Aug 2023, 01:13
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Question Stats:
50% (00:40) correct
50% (01:10) wrong based on 12 sessions
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\(–6x < y + a\)
In the xy plane if the co-ordinates of the origin do not satisfy the above inequality, which of the following must be true?
A. a > 0
B. a < 0
C. \(a \leq 0\)
D. a > 2
E. a > 5
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In the xy plane if the co-ordinates of the origin do not satisfy the above inequality, which of the following must be true?
A. a > 0
B. a < 0
C. \(a \leq 0\)
D. a > 2
E. a > 5
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE Math Essentials - A most comprehensive handout!!
\(\Longrightarrow\) ALL the GRE Quant and Verbal Practice Directories in ONE place (2023)
\(\Longrightarrow\) Best GRE Test Books of 2023
Re: 6x < y + a
[#permalink]
10 Sep 2023, 09:01
10 Sep 2023, 09:01
1
-6x < y + a can be rearranged to be y > -6x - a.
You know that the inequality means that anything above this line is possible for y. Since (0,0) is not viable for this equation, you know that the line has to be at or above the origin. (You know the line can be at the origin since the inequality is y is greater than NOT y is greater than or equal to). From this, you know that a can equal 0. Since a is negative, to ensure the line is at the origin or above it, a needs to be negative to have a positive y-intercept. Therefore a is less than or equal to 0, choice C.
You know that the inequality means that anything above this line is possible for y. Since (0,0) is not viable for this equation, you know that the line has to be at or above the origin. (You know the line can be at the origin since the inequality is y is greater than NOT y is greater than or equal to). From this, you know that a can equal 0. Since a is negative, to ensure the line is at the origin or above it, a needs to be negative to have a positive y-intercept. Therefore a is less than or equal to 0, choice C.
gmatclubot
Re: 6x < y + a [#permalink]
10 Sep 2023, 09:01
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