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y + 2x + 3 < 0
[#permalink]
01 Sep 2023, 06:04
01 Sep 2023, 06:04
Expert Reply
00:00
Question Stats:
50% (00:49) correct
50% (02:02) wrong based on 4 sessions
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\(y + 2x + 3 < 0\)
In xy–plane, which quadrant contains no point (x, y) which satisfies the above inequality?
Indicate all that apply
A. I
B. II
C. III
D. IV
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In xy–plane, which quadrant contains no point (x, y) which satisfies the above inequality?
Indicate all that apply
A. I
B. II
C. III
D. IV
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: y + 2x + 3 < 0
[#permalink]
18 Sep 2023, 03:45
18 Sep 2023, 03:45
Expert Reply
OE
Inequality gives us a collection of points in a region. (Region, which lies on either side
of the line.)
Plotting the line first will help us analyse the region lies on which side of the line.
To plot the line, let’s convert given inequality into equality.
𝑦 + 2𝑥 + 3 = 0
𝑦 = −2𝑥 – 3
Here slope is negative, so the line would be declining or a falling line.
y-intercept is -3.
Region of inequality 𝑦 + 2𝑥 + 3 < 0 would be on either side of line L.
Let’s put coordinates of origin in the inequality. (If coordinates of origin satisfy the
inequality, region of inequality would be on the same side, i.e. the side on which
origin lies)
Putting coordinate of origin in the inequality, we get,
0 + 2(0) + 3 < 0
Gives us, 3 < 0, which is not true. So, the region lies on the opposite side of line, i.e.
opposite to the side on which origin lies.
So clearly, not a single point in the first quadrant is covered in the inequality region.
Ans. (A)
Inequality gives us a collection of points in a region. (Region, which lies on either side
of the line.)
Plotting the line first will help us analyse the region lies on which side of the line.
To plot the line, let’s convert given inequality into equality.
𝑦 + 2𝑥 + 3 = 0
𝑦 = −2𝑥 – 3
Here slope is negative, so the line would be declining or a falling line.
y-intercept is -3.
Region of inequality 𝑦 + 2𝑥 + 3 < 0 would be on either side of line L.
Let’s put coordinates of origin in the inequality. (If coordinates of origin satisfy the
inequality, region of inequality would be on the same side, i.e. the side on which
origin lies)
Putting coordinate of origin in the inequality, we get,
0 + 2(0) + 3 < 0
Gives us, 3 < 0, which is not true. So, the region lies on the opposite side of line, i.e.
opposite to the side on which origin lies.
So clearly, not a single point in the first quadrant is covered in the inequality region.
Ans. (A)
gmatclubot
Re: y + 2x + 3 < 0 [#permalink]
18 Sep 2023, 03:45
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