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In the xy-plane, which quadrant, contains no point (x, y) that satisfi
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01 Sep 2023, 06:09
01 Sep 2023, 06:09
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In the xy-plane, which quadrant, contains no point (x, y) that satisfies the inequality \(y – x \geq 2\) ?
Indicate all that apply
A. I
B. II
C. III
D. IV
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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!!
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\(\Longrightarrow\) Best GRE Test Books of 2023
Re: In the xy-plane, which quadrant, contains no point (x, y) that satisfi
[#permalink]
18 Sep 2023, 03:42
18 Sep 2023, 03:42
Expert Reply
OE
We need to identify region covered by given inequality,
To find out, on which side of the line does region lie, Let’s plot the line first.
To plot the line, let’s convert given inequality into equality.
𝑦 – 𝑥 = 2
𝑦 = 𝑥 + 2
Slope of the line is positive (line would be inclining line) and 𝑦-intercept is 2. (It
would cross 𝑦-axis through point (0, 2))
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)
𝑦 – 𝑥 ≥ 2,
0 – 0 ≥ 2
0 ≥ 2, Which is not true, so the region does not lie on the side in which origin lies.
Clearly means, not a single point from quadrant IV is getting covered in the
region.
So in quadrant IV there will be no point (𝑥, 𝑦) that satisfies the inequality 𝑦 – 𝑥 ≥ 2
Ans. (D)
We need to identify region covered by given inequality,
To find out, on which side of the line does region lie, Let’s plot the line first.
To plot the line, let’s convert given inequality into equality.
𝑦 – 𝑥 = 2
𝑦 = 𝑥 + 2
Slope of the line is positive (line would be inclining line) and 𝑦-intercept is 2. (It
would cross 𝑦-axis through point (0, 2))
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)
𝑦 – 𝑥 ≥ 2,
0 – 0 ≥ 2
0 ≥ 2, Which is not true, so the region does not lie on the side in which origin lies.
Clearly means, not a single point from quadrant IV is getting covered in the
region.
So in quadrant IV there will be no point (𝑥, 𝑦) that satisfies the inequality 𝑦 – 𝑥 ≥ 2
Ans. (D)
gmatclubot
Re: In the xy-plane, which quadrant, contains no point (x, y) that satisfi [#permalink]
18 Sep 2023, 03:42
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