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The figure shows a square. The line y = mx divides the square evenly. 14 Jan 2020, 01:49
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63% (02:11) correct 37% (02:13) wrong based on 195 sessions

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[GMAT math practice question]

Attachment:
1.14ps.png
1.14ps.png [ 13.88 KiB | Viewed 4983 times ]

The figure shows a square. The line \(y = mx\) divides the square evenly. What is \(m\)?

A. \(\frac{1}{2}\)

B. \(\frac{1}{3} \)

C. \(\frac{2}{5}\)

D. \(\frac{5}{6}\)

E. \(1\)
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A
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The figure shows a square. The line y = mx divides the square evenly. 14 Jan 2020, 12:37
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\(\frac{x}{2}=\frac{4-x}{6}\)

6x= 8-2x

x=1

slope = x/2= 1/2




MathRevolution
[GMAT math practice question]

Attachment:
1.14ps.png

The figure shows a square. The line \(y = mx\) divides the square evenly. What is \(m\)?

A. \(\frac{1}{2}\)

B. \(\frac{1}{3} \)

C. \(\frac{2}{5}\)

D. \(\frac{5}{6}\)

E. \(1\)
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The figure shows a square. The line y = mx divides the square evenly. 16 Jan 2020, 00:15
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=>

A line passing through the center of a square divides the square evenly.
The center of the square is \((4, 2).\)

Then the slope is \(\frac{(2 - 0) }{ (4 - 0)} = \frac{2}{4} = \frac{1}{2}.\)

Therefore, A is the answer.
Answer: A
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The figure shows a square. The line y = mx divides the square evenly. 14 Jun 2022, 18:42
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MathRevolution
[GMAT math practice question]

Attachment:
The attachment 1.14ps.png is no longer available

The figure shows a square. The line \(y = mx\) divides the square evenly. What is \(m\)?

A. \(\frac{1}{2}\)

B. \(\frac{1}{3} \)

C. \(\frac{2}{5}\)

D. \(\frac{5}{6}\)

E. \(1\)
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The figure is not quite drawn to scale. If it were, a line that divides the square evenly will also replicate the little triangle from the bottom left into the upper right. The right-most point that triangle is at (8,4). Line that passes through (0,0) and (8,4) has a slope 1/2.

Answer choice A.
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The figure shows a square. The line y = mx divides the square evenly. 01 Aug 2025, 02:21
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The Correct Answer is A (1/2).

The Fast Solution: The Center-Point Hack

1. Identify the Core Principle: Any straight line that cuts the area of a square (or rectangle) exactly in half must pass through the geometric center of that square.

2. Find the Square’s Center:
• The square’s x-values run from 2 to 6. The midpoint is (2 + 6) / 2 = 4.
• The square’s y-values run from 0 to 4. The midpoint is (0 + 4) / 2 = 2.
• So, the center of the square is the point (4, 2).

3. Calculate the Slope (m): The line `y = mx` passes through the origin (0, 0) and the square’s center (4, 2).
• Slope `m` = (change in y) / (change in x) = (2 - 0) / (4 - 0) = 2/4.
• `m = 1/2`.

This directly matches answer choice A.
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The figure shows a square. The line y = mx divides the square evenly. 05 Aug 2025, 07:33
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But shouldn't the center point hack be a part of Geometry?

lavendra
The Correct Answer is A (1/2).

The Fast Solution: The Center-Point Hack

1. Identify the Core Principle: Any straight line that cuts the area of a square (or rectangle) exactly in half must pass through the geometric center of that square.

2. Find the Square’s Center:
• The square’s x-values run from 2 to 6. The midpoint is (2 + 6) / 2 = 4.
• The square’s y-values run from 0 to 4. The midpoint is (0 + 4) / 2 = 2.
• So, the center of the square is the point (4, 2).

3. Calculate the Slope (m): The line `y = mx` passes through the origin (0, 0) and the square’s center (4, 2).
• Slope `m` = (change in y) / (change in x) = (2 - 0) / (4 - 0) = 2/4.
• `m = 1/2`.

This directly matches answer choice A.
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