CGM Practice Questions

19 Total Questions Quantitative Reasoning

Master GMAT CGM with comprehensive practice questions. Build your quantitative reasoning skills through detailed explanations and strategic practice.

Key Skills

Problem Solving
Analytical Thinking
Mathematical Reasoning
Strategic Analysis

Study Tips

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Question 1 of 5 Medium

In the figure shown, point P(–√3, 1) and Q (s, t) lie on the circle with center O. What is value of s?

$\frac{1}{2}$

$1$

$\sqrt{2}$

$\sqrt{3}$

$\frac{\sqrt{2}}{2}$

View Explanation

Correct Answer: B

Slope of line OP is $-\frac{1}{\sqrt{3}}$

slope of OQ is $\frac{t}{s}$, so $\frac{t}{s} \times \left(-\frac{1}{\sqrt{3}}\right) = -1$, $t = \sqrt{3}s$

$OQ = OP = 2$, $t^2 + s^2 = 4$. Combined above, $s = \pm 1 \Rightarrow s = 1$
Answer is B

Question 2 of 5 Medium

For any triangle $ T $ in the xy-coordinate plane, the center of $ T $ is defined to be the point whose x-coordinate is the average (arithmetic mean) of the x-coordinates of the vertices of $ T $ and whose y-coordinate is the average of the y-coordinates of the vertices of $ T $. If a certain triangle has vertices at the points $ (0,0) $ and $ (6,0) $ and center at the point $ (3,2) $, what are the coordinates of the remaining vertex?

$ (3,4) $

$ (3,6) $

$ (4,9) $

$ (6,4) $

$ (9,6) $

View Explanation

Correct Answer: B

Let the third vertex be $ (x, y) $.
Center x:
$$ \frac{0 + 6 + x}{3} = 3 \implies 6 + x = 9 \implies x = 3 $$
Center y:
$$ \frac{0 + 0 + y}{3} = 2 \implies y = 6 $$
Vertex is $ (3, 6) $.
The correct answer is B.

Question 3 of 5 Medium

In the xy-plane, line $ k $ has positive slope and x-intercept 4. If the area of the triangle formed by line $ k $ and the two axes is 12, what is the y-intercept of line $ k $?

$ -6 $

$ -4 $

$ -3 $

$ 3 $

$ 6 $

View Explanation

Correct Answer: A

Triangle vertices are $ (0,0) $, $ (4,0) $, and $ (0,y) $.
Area:
$$ \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times |y| = 2|y| $$
$$ 2|y| = 12 \implies |y| = 6 $$
Slope:
$$ \frac{y-0}{0-4} = -\frac{y}{4} $$
Since slope is positive, $ -\frac{y}{4} > 0 \implies y < 0 $.
So $ y = -6 $.
The correct answer is A.

Question 4 of 5 Medium

Line $ l $ is defined by the equation $ y - 5x = 4 $ and line $ w $ is defined by the equation $ 10y + 2x + 20 = 0 $. If line $ k $ does not intersect line $ l $, what is the degree measure of the angle formed by line $ k $ and line $ w $?

It cannot be determined from the information given.

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Question 5 of 5 Medium

In the rectangular coordinate plane, points $ X $ and $ Z $ lie on the same line through the origin and points $ W $ and $ Y $ lie on the same line through the origin. If $ a^2 + b^2 = c^2 + d^2 $ and $ e^2 + f^2 = g^2 + h^2 $, what is the value of length $ XZ - WY $?

$ -2 $

$ -1 $

$ 0 $

$ 1 $

$ 2 $

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