Qudurat GAT (Saudi Arabia) · Quantitative Reasoning

Advanced Algebra, Geometry and Data Analysis

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If $3^{2 x - 1} = 81$ , what is the value of $x$ ?
A car travels 240 kilometers at 80 km/h and returns the same distance at 120 km/h. What is the average speed of the car for the entire round trip?
In a triangle, the ratio of the three interior angles is $2 : 3 : 4$ . What is the degree measure of the largest angle?
A merchant sells an article for 450 SAR, incurring a loss of 10% on the cost price. At what selling price should the merchant sell the article to achieve a 20% profit?
If $x + 7 = 5$ , what is the numerical value of $(x - 3)^{2}$ ?
A water tank can be filled by Pipe A in 6 hours and by Pipe B in 12 hours. If both pipes are opened simultaneously, how many hours will it take to fill the empty tank completely?
What is the radius of a circle whose area is numerically equal to its circumference?
If $a + b = 10$ and $a^{2} + b^{2} = 58$ , what is the numerical value of the product $a \times b$ ?
The perimeter of a rectangle is 46 cm and its diagonal is 17 cm. What is the area of the rectangle?
A class of 30 students took an exam. 18 passed mathematics, 16 passed science, and 4 failed both subjects. How many students passed both mathematics and science?
If $x$ is an integer such that $- 3 < 2 x + 1 \leq 9$ , what is the number of integer values that $x$ can take?
What is the units digit of the number $7^{105}$ ?
If a polygon has 9 sides (a nonagon), what is the sum of its interior angles?
The ratio of the volume of two cubes is $27 : 64$ . What is the ratio of their total surface areas?
If $f (x) = 2 x^{2} - 3 x + 5$ , what is the numerical value of $f (- 2)$ ?
A bag contains 5 red balls, 4 blue balls, and 3 green balls. If one ball is drawn at random, what is the probability that it is NOT red?
If $x + \frac{1}{x} = 4$ , what is the numerical value of $x^{2} + \frac{1}{x ^{2}}$ ?
Two numbers have a sum of 40 and a difference of 14. What is the value of the smaller number?
A cylinder has radius $r = 3 cm$ and height $h = 7 cm$ . What is its volume in terms of $π$ ?
If a worker earns 1,800 SAR in 6 days, how many SAR will the worker earn in 14 days at the same daily rate?
What is the slope of the linear equation $3 x - 4 y = 12$ ?
If the arithmetic mean of 5 numbers is 18, and four of the numbers are 12, 16, 20, and 22, what is the fifth number?
A 20% discount on a jacket saves a customer 60 SAR. What was the original retail price of the jacket before the discount?
What is the sum of the roots of the quadratic equation $2 x^{2} - 10 x + 7 = 0$ ?
If $4^{x + 1} = 64$ , what is the numerical value of $3^{2 x}$ ?
A ladder 10 meters long leans against a vertical wall. If the base of the ladder is 6 meters from the wall, how high up the wall does the ladder reach?
A car depreciates in value by 15% each year. If its value at the beginning of the year is 80,000 SAR, what is its value at the end of the year?
If $lo g_{10} (x) + lo g_{10} (5) = 2$ , what is the numerical value of $x$ ?
What is the total surface area of a cube with edge length $4 cm$ ?
If 8 men can build a wall in 15 days, how many days will it take 12 men working at the identical rate to build the same wall?
In a right triangle, the hypotenuse is 13 cm and one leg is 5 cm. What is the area of the triangle?
If $x$ and $y$ are positive integers such that $x^{2} - y^{2} = 29$ , what is the numerical value of $x$ ?
A sequence begins $2, 6, 18, 54, \dots$ What is the 6th term of this geometric sequence?
A circle is inscribed in a square of side length 14 cm. What is the area of the region inside the square but outside the circle (use $π = 22/7$ )?
If $\frac{2 a + b}{a - 2 b} = 3$ , what is the ratio of $a$ to $b$ ?
A test score has a mean of 75 and a standard deviation of 8. What is the z-score of a student who scored 91?
What is the remainder when $2^{35}$ is divided by 7?
In how many distinct ways can a committee of 3 members be selected from a group of 8 eligible candidates?
A 20-liter solution is 30 percent alcohol. How many liters of pure alcohol must be added to make it 50 percent alcohol?
If $x + y = 14$ and $x^{2} - y^{2} = 56$ , what is the value of $x^{2} + y^{2}$ ?
The equation $x^{2} - 6 x + k = 0$ has two real roots that differ by 4. What is the value of $k$ ?

Advanced Algebra, Geometry and Data Analysis

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