Practice Test 2 - GMAT Quantitative

20 questions. Answer them in any order, then submit to see your score and every explanation.

Use the dot plot below to determine the mean exam score.
If $\frac{x + y}{2} = 5$ and $\frac{x - y}{3} = 2$ , what is the value of $x^2 - y^2$ ?
A farmer has $180$ feet of fencing to enclose a rectangular garden. One side of the garden will be against an existing wall, so fencing is needed for only three sides. If the farmer wants to maximize the area of the garden, what should be the length of the side parallel to the wall?
If $f(x) = 2x + 1$ and $g(x) = x^2 - 3$ , what is the domain of the composite function $\frac{f(x)}{g(x)}$ ?
Use the histogram shown to calculate the approximate mean age of the 40 participants.
If the GCF of two positive integers $a$ and $b$ is 12, and their LCM is 180, what is the value of $ab$ ?
Six people consisting of three married couples are to be seated in a row of six chairs. In how many seating arrangements does no married couple sit in adjacent chairs?
A fertilizer company sells two soil mixes. Mix R contains 10% peat moss by weight, and Mix S contains 25% peat moss by weight. If a landscaper wants exactly 40 kilograms of soil that is 16% peat moss, how many kilograms of Mix R should be used?
If $0<p<1$ , which of the following expressions is always greater than 1?
For $x\neq 0,-7$ , simplify $ $\dfrac{(x^{2}+3x)^{2}-16x^{2}}{x(x+3)+4x}.$
For all $x \neq \pm 2$ , which of the following is equivalent to the expression $\dfrac{2x^{2}-8}{x^{2}-4}$ ?
If $P = \frac{x^2 - 1}{x + 1}$ and $Q = \frac{x^2 + 2x + 1}{x + 1}$ , then $P - Q$ equals: Give your answer in simplest form.
A consulting firm charges clients based on a complex fee structure: a base rate of $200 per hour for the first $10$ hours of work, then $150 per hour for the next $20$ hours, and $100 per hour for any hours beyond $30$ . If the firm worked $h$ hours on a project where $h > 30$ , which expression represents the total fee charged?
For which values of $a$ does the system $\begin{cases} 2x + 3y = 6 \\ ax + 6y = 12 \end{cases}$ have infinitely many solutions?
Based on the bar chart shown, what is the median number of books read by the seven students last month?
Refer to the diagram. How many of the readers surveyed read exactly one of the three newspapers?
A runner leaves a trailhead and jogs at 6 mph along a straight road. One hour later a bus departs the same trailhead, traveling the same direction at 45 mph. How long after the bus departs will the bus be exactly 25 miles ahead of the runner?
If $\sqrt{x^4 + 8x^2 + 16} = x^2 + 4$ for all real values of $x$ , which of the following must be true?
A five-section spinner, with sectors numbered 1 through 5 of equal size, is spun twice. What is the probability that the product of the two numbers obtained is divisible by 6?
The function $p(x) = ax^2 + bx + c$ passes through the points $(1, 4)$ , $(2, 9)$ , and $(3, 16)$ . What is the value of $a + b + c$ ?

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