Practice Test 4 - GMAT Quantitative

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

Which of the following values of $t$ satisfies both $|t-4|<3$ and $2t+1>9$ ?
The number of bacteria in a culture triples every 4 hours. If there are currently 2,400 bacteria, how many were there 12 hours ago?
A manufacturing machine produces 40 widgets per hour for the first 3 hours of operation and then 60 widgets per hour thereafter. If the machine produced a total of 540 widgets during one continuous run, for how many hours did it operate?
Two runners start together on a 400-meter circular track and move in the same direction. Runner 1 maintains a constant speed of 2.5 meters per second, whereas Runner 2 maintains 3 meters per second. After how many seconds will Runner 2 have completed exactly one full lap more than Runner 1?
Coffee blend X costs $5 per pound and blend Y costs $9 per pound. How many pounds of blend X must be mixed with 6 pounds of blend Y to obtain a mixture costing exactly $7 per pound?
If real numbers $x$ and $y$ satisfy $|x-3|+|y+1|\le4,$ what is the maximum possible value of $x+y$ ?
The inequality $\frac{x + 2}{x - 1} \geq 3$ is equivalent to which of the following?
The quadratic $ax^2 + bx + c = 0$ has discriminant $\Delta = 25$ . If the quadratic $ax^2 + bx + (c + 6) = 0$ has discriminant $\Delta'$ , what is $\Delta - \Delta'$ ?
The 5-digit integer $5k38$ is divisible by 11. What is the value of the digit $k$ ?
If $x^2 - 4x + k = (x - a)^2 + b$ for all values of $x$ , and $k = 7$ , what is the value of $a^2 + b^2$ ?
Three tasks require $9$ , $12$ , and $15$ days, respectively, to complete one full cycle. If all three tasks begin today, in how many days will they next all begin a new cycle on the same day?
If $a$ and $b$ are positive integers such that $\gcd(a,b) = 12$ and $\text{lcm}(a,b) = 180$ , what is the value of $ab$ ?
In a data set of 20 values, the mean is 50 and the median is 48. If the 5 largest values are each decreased by 8, what is the new mean?
If $x^{2}-\dfrac{1}{x^{2}}=15$ and $x>1$ , what is the value of $x-\dfrac{1}{x}?$
For $x\neq 3$ , the expression $\dfrac{x^{3}-27}{x^{2}+3x+9}$ simplifies to
An employee receives a 12% salary increase in January, followed by a 15% bonus based on the new salary in March. If the employee's total annual compensation (salary plus bonus) is $64,400, what was the original salary in December?
Machine A can print 300 pages in 8 minutes, whereas Machine B can print the same 300 pages in 12 minutes. Working together, the two machines must print 1,800 pages. If both machines start at the same time but Machine A jams and stops after exactly 12 minutes, for how many additional minutes must Machine B work alone to finish the 1,800-page job?
For how many positive integers $k < 100$ is $\frac{k^3 - k}{6}$ an integer?
What is the least common multiple of $84$ and $120$ ?
Based on the pie chart shown, what is the median number of clients per department?

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