Practice Test 10 - GMAT Quantitative

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

In a survey of 100 people, 55 read magazine A, 45 read magazine B, and 35 read magazine C. Exactly 20 read both A and B, 15 read both A and C, 10 read both B and C, and 5 read all three magazines. How many of the people surveyed read none of the three magazines?
Two investment portfolios have the same expected annual return of 8%. Portfolio X has a standard deviation of 12%, while Portfolio Y has a standard deviation of 18%. An investor creates a new portfolio by investing equal amounts in both Portfolio X and Portfolio Y. Which statement about the risk (standard deviation) of the combined portfolio is correct?
Company A and Company B both have 100 employees with mean salaries of $75,000. Company A has a standard deviation of $15,000, while Company B has a standard deviation of $5,000. If both companies decide to give every employee a $10,000 raise and then a 10% bonus on their new salary, which statement about the resulting standard deviations is correct?
Based on the pie charts shown, which department's monthly expenses are likely to have the smaller standard deviation over the year?
If $a$ and $b$ are real numbers such that $|a - b| = 5$ and $|a + b| = 3$ , what is the value of $|a^2 - b^2|$ ?
For how many integer values of $k$ does the system of inequalities $|x - 2| < k$ and $|x - 8| < k$ have at least one solution?
If $y$ is 3 more than the square of $x$ and $z$ is twice the difference between $y$ and 4, which of the following expresses $z$ solely in terms of $x$ ?
If $|3y-7|\le2$ and $y$ is an integer, how many possible values of $2y$ are less than 10?
A city's population decreases by 5% each year due to migration. Additionally, the birth rate exceeds the death rate by 2% per year. What is the net annual percentage change in the city's population?
A river flows at 3 mph. A boat can travel 24 miles downstream in the same time it takes to travel 16 miles upstream. What is the speed of the boat in still water?
If $\operatorname{lcm}(r,s)=144$ and $r=2^{3}\!\cdot\!3^{2}$ , which of the following must equal $\gcd(r,s)$ ?
From a group of 4 men and 5 women, a committee of 3 people is formed at random. What is the probability that the committee contains at least 2 women?
A car rental company offers two pricing plans. Plan A charges $40 per day plus $0.25 per mile. Plan B charges $25 per day plus $0.40 per mile. For what daily mileage would both plans cost the same amount?
If $x\neq 3,-3$ , the product $\dfrac{x^{2}-9}{x^{2}-6x+9}\cdot\dfrac{x-3}{x+3}$ is equal to
For how many positive integers $n\le 100$ does $\operatorname{lcm}(n,15)=60$ ?
Bartender A has 15% alcohol punch, and Bartender B has 35% alcohol punch. They will combine the two to make 10 liters of a punch that is exactly 25% alcohol. How many liters must Bartender A contribute?
A motorboat travels 30 miles upstream and then returns to its starting point. The boat's speed in still water is 12 mph, and the river's current is 3 mph. What is the total time, in hours and minutes, required for the round trip?
A company's profit $P$ (in thousands of dollars) is given by $P = 3n - 12$ , where $n$ is the number of units sold (in hundreds). If the company needs a profit of at least $18,000 and can sell at most 1,500 units, what is the range of units they can sell?
The price of an item is reduced by 30%, then increased by 40%, then reduced by 25%. What is the overall percentage change in price?
What is the value of $\dfrac{16^{3/4}}{2^{1/2}}$ ?

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