Practice Test 7 - GMAT Quantitative

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

Machine X can produce 120 parts per hour. Machine Y can produce 80 parts per hour. Machine X works alone for exactly 2 hours and then breaks down; immediately, Machine Y is started and runs at its usual rate until a total of 760 parts have been produced. For how many hours does Machine Y run?
The greatest common factor of integers $p$ and $q$ is $18$ and $q=162$ . Which of the following cannot be the least common multiple of $p$ and $q$ ?
A quality inspector measures the diameter of ball bearings from Machine 1 and finds a standard deviation of 0.05 mm. When Machine 2 is introduced, producing bearings with a standard deviation of 0.03 mm, the supervisor concludes that Machine 2 is superior. However, Machine 1 produces bearings with diameters averaging 10.00 mm (target), while Machine 2 produces bearings averaging 9.97 mm. How should the relative quality of these machines be evaluated?
If $2x^{2}-7x-4=0$ , what is the smaller of the two real solutions?
Refer to the diagram. If exactly 100 students are represented in total, how many belong to all three study groups?
Positive numbers $r, s, t$ satisfy $r^{2}=s^{3}=t^{5}=k$ . Which of the following is equal to $k^{\,1/30}$ ?
A certain bacterial culture doubles every 3 hours. If the culture contains $N$ bacteria after 9 hours, how many bacteria will it contain after 15 hours?
An investment firm manages two portfolios with different average annual returns: Portfolio A averages 8% annually, while Portfolio B averages 12% annually. At the beginning of the year, the firm had a total of $2,000,000 invested across both portfolios. During the year, they transferred$ 200,000 from Portfolio A to Portfolio B. At year-end, the weighted average return across all investments was 9.6%. What was the initial amount invested in Portfolio A?
Which of the following equals $\sqrt[4]{32}$ ?
For which of the following values of $k$ does the equation $x^{2}-kx+16=0$ have no real solutions?
A box contains 10 balls: 4 red, 3 green, and 3 yellow. If 3 balls are drawn simultaneously, what is the probability that no two balls have the same color? Give your answer in simplest form.
A delivery service charges a base fee of $5 plus $0.75 per mile for the first $20$ miles, and $0.50 per mile for each additional mile beyond $20$ miles. If a customer's total bill was $23, how many miles was the delivery?
Refer to the pie chart below. Approximately what percent of households own at least one of the two vehicle types?
If $f(x) = \sqrt{x + 5}$ and the domain of $f$ is restricted so that $f$ has an inverse function, what is $f^{-1}(3)$ ?
If $a > 0$ and $|x - a| + |x + a| \leq 6a$ , what is the length of the interval of all possible values of $x$ ?
A bag contains 4 red balls, 6 blue balls, and 5 green balls. Three balls are drawn without replacement. What is the probability that all three balls are different colors? Give your answer in simplest form.
If real numbers $a$ and $b$ satisfy $|a-2|=|b+3|$ and $a+b=2,$ what is $|a-b|\ ?$
Among 300 students surveyed about their extracurricular activities, 180 participate in sports, 150 participate in clubs, and 120 participate in volunteer work. The number of students participating in exactly one activity is 150, and 30 students participate in all three activities. How many students participate in exactly two activities?
What is the smallest positive integer that leaves a remainder of $2$ when divided by each of $5$ , $9$ , and $12$ ?
If $m$ and $n$ are positive integers such that $\gcd(m,n) = 1$ and $m^2 + n^2$ is divisible by $mn$ , what is the smallest possible value of $m + n$ ?

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