Practice Test 1 - GMAT Quantitative

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

If $f(x) = 2x^2 - 3x + 1$ and $g(x) = x - 2$ , what is the value of $f(g(3))$ ?
Combine and simplify: $\dfrac{3}{x}+\dfrac{2}{x+1}$ for $ $x\neq 0,-1.$
The quadratic equation $x^{2}+mx+n=0$ has integer coefficients, and one of its roots is $2+\sqrt{3}$ . Which of the following is the value of $n$ ?
Suppose $\sqrt{5+2\sqrt{6}}=\sqrt{a}+\sqrt{b}$ where $a$ and $b$ are positive integers with $a>b$ . What is the value of $a-b$ ?
Based on the stacked bar chart, what is the probability that an employee chosen at random from those who use at least one of the two software programs uses both programs?
If $n$ is a positive integer such that $n^2 + n$ is divisible by 12, what is the remainder when $n$ is divided by 6?
A company's revenue increased by 25% in the first quarter, then decreased by 20% in the second quarter. If the revenue at the end of the second quarter was $300,000, what was the revenue at the beginning of the first quarter?
For the function $h(x) = \frac{2x - 1}{x + 3}$ , what is the horizontal asymptote?
An urn contains 5 red, 4 blue, and 3 green balls. If two balls are drawn at random without replacement, what is the probability that the two balls drawn are of the same color?
A 3-digit number is formed by choosing digits from 1 through 7 without repetition. What is the probability that the number formed is even?
When $(2x-3)^{3}+(3x-2)^{3}$ is expanded and like terms are combined, what is the coefficient of $x^{2}?$
A high-capacity printer runs at 45 pages per minute but must cool for exactly 1 minute after every 5 minutes of printing. Starting from the first printing minute, how much total time is required for the machine to print exactly 2,250 pages?
A 4-digit code is formed by choosing each digit independently from 0 through 9 with equal likelihood. What is the probability that at least one digit repeats within the code?
If $\dfrac1{|z-2|}\le0.2$ and $z\neq2,$ which of the following must be true?
A pump can fill an empty storage tank in 3 hours, but two leaks are also present: Leak A can drain a full tank in 5 hours, and Leak B in 8 hours. If the pump and both leaks operate simultaneously on an empty tank, approximately how many hours will it take to fill the tank completely?
A company's 200 employees were surveyed about their language skills. The results showed that 140 speak English, 80 speak Spanish, and 60 speak French. Among these, 40 speak both English and Spanish, 30 speak both English and French, and 20 speak both Spanish and French. If the number of employees who speak all three languages is $x$ , what is the maximum possible value of $x$ such that every employee speaks at least one of these languages?
Find the integer $n$ such that $3^{n}<500<3^{n+1}$ .
For all real $x$ such that $x^{2}-6x+5\le0,$ which statement must be true?
The equation $x^4 - 5x^2 + 4 = 0$ can be solved by substitution. How many distinct real solutions does this equation have?
An electronics store sets a sticker price by marking its wholesale cost up by 40\%. During a sale, the store gives a 15\% discount off the sticker price. If after the discount the store makes a profit of $51 on a tablet, what was the wholesale cost of the tablet?

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