Practice Test 3 - GMAT Quantitative

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

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1. If $\frac{1}{1+x} + \frac{1}{1-x} = \frac{k}{1-x^2}$ for all valid values of $x$, then $k$ equals:
2. If $a = \frac{2x}{x-1}$ and $b = \frac{x+1}{x-1}$, then $\frac{a-b}{a+b}$ equals:
3. Two positive integers have product $720$ and greatest common factor $12$. What is their least common multiple?
4. How many integers $n$ satisfy $-20<n<5$ and $|n+3|\ge10$?
5. The function $k(x) = \begin{cases} x^2 & \text{if } x \leq 1 \\ 2x - 1 & \text{if } x > 1 \end{cases}$ is defined piecewise. What is $k(k(0.5))$?
6. A factory produces widgets in batches of 84, 90, and 126 units. What is the minimum number of widgets that must be produced to have complete batches of each type with no widgets left over?
7. If $(x-3)(x+2)=5$, what is the sum of all real solutions for $x$?
8. The expression $x^2 + bx + c$ can be factored as $(x + p)(x + q)$ where $p$ and $q$ are integers. If $b = -5$ and $c > 0$, how many possible values of $c$ are there?
9. If $\operatorname{lcm}(20,t)=100$, what is the sum of all distinct positive integers $t$ that satisfy the equation?
10. A rectangular floor can be completely tiled using square tiles of side length 15 cm, 20 cm, or 25 cm with no cutting required. What is the minimum possible area of the floor in square meters?
11. Train B leaves Central Station at 1:00 p.m. traveling 75 km/h toward Easton. Train A leaves the same station on the same track at 1:30 p.m. traveling 90 km/h toward Easton. At what time after Train A departs will Train A overtake Train B?
12. If $f(x) = x^2 + 2x - 3$ and $g(x) = x^2 - 4x + 3$, for how many values of $x$ does $f(x) = g(x)$?
13. If $\left(9^{x}\right)^{1/2}\,\times\,\left(27^{x}\right)^{1/3}=3^{10}$, what is the value of $x$?
14. An investment account loses 12% of its value in Year 1, gains 15% in Year 2, and loses 8% in Year 3. If the account has $11,628 at the end of Year 3, what was the initial investment amount?
15. 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?
16. In the system $3x + 2y = k$ and $6x + 4y = 2k + 3$, for which value of $k$ does the system have no solution?
17. Dataset P has 20 values with a mean of 50 and standard deviation of 8. Dataset Q has 30 values with a mean of 60 and standard deviation of 6. If one outlier with value 120 is added to Dataset P, and the new standard deviation becomes approximately 12, what can be concluded about the relative variability of the modified Dataset P compared to Dataset Q?
18. Events $A$ and $B$ satisfy $P(A)=0.4$, $P(B)=0.5$, and $P(A\cup B)=0.7$. What is the probability that neither $A$ nor $B$ occurs?
19. A pallet can be filled either by Conveyor A alone in 9 minutes or by Conveyor B alone in 15 minutes. The conveyors run together for 4 minutes, after which Conveyor A stops. How many additional minutes must Conveyor B run by itself to finish filling the pallet?
20. A swimming pool that holds 12{,}000 gallons is half full. Pipe A can fill the entire pool in 6 hours, whereas drain B can empty a full pool in 9 hours. If both pipe A and drain B are opened at the same time, how many hours will it take for the pool to become completely full?

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