Practice Test 9 - GMAT Quantitative

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

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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?
2. Look at the bar chart. Which classroom's quiz scores exhibit a smaller standard deviation, and why?
3. For all real numbers $x,$ the inequality $|x|<x+2$ is equivalent to which of the following?
4. For $x\neq -2$, simplify $\dfrac{x^{3}+8}{x^{2}-2x+4}.$
5. The sum of three consecutive integers is 75. What is the least of the three integers?
6. The positive integer $N$ has the property that when $N$ is divided by 7, the quotient is $q$ and the remainder is $r$, where $q$ and $r$ are both positive. If $q + r = 10$ and $N < 100$, how many possible values are there for $N$?
7. If $\sqrt[3]{8x^{6}}=2x^{m}$ for all positive real $x$, what is the value of $m$?
8. A train traveling at 80 km/h passes a stationary train of length 200 meters in 12 seconds. What is the length of the moving train?
9. For what values of $m$ does the equation $mx^2 - (m+2)x + 2 = 0$ have exactly one solution?
10. A chemist needs 20 liters of a 30% saline solution. She has an unlimited supply of a 25% saline solution and a 40% saline solution. How many liters of the 25% solution should she use?
11. If $\dfrac{3}{x}+\dfrac{2}{x-1}=1$ and $x\neq0,1$, what is the sum of all real solutions of the equation?
12. If $x^2 - 6x + k = 0$ has two distinct real roots, and one root is twice the other root, what is the value of $k$?
13. A jeweler has $42$ red beads and $70$ blue beads. She wants to create the greatest possible number of identical bracelets, each containing the same number of red beads and the same number of blue beads, with no beads left over. How many bracelets can she make?
14. A food stand sells hot dogs for $3 each and sodas for $2 each. Yesterday the stand sold a total of 50 items and collected $128 in revenue. How many hot dogs were sold?
15. A chemistry lab has two acid solutions: Solution A contains 25% acid by volume, and Solution B contains 60% acid by volume. If 40 liters of Solution A is mixed with some amount of Solution B to create a mixture that is 45% acid, how many liters of Solution B were added?
16. Refer to the line graph. What is the range, in degrees Fahrenheit, of the daily high temperatures shown?
17. A car travels 60 miles at an average speed of $v$ mph and then another 60 miles at a speed that is 30 mph faster. If the average speed for the entire 120-mile trip is exactly 72 mph, what is $v$?
18. Which of the following equals $6y^{2}-19y+10$?
19. A store marks up items by 60% above cost, then offers a 25% discount during a sale. If the sale price of an item is $96, what was the original cost to the store?
20. If $x^2 - px + q = 0$ has roots $r$ and $s$, and $x^2 - qx + p = 0$ has roots $t$ and $u$, what is the relationship between $r + s + t + u$ and $p + q$?

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