GRE Math

1. Simplify:\displaystyle \frac{x^{2}y-5x^{2}y^{2}}{x^{2}y}
2. A function f(x) = –1 for all values of x. Another function g(x) = 3x for all values of x. What is g(f(x)) when x = 4?
3. 25x2 – 36y2 can be factored into:
4. If –1 < w < 1, all of the following must also be greater than –1 and less than 1 EXCEPT for which choice?
5. In the equation below, m , p, and k are non-zero numbers. What is the value of m in terms of p and k?
\displaystyle \frac{1}{m^3}-\frac{1}{k^2}=\frac{1}{p}
For the quantities below, x<y and x and y are both integers.

6. Please elect the answer that describes the relationship between the two quantities below:

Quantity A
x^5y^3 Quantity B
7. Solve the inequality 6(x−1)<7(3−x).
8. \displaystyle \small h\left ( x\right )=\frac{28}{x+4}
For which of the following values of x is the above function undefined?
9. If 4xs = v, v = ks , and sv ≠ 0, which of the following is equal to k ?
10. 3x2 – 11x = –10
Which of the following is a valid value for x?
11. Evaluate:
\displaystyle y=\frac{3^{13}-9^{5}}{\left ( \frac{1}{27} \right )^{-3}}
12. Solve for x.
13. 0.0075⋅0.0126=?
14. A five-year bond is opened with $5000 in it and an interest rate of 2.5%, compounded annually. This account is allowed to compound for five years. Which of the following most closely approximates the total amount in the account after that period of time?
15. In a four-digit positive interger \dpi{100} \small y, the thousand's digit is three times the units digit.

Quantity A
Unit's digit of y Quantity B
16. Choose the answer which best simplifies the expression below:
\displaystyle \frac{2a}{14-y} - \frac{3}{8 +a}
17. x and y are non-zero integers.

Quantity A: (x – y)^2
Quantity B: (x + y)^2
18. Simplify the following:
\displaystyle \sqrt{125}+\sqrt{245}+\sqrt{80}
19. Simplify:
\displaystyle \frac{\sqrt{250}}{\sqrt{10}}
20. The number of people in group B who own a minivan is how much greater or less than the number of people in group A who own a minivan?
21. Find the square root of the following decimal:
\displaystyle \small \sqrt{0.004}
22. Let Z represent a sequence of numbers (z1,z2,z3,z4,...,zn) wherein each term is defined as seven less than three times the preceding term. If z3+z5=142, what is the first term in the sequence?
23. Evaluate.
\displaystyle \frac{\frac{0.48}{3}}{5}
24. Mohammed is being treated to ice cream for his birthday, and he's allowed to build a three-scoop sundae from any of the thirty-one available flavors, with the only condition being that each of these flavors be unique. He's also allowed to pick 2 different toppings of the available 10, although he's already decided well in advance that one of them is going to be peanut butter cup pieces. Knowing these details, how many sundae combinations are available?
25. Alice has a puppy and a kitten. The puppy weighs 4 pounds and grows at a rate of 1 pound per month. The kitten weighs 2 pounds and grows at a rate of 2 pounds per month.

Quantity A: Weight of the puppy after 8 months
Quantity B: Weight of the kitten after 7 months
26. If m and n are both odd integers, which of the following is not necessarily odd?
27. Which of the following inequalities is represented by the number line shown above?
28. Product X costs $27 to manufacture at the rate of 50 per hour. Production can only be increased in groups of 10 units per hour. For each such increase, the production cost increases 30% of its previous amount. If the output is to be doubled, for how much must each unit be sold to make at least a 25% profit?
29. In a bowl containing 10 marbles, 5 are blue and 5 are pink. If 2 marbles are picked randomly, what is the probability that the 2 marbles will not both be pink?
30. The average of four numbers is 25. The average of three of these numbers is 20.

Quantity A: The value of the fourth number
Quantity B: 35
31. What is the equation of a line that is parallel to 3x+5y=8 and passes through (10,4)?
32. A clock has two equally long hands on it, each measuring 5 inches. If the minute hand is directly on 12 and the hour hand is directly on 4, what is the distance between the two hands?
33. A circular fence around a monument has a circumference of 215 feet. What is the radius of this fence?
34. Find the area of the parallelogram shown above, excluding the interior space occupied by the blue rectangle.
35. Square PQRS is on a coordinate plane, and each side of the square is parallel to either the x-axis or y-axis. Point P has the coordinate (−2,−1) and Point R has the coordinate (3,4).

Quantity A: The area of square PQRS
Quantity B: 24
36. An equilateral triangle is inscribed into a circle of radius 10. What is the area of the triangle?
37. An isosceles triangle has an angle of 110°. Which of the following angles could also be in the triangle?
38. Quantitative Comparison

Quantity A: The area of a triangle with a height of 6 and a base of 7
Quantity B: Half the area of a trapezoid with a height of 6, a base of 6, and another base of 10
39. A cylinder with volume of \displaystyle 192\pi\:in^3 and a radius of \displaystyle 4\:in has its radius doubled. What is the volume of the new cylinder?
40. What is the surface area of her prism if it is 6 inches tall and has a diameter of 3 inches? Round to the nearest whole number.
GRE Math
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