GRE Quantitative Reasoning Practice Questions
Answer Key
1. E. To solve this problem, first determine through trial and error the number that equals 16 when taken to the 4th power (in other words, when multiplied by itself four times). The number is 2. Then square 4.
2. D. The rate of gas use and the time it will last exist in an inverse relationship. If Arnold uses 3/2 as much gas, he will go through it in 2/3 the time. Multiply 2/3 by 30 to find the solution.
3. B. Solve both of the inequalities for x, thus determining that 16 > x >12.
4. A. Dan travels 40 miles in an hour, and he needs to go half this distance to reach Cheryl's house (that is, he has traveled two-thirds of the way and needs to travel one more third). Divide 40 by 2 to determine a third of the total distance, and then add this to the distance traveled so far: 40 + 20 = 60.
5. D. The problem requires an understanding of absolute value, the distance from zero on a number line. For instance, the absolute value of -5 is 5.
6. C. The volume of a cube is the length of one side taken to the third power. In order to solve this problem, find the cube root of 343 through trial and error.
7. A. To solve for x, first add x to both sides of the equation. Then add 6 to both sides and divide each side by 4.
8. E. To factor a polynomial of this kind, find the set of numbers that have a sum equal to the coefficient of the second term and a product equal to the coefficient of the third term. In this case, -6 and 3 have a sum of -3 and a product of -18.
9. D. Each team plays 45 games (9 other teams multiplied by 5 games against each). Multiply 45 by the number of teams, and then divide by 2 since each game includes two teams.
10. B. Simply substitute 2 into the equation and solve. Cube the two in parentheses before squaring.
11. A. The number in the hundredths place of Column A is larger, so it is a greater number even though the numbers in the thousandths, ten-thousandths, and hundred-thousandths places are smaller.
12. D. It is impossible to tell which value is larger without knowing the value of x. There are possible values for x that make either column larger.
13. A. This problem can be easily solved by remembering that multiplying 3/4 by itself is the same as finding 3/4 of 3/4, which will necessarily be a smaller number. If this is not apparent, however, the problem can be easily solved by solving the problems: 3/4 + 3/4 = 6/4 = 1 1/2 and 3/4 x 3/4 = 9/16.
14. B. Since the value of the digit x must be twice the value of the digit y, y can only be 4, 3, 2, or 1.
15. C. There is a 5 in 15 chance of selecting a green marble. This is equivalent to a 1 in 3 chance.