McGraw-Hill Education 8 GRE Practice Tests by Kathy A. Zahler

Author:Kathy A. Zahler
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2018-05-25T04:00:00+00:00

Section 6. Quantitative Reasoning

1. C. Quantity A is and Quantity B is .

2. B. Quantity A is −9 and Quantity B is (−3)(−3) = 9.

3. B. The number 351 can be divided by 9 because its digits sum to 3 + 5 + 1 = 9. When divided, 351 ÷ 9 = 39. This makes it easy to see that the prime factorization of 351 is 3 × 3 × 3 × 13, so Quantity A is 13. Similarly, 42 factors into 2 × 3 × 7 and 140 factors into 2 × 2 × 5 × 7, so their greatest common factor is 2 × 7 = 14. Thus Quantity B is 14, larger than 13, Quantity A.

4. D. It cannot be ruled out that all members of the math club play basketball, in which case the two together would total 90. It would also be possible for the two teams to be disjoint, in which case their total would be 90 + 65 = 155.

5. A. Quantity A is (x − 1)(x + 1) = x2 − 1 and Quantity B is (x + 3)(x − 3) = x2 − 9, so Quantity B will always be 8 units less than Quantity A.

6. D. It is possible for x = 0, because |0| < 1, in which case quantities A and B will both equal 0. However, if , which also satisfies , then Quantity A is , while Quantity B is . Thus it is impossible to say which quantity is larger.

7. C. Because , the vertical distance between these two lines is always the same, and thus the heights of the two triangles are equal. Both triangles have the same base . With the same heights and bases, the triangle areas are equal.

8. B. If you solve 4x − y = 7 for y, you obtain y = 4x − 7. When you substitute this in for y in 2x + 2y = 4, you obtain 2x + 2(4x −7) = 4, which simplifies to 10x = 18, so . Thus Quantity B is bigger than Quantity A.

9. D. In a case like M = N = 0, the quantities are equal. In a case like M = N = 1, we have |M − N| = 0 and M + N = 2. Thus the relationship cannot be determined.

10. B. The trick is to factor all the numbers into primes: 2, 3, 2 × 2, 5, 2 × 3, 7, 2 × 2 × 2, 3 × 3, 2 × 5. The smallest multiple will need to have enough copies of each prime to cover all of these: 2 × 2 × 2 × 3 × 3 × 5 × 7 = 2,520.

11. C, E. The numbers between and include 0.424 and 0.519, but 0.525 is too big and both 0.411 and 0.409 are too small.

12. E. The internal angle of a regular polygon with n sides is , so when n = 3 the

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