GRE Mathematics 1

1. If $x(y+z) = w$ and $x$, $y$, $z$ and $w$ are all integers, which of the following must be true?

2. A salesperson works 50 weeks each year and makes an average of 100 sales per week. If each sale is worth an average of $1000, then what is the total value of sales made by the salesperson in a year?

3. If $x$ is an even integer and $y$ is an odd integer, then which of the following is an even integer?

4. If $x^3 <x^2<x$ then the value of $x$ could be

5. If $n-5$ is an even integer, what is the next larger consecutive even integer?

6. If $2x + 3y = 8$, and $y = 2x$ then what is the value of $x$?

7. Which of the following numbers does NOT satisfy the inequality $5x – 2 < 3x – 1$?

8. $ 5^2 + 12 ^2 = ?$

9. If the areas of the three different sized faces of a rectangular solid are 6, 8, and 12, then what is the volume of the solid?

10. If $pq \ne 0$ and $p=\frac{1}{3}q$, then the ratio of $p$ to $3q$ is

11. When 20 is subtracted from $-4$ the result is

12. Ali paid $48 for a jacket that was on sale for 25% of the original price. What was the original price of the jacket?

13. If a certain chemical costs $50 for 30 gallons, then how many gallons of the chemical can be purchased for $625?

14. Usman left home with $60 in his wallet. He spent $\frac{1}{3}$ of that amount at the supermarket, and he spent $\frac{1}{2}$ of what remained at the drugstore. If Usman made no other expenditures, how much money did he have when he returned back home?

15. If the square root of $x$ is greater than $x$ then $x$ could be

16. If $x=1$ and $y=-2$, then $\frac{x^2 – xy}{y}=$?

17. If $x$ and $y$ are both odd integers which of the following MUSt also be an odd integer?

18. Which of the following can be expressed as the sum of three consecutive integers?