Gre math Review 1 Arithmetic

Arithmetic Exercises

1. Evaluate the following.

a.   15 minus the quantity, open parenthesis, 6 minus 4, close parenthesis, times negative 2
b.   open parenthesis 2 minus 17, close parenthesis, divided by 5
c.  open parenthesis, 60 divided by 12, close parenthesis, minus, open parenthesis, negative 7 + 4, close parenthesis
d.   open parenthesis, 3, close parenthesis, to the fourth power, minus, open parenthesis negative 2, close parenthesis, to the third power
e.  the quantity, negative 5 times negative 3, minus 15
f.   open parenthesis, negative 2, close parenthesis, to the fourth power, times open parenthesis, 15 minus 18, close parenthesis, to the fourth power
g.   open parenthesis, 20 divided by 5 , close parenthesis, squared times, open parenthesis, negative 2 + 6, close parenthesis, cubed
h.   negative 85 times 0, minus negative 17 times 3

2. Evaluate the following.

a.   1 half minus 1 third + 1 twelfth
b.   open parenthesis, 3 fourths + 1 seventh, close parenthesis, times, open parenthesis, negative 2 over 5, close parenthesis
c.  open parenthesis, 7 over 8, minus 4 over 5, close parenthesis, squared
d.   open parenthesis, 3 over negative 8, close parenthesis, divided by, open parenthesis, 27 over 32

3. Which of the integers 312, 98, 112, and 144 are divisible by 8 ?

4.
a. What is the prime factorization of 372 ?
b. What are the positive divisors of 372 ?

5.
a. What are the prime divisors of 100 ?

b. What are the prime divisors of 144 ?

6. Which of the integers 2, 9, 19, 29, 30, 37, 45, 49, 51, 83, 90, and 91 are prime numbers?

7. What is the prime factorization of 585 ?

8. Which of the following statements are true?

a.   negative 5 is less than 3.1
b.   the positive square root of 16 = 4
c.   7 divided by 0 = 0
d.   0 is less than the absolute value of the negative of the fraction 1 over 7
e.   0.3 is less than 1 third
f.   open parenthesis, negative 1, close parenthesis, to the power 87 = negative 1
g.   the positive square root of the quantity, open parenthesis, negative 3, close parenthesis, squared, is less than 0
h.   21 over 28 = 3 over 4
i.  the negative of the absolute value of negative 23 = 23
j.   1 half is greater than 1 over 17
k.   59 cubed, times 59 squared = 59 to the power 6
l.  the negative square root of 25 is less than negative 4

9. Find the following.

a. 40% of 15
b. 150% of 48
c. 0.6% of 800
d. 15 is 30% of which number?
e. 11 is what percent of 55 ?

10. If a person’s salary increased from $200 per week to $234 per week, what was the percent increase in the person’s salary?

11. If an athlete’s weight decreased from 160 pounds to 152 pounds, what was the percent decrease in the athlete’s weight?

12. A particular stock is valued at $40 per share. If the value increases by 20 percent and then decreases by 25 percent, what will be the value of the stock per share after the decrease?

13. If the ratio of the number of men to the number of women on a committee of 20 members is 3 to 2, how many members of the committee are women?

14. The integer a is even and the integer b is odd. For each of the following integers, indicate whether the integer is even or odd.

a. a + 2b
b. 2a + b
c. a b
d.  a to the power b
e.   open parenthesis, a + b, close parenthesis, squared
f.   a squared, minus, b squared
15. When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. What is the least possible value of n ?