## Numbers and Operations Review

**Percent** means a number out of 100. For example, 10% means 1/10 or .1.

**Example of SAT question with percent:** What is the sum of 10% of x and 20% of 2x?

(a) 10% of x

(b) 20% of x

(c) 30% of x

(d) 50% of x

(e) 100% of x

Answer: 10% of x is .1x

20% of 2·x = .2·2·x = .4·x

The sum of 10% of x and 20% of 2·x is .1·x + .4·x = .5·x. In conclusion the sum is 50% of x.**Speed, Distance, Time Questions**

**Example of SAT question:** A cyclist bikes from town A to town B and back to town B in 3 hours. From A to B he bikes at a speed of 15 miles/hour while the return speed is 10 miles/hour. What is the distance between the 2 towns?

(a) 18 miles

(b) 15 miles

(c) 12 miles

(d) 10 miles

(e) 11 miles

Answer: The total time t = t_{AB} + t_{BA} = d_{AB}/(15 miles/hour) + d_{AB}/(10 miles/hour) = d_{AB}/(6 miles/hour).

d_{AB} = (6 miles/hour) · 3 hours = 18 miles. (a) is the correct answer.

**Integers**: . . . , –3, –2, –1, 0, 1, 2, 3, . . .

**Consecutive integers** are integers that follow in sequence; for example, 5, 6, 7.

**Odd integers **are integers that can be writen as 2n + 1, where n is an integer.

**Even integers** are integers that can be writen as 2n, where n is an integer.

**Example of SAT question with integers:** If a^{2} + 3 is divisible by 7, which of the following values can be a?

(a) 7

(b) 8

(c) 9

(d) 11

(e) 4

Answer: 7^{2} + 3 = 52 = 2 · 2 · 13

8^{2} + 3 = 67

9^{2} + 3 = 84 = 2 · 2 · 3 · **7**

11^{2} + 3 = 124 = 2 · 2 · 31

4^{2} + 3 = 17

The correct answer is a = 9

Test your SAT knowledge with our multiple choice tests.