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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 = tAB + tBA = dAB/(15 miles/hour) + dAB/(10 miles/hour) = dAB/(6 miles/hour).
dAB = (6 miles/hour) &#183 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 a2 + 3 is divisible by 7, which of the following values can be a?
(a) 7
(b) 8
(c) 9
(d) 11
(e) 4
Answer: 72 + 3 = 52 = 2 · 2 · 13
82 + 3 = 67
92 + 3 = 84 = 2 · 2 · 3 · 7
112 + 3 = 124 = 2 · 2 · 31
42 + 3 = 17
The correct answer is a = 9

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