A proofreader can read 40 pages in one hour. How many pages can this proofreader read in 90 minutes?

Solution
Since 90 minutes is equal to 1.5 hours, a proofreader who can read 40 pages in one hour can read (1.5)(40) or 60 pages in 1.5 hours.
When n = ^{1}⁄_{4}, what is the value of \(\frac{2n − 5}{n}\)?

Solution
Which of the following expressions is a polynomial factor of a^{16} − 16?

Solution
Remember that a difference of squares factors easily, such as: a^{2} − b^{2} = (a + b)(a − b).
Using the same technique, you can factor a^{16} − 16 into (a^{8} + 4)(a^{8} − 4).
The factor (a^{8} − 4) is another difference of squares, so it can be factored further into itself: (a^{8} − 4) = (a^{4} + 2)(a^{4} − 2).
Of these factors, only (a^{4} + 2) is an answer choice
What is the product of the 2 solutions of the equation x^{2} + 3x − 21 = 0?

Solution
The easiest way to solve this problem is to remember that when two binomial expressions are multiplied, there is a predictable result.
Take the following generalized example: (x + a)(x − b) = x^{2} − bx + ax − ab. If x^{2} − bx + ax − ab = 0, then the solutions to the equation are x = −a and x = b.
The product of the solutions is −ab. With this expression, x^{2}+3x−21 = 0, the product of the solutions (−ab) is −21.
The perimeter of a square is 48 centimeters. What is its area, in square centimeters?

Solution
If a square has side x, then its perimeter is 4x; this is because a square is defined as a rectangle where all four sides are of equal length.
Since the perimeter of the square is 48, then 48 = 4x and x = \(\frac{48}{4}\) = 12.
Thus, the length of one side of the square is 12.
The area of a square is defined as (side)2; therefore the area of this square is 12^{2} or 144.
What is the 217th digit after the decimal point in the repeating decimal 0.3456?

Solution
To solve this problem, recognize that the repeating decimal has four places (0.3456), and that the fourth place is occupied by the number 6.
Therefore, every place that is a multiple of 4 will be represented by the number 6. Since 217 is not divisible by 4, you know that the 217th digit cannot be 6;
eliminate answer choice E. Because 216 is a multiple of 4, the 216th digit will be 6.
Therefore, the 217th digit must be 3, the next digit in the repeating decimal.
(n^{7})^{11} is equivalent to:

Solution
Remember that the rule for exponents states that for base number b and exponents x and y, (b^{x})^{y} = b^{xy}.
Thus, when you apply the numbers from this problem, you find that (n^{7})^{11} = n^{(7)(11)} = n^{77}.
For all x, 13 − 2(x + 5) = ?

Solution
To solve this problem, you must distribute and add like terms, as follows:
13 − 2(x + 5) =
13 − 2x − 10 = 2x + 3
For all m and n, (3m + n)(m^{2} − n) = ?

Solution
Since this problem requires you to multiply two binomials, you can utilize the FOIL (First, Outside, Inside, Last) method to multiply the expressions.
First: (3m)(m^{2}) = 3m^{3}
Outside: (3m)(−n) = −3mn
Inside: (n)(m^{2}) = m^{2}n
Last: (n)(−n) = −n^{2}
Finally, add all these terms up to come up with your final answer. (3m + n)(m^{2} − n) = 3m^{3} − 3mn + m^{2}n − n^{2}.
What is the value of 5 − a if a = 9?

Solution
The absolute value of a number is its distance from zero, regardless of whether it is positive or negative.
Therefore, the value of 5 − 9=− 4 = 4.