Justin owns 6 different dress shirts, 3 different pairs of pants, and 5 different ties. How many distinct outfits, each consisting of a shirt, a pair of pants, and a tie, can Justin make?

Solution
To find the number of distinct outfits that Justin can make from 6 different dress shirts, 3 different pairs of pants, and 5 different ties, multiply the numbers of the three different components together. Thus there are (6)(3)(5), or 90 distinct outfits that Justin can make.
If g is an integer, which of the following could NOT equal g_{2} ?

Solution
To solve this problem, you should realize that if g is an integer, √g^{2} would also be an integer. Of the answer choices, only √8 is not an integer; in fact, it is an irrational number.
What is the slope of a line that passes through the origin and the point (−6, 2) ?

Solution
To solve this problem, recall that the formula for finding the slope of a line between the two points (x_{1}, y_{1}) and (x_{2}, y_{2}) is (y_{2} − y_{1})/(x_{2} − x_{1}). Also recall that the origin lies at point (0,0). Therefore, the points are (−6,2) and (0,0). You can use either set of points as (x_{1}, x_{2}) and (y_{1}, y_{2}), as long as you use them consistently within the formula, as follows: (2 − 0)/(−6 − 0) = 2/−6 = −1/3
If g is an integer, which of the following could NOT equal g^{2} ?

Solution
To find the number of barrels of gasoline that can be produced from 3,500 barrels of crude oil when, for every 10,000 barrels of crude oil supplied the refinery can produce 6,500 barrels of gasoline, you can set up a proportion with ratios of barrels of gasoline to barrels of crude oil: \(\frac{6,500}{10,000}=\frac{barrels\: gasoline}{3,500}\) , resulting in 2,275 barrels of gasoline produced.
If b = a − 4, then (a − b)^{3} = ?

Solution
To find (a − b)^{3} given b = a − 4, you could solve the equation for a − b. By subtracting b and −4 from both sides, you get 4 = a−b. Substituting 4 for a−b in (a−b)^{3} yields (4)^{3}, or 64.
If you got stuck on this one, you could try choosing a specific value for a, such as 2. Then b = −2 and (a − b)^{3} = (2 + 2)^{3} = 4^{3}, or 64.
On a map, 1/4 inch represents 12 miles. If a road is 66 miles long, what is its length, in inches, on the map?

Solution
To solve this equation, first calculate how many 1/4inch segments there will be. Dividing 66 by 12, you can see that there will be 5.5 1/4inch segments. Thus, the road’s length in inches will be 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/8 = 1 1/4 + 1/8 = 1 3/8.
Gary has turtles, cats, and birds for pets. The number of birds he has is 4 more than the number of turtles, and the number of cats is 2 times the number of birds. Of the following, which could be the total number of Gary’s pets?

Solution
To solve this problem, realize that the number of pets that Gary has is determined through relationships between the quantities of the different types of pets: turtles (t), cats (c), and birds (b). Because the number of birds, b, is 4 more than the number of turtles, t, this can be expressed as b = t + 4. Also, since the number of cats, c, is 2 times the number of birds, this can be expressed as c = 2b. You might wish to use a table to show the numerical relationship between the numbers of each pet and the total number of pets, using the answer choices as a guideline:
According to this matrix, Gary could have a total of 20 pets, but he could not have a total of 14, 18, 22, or 26 pets.
Which of the following is a simplified form of 4x − 4y + 3x?

Solution
To find a simplified form of 4x − 4y + 3x, combine like terms (all of the x’s and all of the y’s) to get 7x − 4y. Notice that you cannot subtract 4y from 4x because the variables are different.
A partial deck of cards was found sitting out on a table. If the partial deck consists of 6 spades, 3 hearts, and 7 diamonds, what is the probability of randomly selecting a red card from this partial deck? (Note: diamonds and hearts are considered “red,” while spades and clubs are considered “black.”)

Solution
The probability that the card chosen will be red when there are 6 spades, 3 hearts, and 7 diamonds, is the number of favorable outcomes divided by the number of total outcomes. The number of favorable outcomes is 10 because there are 3 hearts and 7 diamonds, which constitute the “red” cards. The total number of outcomes is 6 + 3 + 7 = 16. Thus the probability of the card being “red” is ^{10}⁄_{16}, or ^{5}⁄_{8} when reduced.
−−16 − (−16) = ?

Solution
This question is testing your knowledge of absolute value. The absolute value of −16 is 16. Notice that you must take the negative of the absolute value, or −16. You must then add −16 to 16, which results in 0.