Grid-in Solution- Math:

The question asks for a 2-permutation of 5 colors. In other words, one region can receive any of 5 colors and the other region can receive any of 4 colors, since the colors must be distinct. Therefore, the coloring can be done in 5×4=20 ways.

Sentence Correction Solution- Writing:

The error is D) “most.” In this scenario, only two things- the Beatles album and the Rolling Stones album- are being compared. Therefore, the word “more” should be used. The word “most” can only be used in reference to three or more things that are being compared.

Multiple Choice Solution- Math:

Note that the sum of consecutive integers from -20 to 20 is 0. Also note that 21+22+23=66. Therefore, the sum of consecutive integers from -20 to 23 is 66. Therefore, n=23.

The operative word in the sentence is yearned, for it shows that the high school senior was eagerly awaiting the dance. Eliminate all choices that have negative or neutral connotations: asperity (bitterness), consternation (dismay), and indifference (apathy). Tenacity denotes determination, which does not fit in the given context. The answer is D) alacrity, meaning eagerness.

Sentence Correction Solution- Writing:

The error in the sentence occurs at C (“they”). “They” is intended to refer to the antecedent “school board.” However, since “school board” is singular, the word “it” should be used instead. This error is commonly featured on the SAT and is often easily overlooked because the school board consists of several members; since the board itself is mentioned, though, the plural pronoun should not be used.

Multiple Choice Solution- Math:

The correct answer is D) 17.

In this type of problem, it is unnecessary to solve for x and y. Instead, expand (x+y)2 = x2+2xy+y2=x2+y2+2xy=11+2(3)=17.

Multiple Choice Solution- Math:

The correct answer is C) 5.

This type of remainder problem is common on the SAT. Once you develop a viable way of solving it, you will know how to do every type of remainder problem! Here is one method:

We know that when k is divided by 7, the remainder is 4. We can thus express k as the following: k = 7m + 4, where m is an integer. Since we want to know the remainder when k2 + 3 is divided by 7, we must first express k2 + 3 in terms of m. We square both sides of the equation and add 3. Therefore, k2 + 3 = (7m+4)2 + 3 = 49m2 + 56m + 19. Given that we are dividing this quantity by 7, we must manipulate the expression into the form 7q + r, where q is the number of times 7  fully divides the expression and r is the remainder. We rewrite the expression 49m2 + 56m + 19 as 49m2 + 56m + 14 + 5 because 14 is the greatest number less than or equal to 19 that is divisible by 7. We again rewrite the expression, this time to resemble the form 7q+r: 49m2 + 56m + 14 + 5= 7(7m2 + 8m + 2) + 5. Since r represents the remainder when the expression k2 + 3 is divided by 7, the remainder is 5.

Grid- in Solution- Math:

The correct answer is 4/7 hours.

Distance problems can be tricky on the SAT. They require you to synthesize the given information and to apply formulas that relate distance, rate, and time. Keep in mind that distance = rate x time, and that you can manipulate this equation such that rate = distance/time and time = distance/rate.

In the problem, it is crucial to recognize that the distance Mary travels to work is equal to the distance Mary travels from work, because she travels along the same route. We know that her speed on the way to work is 45 miles/hour and it takes her 15 minutes, or 1/4 hours. Plugging these values into distance = rate x time, we know that Mary’s route is (45 miles/hour) x (1/4 hours) = (45/4 miles). We can now find the amount of time it takes Mary to travel home from work because we know her speed and the distance of her route. Since time = distance/rate, the time it takes Mary to travel home is (45/4 miles)/(35 miles/hours), which equals 9/28 hours.  Since the question asks for the total distance travelled, we add the two times: 1/4 hours + 9/28 hours = 4/7 hours.

Sentence Correction Solution- Writing:

The correct answer choice is D)

The mistake occurs in the form of a misplaced modifier. Since the phrase “practicing tirelessly” modifies (describes) the proper noun “Mary,” the clause following the comma must begin with “Mary.”