Ohm’s Law, which can be written as IR = V, relates the current I in amperes that flows through a conductive material with resistance R ohms to the voltage V between the two ends. The power P in watts can be related to I and R by the equation I = \(\sqrt{\frac{P}{R}}\). Which of the following gives P in terms of V and R ?

Solution
Whenever there are variables in the question and in the answer choices, think Plugging In, picking numbers that ensure that I is an integer.
If P = 18 and R = 2, then I = \(\sqrt{\frac{P}{R}} = \sqrt{\frac{18}{2}} = \sqrt{9} = 3\).
Because V = IR, V = 3 × 2 = 6. Plug P = 18, R = 2, and V = 6 into the answers to see which answer works.
Choice (A) becomes 18 = \(\frac{2}{6^{2}}\).
Solve the right side of the equation to get 18 = \(\frac{2}{36}\).
This statement is not true, so eliminate (A).
Choice (B) becomes 18 = \(\frac{6}{2}\).
This statement is not true, so eliminate (B).
Choice (C) becomes 18 = \(\frac{6^{2}}{2}\).
Solve the left side of the equation to get 18 = \(\frac{36}{2}\).
This statement is true, so keep (C), but check the remaining answer just in case.
Choice (D) becomes 18 = (6^{2})(2^{3}) or 18 = 36 × 8. This statement is not true, so eliminate (D).
The correct answer is (C).
Clark’s Rule is a formula used to determine the correct dosage of adult overthecounter medicine a child can receive. The child’s weight, in pounds, is divided by 150, and the result is multiplied by the adult dose of the medicine. A mother needs to give her daughter acetaminophen, which has an adult dose of 1,000 milligrams. She does not know her daughter’s exact weight, but she knows the weight is between 75 and 90 pounds. Which of the following gives the range of correct dosage, d, in milligrams of acetaminophen the daughter could receive?

Solution
Start by calculating the least amount of acetaminophen the child needs.
If the child is 75 pounds, then the amount of acetaminophen needed can be calculated as \(\frac{75}{150} \times 1,000 = \frac{1}{2} \times 1,000 = 500\).
Since, only (B) gives 500 as the lowend value, the correct answer is (B).
In the circle with center O and radius 10 shown above, ∠AOB = \(\frac{2 \pi}{5}\). What is the length of minor arc AB ?

Solution
Use the formula arc = rθ, where r is the radius and θ is the measure of the central angle in radians.
Because the angle is already in radians, you just need to plug in 10 for the radius and the angle \(\frac{2 \pi}{5}\) into the formula.
You then get s = (10)\(\frac{2 \pi}{5}\) or 4π, which is (C).
The price of an item that cost $43 in 2010 always increases by $3 per year. The current price in dollars, P, of the item can be represented by the equation P = 3t + 10, where t is the number of years since the item was first manufactured. Which of the following best explains the meaning of the number 10 in the equation?

Solution
Use Process of Elimination to solve this question.
According to (A), the price of the item in 1999 was $10.
According to the question, the price of the item in 2010 was $43, and the price of the item increased by $3 every year.
1999 is 11 years before 2010. Therefore, the price of the item in 1999 can be calculated as 43  11(3) = 10.
Keep (A) but check the other answer choices just in case.
Eliminate (B) and (C), since these answers could not also be correct.
Eliminate (D) because the annual price increase is given as $3 in the question.
Therefore, the correct answer is (A).
Which of the following equations best describes the figure above?

Solution
The graph shown is a regular parabola that has been turned upside down and moved down 6.
The equation of a regular parabola that points upward is y = x^{2}.
Therefore, the graph of a parabola that points downwards is y = x^{2}.
Eliminate (D) because that answer is missing the negative sign.
To move a parabola down 6 units, a 6 must be subtracted from the equation of the parabola.
Eliminate (A) and (C), which add 6 instead.
Choice (B) can be rewritten as y = x^{2}  6.
The correct answer is (B).
Régine is measuring how many solutions from Batch x and Batch y are acidic. She measured a total of 100 solutions from both batches. 40% of the solutions from Batch x and 70% of the solutions from Batch y were acidic, for a total of 48 acidic solutions. Solving which of the following systems of equations yields the number of solutions in Batch x and Batch y ?

Solution
Start with the easier equation first and use Process of Elimination.
The easier equation has to do with the total number of solutions.
According to the question, Régine measures a total of 100 solutions.
This information can be expressed as x + y = 100.
Eliminate (B) and (C) because neither of these answers includes this equation.
Remember that percentage means divided by 100.
Therefore, 40% = 0.4 and 70% = 0.7.
Given this information, x should be associated with 0.4 and y should be associated with 0.7.
On this basis eliminate (D).
The correct answer is (A).
Which of the following is equivalent to the expression \(\frac{x^{3} + x^{2}}{x^{4} + x^{3}}\)?

Solution
Factor the expression to get \(\frac{x^{2}\left ( x + 1 \right )}{x^{3}\left ( x + 1 \right )}\).
Reduce the fraction to get \(\frac{x^{2}}{x^{3}} \;\; or \;\; \frac{1}{x}\).
Another way of writing ^{1}⁄_{x} is x^{1}.
Therefore, the correct answer is (D).
If f is a function and f(4) = 5, which of the following CANNOT be the definition of f ?

Solution
Since the question states f(4) = 5, then when x = 4, the result should be 5.
Plug in x = 4 into each answer choice to see which equation does NOT equal 5.
Choice (A) becomes f(4) = 4 + 1 = 5.
This works, so eliminate (A).
Choice (B) becomes f(4) = 2(4)  3 = 8  3 = 5.
Eliminate (B).
Choice (C) becomes f(4) = 3(4)  2 = 12  2 = 10.
The correct answer is (C).
A website hopes to sign up 100,000 subscribers. So far, the website has signed up an average of 500 subscribers per day for d days. Which of the following represents the number of additional subscribers, W, the website must sign up to reach its goal?

Solution
Whenever there are variables in the question and in the answers, think Plugging In.
Let d = 2. The number of subscribers the website has signed up so far can be calculated as 500(2) = 1,000.
Therefore, the website needs to sign up 100,000  1,000 = 99,000 additional subscribers.
Plug 2 in for w in the answers to see which answer equals the target number of 99,000.
Choice (A) becomes W = 500(2) = 1,000.
This doesn't match the target number, so eliminate (A).
Choice (B) becomes W = 99,500(2) = 199,000.
Eliminate (B).
Choice (C) becomes W = 100,000  500(2) = 100,000  1,000 = 99,000.
Keep (C), but check (D) just in case it also works.
Choice (D) becomes W = 100,000 + 500(2) = 100,000 + 1,000 = 101,000.
Eliminate (D).
The correct answer is (C).
Marco is ordering salt, which is only sold in 30pound bags. He currently has 75 pounds of salt, and he needs to have a minimum of 200 pounds. Which of the following inequalities shows all possible values for the number of bags, b, that Marco needs to order to meet his minimum requirement?

Solution
Because Marco already has 75 pounds of salt, he needs 200  75 = 125 additional pounds.
Estimate the number of bags he needs. 125 is close to 120, and 120 ÷ 30 = 4, so he must need more than 4 bags (because 125 is more than 120).
This means that Marco needs at least 5 more bags. Therefore, the correct answer is (B).