The populations and areas of five countries are shown in the graphs above. If population density is defined as \(\frac{population}{area}\), which of the five countries has the highest population density?

Solution
The top graph is of the countries' populations, and the bottom graph is of the countries' areas. Find the population density, \(\frac{population}{area}\), for each country by taking its number from the top graph and dividing that by its number from the bottom graph:
Ecuador = \(\frac{10}{0.3}\), which equals 33.33
Uruguay = \(\frac{2.5}{0.2}\), which equals 12.5
Venezuela = \(\frac{20}{1.0}\), which equals 20
Chile = \(\frac{15}{0.8}\), which equals 18.75
The highest value among the countries is that of Ecuador, which is (A).
Steve ran a 12mile race at an average speed of 8 miles per hour. If Adam ran the same race at an average speed of 6 miles per hour, how many minutes longer did Adam take to complete the race than did Steve?

Solution
Use the rate pie to calculate the time for each runner. Steve runs 12 miles at 8 miles per hour, so his pie looks like this:
To find his time, divide his distance by his rate, which means that he runs for 1^{1}⁄_{2} hours (or 1.5 if you're using your calculator). Adam runs the same 12 miles at 6 miles per hour, so this is his rate pie:
This means that Adam runs for 2 hours.
Adam takes half an hour longer to complete the race, and half an hour is 30 minutes: (D).
A lapping slurry contains microbeads suspended in a solution and is used to polish a silicon wafer by abrasion of the surface. The distribution of the particle size, in micrometers, is shown above. If the particle size distribution ranges were changed to 020 micrometers and 2140 micrometers, which of the following is the closest to the ratio of the number of 020 micrometer microbeads to the number of 2140 micrometer microbeads?

Solution
In the new groupings, 79% of the particles are in the 020 micrometer grouping (33% + 46% = 79%) and 21% of the particles are in the 2140 micrometer grouping (16% + 5%) = 21%.
That is a ratio of 79:21.
Because the question is asking for the closest ratio, round the numbers to get a ratio of 80:20, or 4:1.
The correct answer is (B).
20 – 2x
20 – x
20
20 + x
20 + 2x
What is the average (arithmetic mean) of the list of numbers above?

Solution
Variables in the answers? Plug in! Make up a value for x.
Let's say that x is 3. The list of numbers then becomes 20  2(3), 20  3, 20, 20 + 3, 20 + 2(3), so the list is 14, 17, 20, 23, and 26.
To find the average, make an average pie:
We know the number of things (5) and the total (14 + 17 + 20 + 23 + 26 = 100), so the average is 100 ÷ 5 = 20, which is (A).
There are k gallons of gasoline available to fill a tank. After d gallons have been pumped, in terms of k and d, what percent of the gasoline has been pumped?

Solution
Variables in the answer choices? Plug in! This is a percent question, so make k = 100 and d = 40.
If 40 out of the 100 gallons have been pumped, that equals 40%.
So 40% is your target answer.
When you plug k = 100 and d = 40 into the answers, only (A) gives you 40.
Plugging In turns a hard question into a much easier question.
A gas station sells regular gasoline for $2.39 per gallon and premium gasoline for $2.79 per gallon. If the gas station sold a total of 550 gallons of both types of gasoline in one day for a total of $1,344.50, how many gallons of premium gasoline were sold?

Solution
When asked for a specific value, try Plugging In the Answers.
Label them as gallons of premium and start with the value in (B).
If 75 gallons of premium were sold, the station would make 75($2.79) = $209.25 for those sales.
A total of 550 gallons was sold, so the station would have sold 550  75 = 475 gallons of regular gasoline.
The sales for the regular gasoline would be 475($2.39) = $1,135.25.
The total sales for both types of gasoline would be $209.25 + $1,135.25 = $1,344.50.
That matches the information in the question, so (B) is correct.
If c = ^{1}⁄_{x} + ^{1}⁄_{y} and x > y > 0, then which of the following is equal to ^{1}⁄_{c}?

Solution
Here's yet another chance to plug in because of the variables in the answer choices.
In this case, you have several variables.
You should start by plugging in values for x and y, and then work out c.
Because x > y > 0, let's say x = 6 and y = 3. Therefore, c = ^{1}⁄_{3} + ^{1}⁄_{3} = ^{1}⁄_{3} + ^{2}⁄_{6} = ^{3}⁄_{6} = ^{1}⁄_{2}.
The question asks for the value of, which is the reciprocal of, or 2.
This is your target answer.
If you plug x = 6 and y = 3 into all of the answer choices, you'll find that only (D) equals 2.
If a is 63% of x and c is ^{3}⁄_{8} of x, which of the following is the closest equivalent of the ratio of a to c ?

Solution
Since you are never told what x is, and there is no way to find it, plug in for x.
Say that x = 100. 63% of 100 is 63, and ^{3}⁄_{8} of 100 is 37.5.
The ratio of a to c is ^{a}⁄_{c}. So, ^{63}⁄_{37.5} = 1.68.
To save time, you can ballpark the answer, since a > c and (D) is the only choice greater than 1.
Nails are sold in 8ounce and 20ounce boxes. If 50 boxes of nails were sold and the total weight of the nails sold was less than 600 ounces, what is the greatest possible number of 20ounce boxes that could have been sold?

Solution
This is a perfect question for PITA. The question asks for the greatest possible number of 20ounce boxes.
Start with (B).
If there are twentyfive 20ounce boxes, then there are twentyfive 8ounce boxes because a total of 50 boxes was purchased.
In this case, the twentyfive 20ounce boxes weigh 500 ounces, and the twentyfive 8ounce boxes weigh 200 ounces; the total is 700 ounces.
This is too big because the question says the total weight was less than 600.
If (B) is too big, (A) must also be too big; eliminate both answers.
If you try (C), the total weight is 604 ounces, which is still too big.
So the answer must be (D).
If Alex can fold 12 napkins in x minutes, how many napkins can he fold in y hours?

Solution
Two variables tells you this is a great place to plug in.
Let's pick numbers that make the math easy. You can try x = 30 and y = 2.
So in 2 hours there are 4 periods of 30 minutes each: 12 × 4 = 48.
Alex can fold 48 napkins in 2 hours. 48 is your target.
Plugging into your answer choices gives you (C) as the only correct answer.