Chapter 17
After taking Practice Exam 1 in Chapter 16, use this chapter to check your answers and see how you did. Carefully review the explanations because doing so can help you understand why you missed the questions you did and also give you a better understanding of the thought process that helped you select the correct answers. If you’re in a hurry, flip to the end of the chapter for an abbreviated answer key.
Have a friend read your essays: Refer that helpful person to Chapters 14 and 15 for scoring guidelines, and if the essays are clear, persuasive, and grammatically sound, you probably got it.
B, D, I. The second sentence references a democracy in early development, so it must be a nascent (emerging) democracy that would need to be built on certain precepts (principles or guidelines) in order to be strong. Otherwise, the government would be prone (disposed to) to evolving into a dictatorship.
For the first blank, you can rule out well-established, which is the opposite of nascent, and representative, which is just a type of democracy (direct or representative). For the second blank, both criteria and precedents would be good second choices, but because the second sentence mentions the right to vote and the rule of law, precepts is more accurate. For the third blank, you can rule out dedicated, because no democracy dedicates itself to becoming a dictatorship. You can rule out resolute (determined) for much the same reason.
C. You find the probability of an event (selecting one grape candy from the first bowl) by putting the number of possibilities (three grape candies) over the total number of outcomes (five candies total). Thus, the probability of selecting a grape candy from the first bowl is . Similarly, the probability of selecting a grape candy from the second bowl is .
The probability of two independent events occurring together (selecting a grape candy each from the first and second bowls) is the product of the first probability and the second probability:
5. The units digit is the digit in the ones place, just before where the decimal point would be. For example, in the number 123, the units digit is 3. When you’re multiplying two whole numbers, the units digits of the multipliers produce the units digit of the product. So when you multiply , for example, the 2 in 12 times the 3 in 13 produces the 6 in the product, 156.
For this question, 5 times itself any number of times results in a product with a units digit of 5:
and so on.
Quantity A is 7 pounds, which is 1 pound less than Quantity B’s 8 pounds, so Quantity B is greater.
To divide the fractions, flip the bottom fraction and multiply it by the top fraction:
You simplify the resulting fraction with the on-screen calculator; is slightly greater than 0.1, so Quantity A is greater.
and B reads
These products are still too big for the on-screen calculator. To resolve this, eliminate one 999 from each quantity so that A reads
and B reads
Using the on-screen calculator, find the resulting values as 998,000 and 998,001. You see that Quantity B is greater.
A circle with a radius of 5 has a circumference of . Multiply this circumference by the fraction of the circle, giving you a minor arc length of . Therefore, the two values are equal.
where represents one base, represents the other base, and h represents the height. To find the height, set the formula equal to the area and simplify it:
Therefore, the two quantities are equal.
You can’t type the percent symbol into the answer box. Because the percent symbol is already in place and the question asks for the percent, the correct answer is 24, not 0.24.
D. Though actual numbers aren’t provided, you can use the bar graph to approximate the ratios. Because the question asks for an “approximate” answer and the answer choices are far apart, you can eyeball your numbers from the graphs.
Lucky Shapes and Sugar Choc show similar numbers of units sold, but the Lucky Shapes sales number in Glenn County, at $9,000, is about one third that of Sugar Choc in Trinity County, at $27,000. This means, box for box, the price of Lucky Shapes is approximately one third that of Sugar Choc, for a ratio of 1:3.
Now reduce the fraction by subtracting the exponents:
C. First, identify the unknown. You know that you end up with 15 liters of a solution, but you don’t know what its saline concentration is, so you have 15 liters of x.
Ten liters of 6 percent solution plus 5 liters of 9 percent solution gives you 15 liters of x, so set up the equation and simplify:
C. Factor the into . The lowest possible value of y is 3, because in order for the square root of 48y to be an integer, the factors inside the square root must form numbers squared — you have one , and you need to multiply it by another to square it.
You could also plug in the answer choices, starting with the lowest value and working your way up: , which isn’t an integer. , which isn’t an integer. , which is an integer. Factoring is faster though.
A, C, D, E. , so n could be any product of 2, 3, 5, and 7, as long as any factor is used only once. 12 is wrong, because it uses the factor 2 twice.
You could also solve this one by plugging in answer choices, but that’s a lot of math.
Therefore, or –5, but you don’t know which one, so Quantity A could be either equal to or less than Quantity B. Because you don’t know, go with Choice (D).
Each time you multiply 0.99 by itself, the quantity becomes smaller and remains less than 1.
C. From the bar chart, about of the grades are B grades, so about are the other grades. De Beque has 115 students, and the only answer choice that’s about of that is 70.
An approximate estimate is usually good enough for these questions. The answer 70 isn’t really close to the other answers, so if you eyeball the graph differently, you’ll still get the right answer.
A, C. The range is the difference between the lowest and highest numbers. If the range of set S is 9 and none of the given numbers are 9 apart, x has to be either 0 or 11.
The median is the middle number of the set. If x is 0, the median is 5; if x is 11, the median is 7.
0. The correct answer is 0.
The trap here is doing a lot of extra math work. Drop the parentheses to avoid this trap:
Now give the fractions common denominators of either 8 or 10:
The , , and add up to 1, and the , , and add up to –1. The sum, therefore, equals 0.
Note that there are other ways to simplify the fractions. On the GRE, especially with fractions, you’re looking for ways to cancel and simplify.
36. The correct answer is 36.
Combine into , which equals 36.
the value x cannot be equal to 5 or –5. It’s greater than –5 and less than 5, so from the list of answer choices, x could be equal to –3, 0, or 3.
For the area of the circle, you need its radius. Cut the square in half, corner to corner, to form two 45-45-90 triangles, where each hypotenuse is the diameter of the circle. If the side of this triangle is , the hypotenuse is 2, because in a right triangle, the square of the hypotenuse is the sum of the squares of the other two sides:
, so is the circumference of the circle, and the radius of the circle is half the diameter, or 1. Now for the area of the circle:
Subtract the area of the square from the area of the circle for your answer:
Section 1: Verbal Reasoning
Section 2: Quantitative Reasoning
Section 3: Verbal Reasoning
Section 4: Quantitative Reasoning