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GRADUATE RECORD EXAMINATIONS®

Official G R E Quantitative Reasoning

Practice Questions, Volume 1

Chapter 3 – Arithmetic

Answer Key with Answers and Explanations

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Arithmetic

This document begins with the answer key for questions found in the Chapter 3 Arithmetic Practice Questions document. Following the answer key are the complete explanations for each question. If you wish to work through the questions before consulting the answers and explanations, please use the Chapter 3 Arithmetic Practice Questions document.

Answer Key

Question 1.

Answer: Choice B. Quantity B is greater.

Question 2.

Answer: Choice C. The two quantities are equal.

Question 3.

Answer: Choice D. The relationship cannot be determined from the information given.

Question 4.

Answer: Choice A. Quantity A is greater.

Question 5.

Answer: Choice A. Quantity A is greater.

Question 6.

Answer: Choice D. The relationship cannot be determined from the information given.

Question 7.

Answer: Choice C. The two quantities are equal.

Question 8.

Answer: Choice D. 20,100

Question 9.

Answer: Choice D. 11

Question 10.

Answer: Choice B. 9

Question 11.

Answer: Choice D. [pic] the fraction 7 over 15

Question 12.

Answer: Choice E. 1.08s

Question 13.

Answer: Choice E. 24

Question 14.

The answer to question 14 consists of two of the answer choices.

Choice B. Multiplying by 5

Choice C. Dividing by 100

Question 15.

The answer to question 15 consists of one of the answer choices.

Choice A. [pic] z squared is less than or equal to 1

Question 16.

The answer to question 16 consists of two of the answer choices.

Choice C. 10:30 in the morning

Choice H. 1:00 in the afternoon

Question 17.

In question 17 you were asked to enter an integer or a decimal. The answer to question 17 is 12.

Question 18.

In question 18 you were asked to enter an integer or a decimal. The answer to question 18 is 7.

Question 19.

In question 19 you were asked to enter an integer or a decimal. The answer to question 19 is 2,500.

Answers and Explanations

Question 1.

It is given that D is the decimal form of the fraction [pic] 4 over 11.

Quantity A: The 25th digit to the right of the decimal point in D

Quantity B: 4

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.

Explanation for Question 1.

By dividing 4 by 11, you get the decimal form [pic] D = 0 point 3 6 3 6 3 6, dot, dot, dot, where the sequence of two digits “3 6” repeats without end. Continuing the repeating pattern, you see that the 1st digit, the 3rd digit, the 5th digit, and every subsequent odd-numbered digit to the right of the decimal point is 3. Therefore, Quantity A, the 25th digit to the right of the decimal point, is 3. Since Quantity A is 3 and Quantity B is 4, the correct answer is Choice B.

This explanation uses the following strategy.

Strategy 7: Find a Pattern

Question 2.

Quantity A: [pic] The cube root of 270, minus, the cube root of 10

Quantity B: [pic] The cube root of 80

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.

Explanation for Question 2.

You can simplify both quantities. Quantity A can be simplified as follows:

[pic]

The cube root of 270, minus, the cube root of 10, is equal to open parenthesis, the cube root of 27, close parenthesis, times, open parenthesis, the cube root of 10, close parenthesis, minus, the cube root of 10, which is equal to 3 times the cube root of 10, minus, the cube root of 10, which is equal to 2 times the cube root of 10.

Quantity B can be simplified as follows:

[pic]

The cube root of 80 is equal to open parenthesis, the cube root of 8, close parenthesis, times, open parenthesis, the cube root of 10, close parenthesis, which is equal to 2 times the cube root of 10.

Thus the correct answer is Choice C.

This explanation uses the following strategy.

Strategy 5: Simplify an Arithmetic or Algebraic Representation

Question 3.

It is given that n is a positive integer, x = 7n + 2, and y = 6n + 3.

Quantity A: The ones digit of x + y

Quantity B: 5

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.

Explanation for Question 3.

In the question, you are given that x = 7n + 2 and y = 6n + 3.

Substituting the given expressions for x and y in Quantity A, you get

x + y = 13n + 5.

Using trial and error, you can compare Quantity A, the ones digit of 13n + 5, and Quantity B, 5, by plugging in a few values for the positive integer n.

If n = 1, then x + y = 18 and the ones digit is 8, which is greater than 5. So in this case Quantity A is greater than Quantity B.

If n = 2, then x + y = 31 and the ones digit is 1, which is less than 5. So in this case Quantity B is greater than Quantity A.

Since in one case Quantity A is greater than Quantity B, and in the other case Quantity B is greater than Quantity A, you can conclude that the correct answer is Choice D.

This explanation uses the following strategies.

Strategy 10: Trial and Error

Strategy 13: Determine Whether a Conclusion Follows from the Information Given

Question 4.

It is given that r = 2 and [pic] s = negative 7.

Quantity A: [pic] open parenthesis, r minus s, close parenthesis, raised to the 4th power

Quantity B: [pic] r raised to the 4th power, minus, s raised to the 4th power

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.

Explanation for Question 4.

If you substitute the given numbers into the expressions in Quantities A and B, you can compare them.

Substituting in Quantity A gives [pic] open parenthesis, r minus s, close parenthesis, raised to the 4th power, is equal to open parenthesis, 2 minus, open parenthesis, negative 7, close parenthesis, close parenthesis, raised to the 4th power, which is equal to 9 raised to the 4th power.

Substituting in Quantity B gives [pic] r raised to the 4th power, minus, s raised to the 4th power, is equal to 2 raised to the 4th power, minus, open parenthesis, negative 7, close parenthesis, raised to the 4th power, which is equal to 2 raised to the 4th power, minus, 7 raised to the 4th power.

Without further calculation, you see that Quantity A is positive and Quantity B is negative. Thus the correct answer is Choice A.

This explanation uses the following strategy.

Strategy 5: Simplify an Arithmetic or Algebraic Representation

Question 5.

It is given that n is an even negative integer.

Quantity A: [pic] one third raised to the n power

Quantity B: [pic] open parenthesis, negative 3, close parenthesis, raised to the n power

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.

Explanation for Question 5.

Try plugging the first few even negative integers into the expressions in Quantity A and Quantity B to see if a pattern emerges.

If [pic] n = negative 2, Quantity A is [pic] 1 third raised to the negative 2 power, which is equal to 3 squared, and Quantity B is [pic] open parenthesis, negative 3, close parenthesis, raised to the negative 2 power, which is equal to 1 over, open parenthesis, negative 3, close parenthesis, squared, which is equal to 1 over 3 squared.

If [pic] n = negative 4, Quantity A is [pic] 1 third raised to the negative 4 power, which is equal to 3 raised to the 4th power, and Quantity B is [pic]

open parenthesis, negative 3, close parenthesis, raised to the 4th power, which is equal to 1 over, open parenthesis, negative 3, close parenthesis, raised to the 4th power, which is equal to 1 over 3 raised to the 4th power.

If [pic] n = negative 6, Quantity A is [pic] 1 third raised to the negative 6 power, which is equal to 3 raised to the 6th power, and Quantity B is [pic]

open parenthesis, negative 3, close parenthesis, raised to the 6th power, which is equal to 1 over, open parenthesis, negative 3, close parenthesis, raised to the 6th power, which is equal to 1 over 3 raised to the 6th power.

From these three examples, it looks like Quantity A and Quantity B may always be reciprocals of each other, with Quantity A greater than 1 and Quantity B less than 1. You can see this as follows.

If n is an even negative integer, then n can be expressed as [pic] negative 2k, where k is a positive integer. Substituting [pic] negative 2k for n in Quantity A and Quantity B, you get that Quantity A is [pic] 1 third raised to the n power is equal to 1 third raised to the negative 2k power, which is equal to 3 raised to the 2k power, and Quantity B is [pic] open parenthesis, negative 3, close parenthesis, raised to the n power is equal to open parenthesis, negative 3, close parenthesis, raised to the negative 2k power, which is equal to 1 third, raised to the 2k power.

Since for all positive integers k the value of [pic] 3 raised to the 2k power is greater than 1 and the value of [pic] 1 third raised to the 2k power is less than 1, it follows that the correct answer is Choice A.

This explanation uses the following strategies.

Strategy 7: Find a Pattern

Strategy 8: Search for a Mathematical Relationship

Question 6.

Today the price of a table was reduced by 20 percent from what it was yesterday, and the price of a lamp was reduced by 30 percent from what it was yesterday.

Quantity A: The dollar amount of the reduction in the price of the table

Quantity B: The dollar amount of the reduction in the price of the lamp

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.

Explanation for Question 6.

Quantity A is 20 percent of yesterday’s price of the table. Since yesterday’s price is not given, you cannot calculate this quantity. Similarly, you cannot calculate Quantity B. In the absence of further information with which to compare the two quantities, the correct answer is Choice D.

This explanation uses the following strategy.

Strategy 13: Determine Whether a Conclusion Follows from the Information Given

Question 7.

For 5 hours, a photocopier copied at a constant rate of 2 pages every 3 seconds.

Quantity A: The number of pages the photocopier copied in the 5 hours

Quantity B: 12,000

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.

Explanation for Question 7.

Translating the given information, you can calculate Quantity A, the number of pages the photocopier copied in the 5 hours. Copying at the rate of 2 pages every 3 seconds is the same as copying at a rate of 40 pages every 60 seconds, or 40 pages per minute. This rate is the same as copying 2,400 pages every hour, or 12,000 pages in 5 hours. Since Quantity A is equal to 12,000 and Quantity B is 12,000, the correct answer is Choice C.

This explanation uses the following strategy.

Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation

Question 8.

This question has five answer choices, labeled A through E. Select the best one of the answer choices given.

For each integer [pic] n is greater than 1, let [pic] A of n denote the sum of the integers from 1 to n. For example, [pic] A of 100 = 1 + 2 + 3 + dot, dot, dot, + 100, which is equal to 5,050. What is the value of [pic] A of 200 ?

A. 10,100

B. 15,050

C. 15,150

D. 20,100

E. 21,500

Select and indicate the best one of the answer choices given.

Explanation for Question 8.

In the question, you are given that [pic] A of n is equal to the sum of the integers from 1 to n, so [pic] A of 200 = 1 + 2 + 3 + dot, dot, dot, + 100 + 101 + 102 + 103 + dot, dot, dot, + 200. In order to be able to use the given value of [pic] A of 100, or 5,050, you can rewrite the sum as

[pic]

A of 200 is equal to A of 100, + 101 + 102 + 103 + dot, dot, dot, + 200

[pic]

is equal to A of 100, + open parenthesis, 100 + 1, close parenthesis, + open parenthesis, 100 + 2, close parenthesis, + open parenthesis, 100 + 3, close parenthesis, + dot, dot, dot, + open parenthesis, 100 + 100, close parenthesis. 

[pic]

which is equal to A of 100, + open parenthesis, 1 + 2 + 3 + dot, dot, dot, + 100, close parenthesis, + 100 times 100

[pic]

which is equal to A of 100 + A of 100 + 100 times 100

= 5,050 + 5,050 + 10,000

= 20,100

Thus the correct answer is Choice D, 20,100.

This explanation uses the following strategy.

Strategy 12: Adapt Solutions to Related Problems

Question 9.

This question has five answer choices, labeled A through E. Select the best one of the answer choices given.

Which of the following integers CANNOT be expressed as the sum of two prime numbers?

A. 8

B. 9

C. 10

D. 11

E. 12

Select and indicate the best one of the answer choices given.

Explanation for Question 9.

Trying to write each answer choice as a sum of two prime numbers by trial and error, you get

Choice A: 8 = 3 + 5

Choice B: 9 = 2 + 7

Choice C: 10 = 3 + 7

Choice D: 11 = 1 + 10 = 2 + 9 = 3 + 8 = 4 + 7 = 5 + 6

Choice E: 12 = 5 + 7

Of the answer choices given, only 11 cannot be expressed as the sum of two prime numbers. The correct answer is Choice D, 11.

This explanation uses the following strategy.

Strategy 10: Trial and Error

Question 10.

This question has five answer choices, labeled A through E. Select the best one of the answer choices given.

When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n ?

A. 11

B. 9

C. 7

D. 6

E. 4

Select and indicate the best one of the answer choices given.

Explanation for Question 10.

The given information tells you that n can be expressed in the form n = 45k + 18, where k can be any nonnegative integer. Consider how the divisors of 45 and 18 may be related to the divisors of n. Every common divisor of 45 and 18 is also a divisor of any sum of multiples of 45 and 18, like 45k + 18. So any common divisor of 45 and 18 is also a divisor of n. Of the answer choices given, only 9 is a common divisor of 45 and 18. Thus the correct answer is Choice B, 9.

This explanation uses the following strategies.

Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation

Strategy 8: Search for a Mathematical Relationship

Question 11.

This question has five answer choices, labeled A through E. Select the best one of the answer choices given.

[pic]

Figure for Arithmetic Question 11

Begin skippable part of figure description.

The coordinate of point A is [pic] one third, and the coordinate of point D is [pic] one half. Points B and C divide line segment AD into 3 smaller line segments AB, BC, and CD.

End skippable part of figure description.

Points A, B, C, and D are on the number line above, and [pic] the length of AB is equal to the length of CD, which is equal to one third of the length of BC. What is the coordinate of C ?

A. [pic] the fraction 13 over 30

B. [pic] the fraction 9 over 20

C. [pic] the fraction 11 over 24

D. [pic] the fraction 7 over 15

E. [pic] the fraction 29 over 60

Select and indicate the best one of the answer choices given.

Explanation for Question 11.

From the figure you can see that since the coordinate of A is [pic] one third, it follows that the coordinate of C is [pic] one third + the length of AB + the length of BC.

Since you are given that [pic] the length of AB is equal to one third of the length of BC, the coordinate of C can be rewritten in terms of [pic] the length of AB as follows:

[pic]

one third + the length of AB + the length of BC, which is equal to one third + the length of AB + 3 times the length of AB, which is equal to one third + 4 times the length of AB.

To find the coordinate of C, you need to know [pic] the length of AB.

From the figure you know that [pic]

the length of AD is equal to the length of AB

+ the length of BC + the length of CD, which is equal to the length of AB + 3 times the length of AB + the length of AB, which is equal to 5 times the length of AB.

On the other hand, since the coordinate of A is [pic] one third and the coordinate of D is [pic] one half, it follows that [pic]

the length of AD is equal to one half minus one third, which is equal to one sixth.

Therefore you can conclude that [pic]

one sixth is equal to 5 times the length of AB, and the length of AB is equal to one thirtieth.

Thus the coordinate of C is [pic]

one third + 4 times the length of AB, which is equal to one third, + 4 times one thirtieth, or the fraction 7 over 15.

The correct answer is Choice D, [pic] the fraction 7 over 15.

This explanation uses the following strategies.

Strategy 4: Translate from Figures to an Arithmetic or Algebra Representation

Strategy 8: Search for a Mathematical Relationship

Question 12.

This question has five answer choices, labeled A through E. Select the best one of the answer choices given.

Which of the following represents the total dollar amount that a customer would have to pay for an item that costs s dollars plus a sales tax of 8 percent, in terms of s ?

A. [pic] the fraction s over 0.08

B. [pic] the fraction s over 1.08

C. [pic] the fraction s over 8

D. 0.08s

E. 1.08s

Select and indicate the best one of the answer choices given.

Explanation for Question 12.

The total dollar amount that the customer would have to pay is equal to the cost plus 8 percent of the cost. Translating to an algebraic expression, you get that the total amount is s + 0.08s, or 1.08s. Thus, the correct answer is Choice E, 1.08s.

This explanation uses the following strategy.

Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation

Question 13.

This question has five answer choices, labeled A through E. Select the best one of the answer choices given.

Marie earned $0.75 for every mile she walked in a charity walkathon. If she earned a total of $18.00 at that rate, how many miles did she walk?

A. 13.5

B. 17.5

C. 21

D. 22.5

E. 24

Select and indicate the best one of the answer choices given.

Explanation for Question 13.

You can translate the given information into an algebraic equation.

If Marie walks m miles, she earns 0.75m dollars. Since you know that she earned a total of $18, you get 0.75m = 18. Solving for m, you have [pic] m is equal to the fraction 18 over 0.75, which is equal to 24. Thus the correct answer is Choice E, 24.

This explanation uses the following strategy.

Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation

Question 14.

This question has three answer choices, labeled A through C. Select all the answer choices that apply.

Which of the following operations carried out on both the numerator and the denominator of a fraction will always produce an equivalent fraction?

Indicate all such operations.

A. Adding 2

B. Multiplying by 5

C. Dividing by 100

Select and indicate all the answer choices that apply. The correct answer to a question of this type could consist of as few as one or as many as all three of the answer choices.

Explanation for Question 14.

Multiplying both the numerator and the denominator of a fraction by the same nonzero number is equivalent to multiplying the fraction by 1, thus producing an equivalent fraction. The same is true for division. However, adding the same number to both the numerator and denominator does not usually produce an equivalent fraction. Here is an example:

[pic]

the fraction 1 over 2 is not equal to the fraction with numerator 1 + 2 and denominator 2 + 2, which is equal to the fraction 3 over 4

Thus the correct answer consists of two choices, B and C; that is, multiplying by 5 and dividing by 100.

This explanation uses the following strategy.

Strategy 13: Determine Whether a Conclusion Follows from the Information Given

Question 15.

This question has three answer choices, labeled A through C. Select all the answer choices that apply.

If [pic] the absolute value of z is less than or equal to 1, which of the following statements must be true?

Indicate all such statements.

A. [pic] z squared is less than or equal to 1.

B. [pic] z squared is less than or equal to z.

C. [pic] z cubed is less than or equal to z.

Select and indicate all the answer choices that apply. The correct answer to a question of this type could consist of as few as one or as many as all three of the answer choices.

Explanation for Question 15.

The condition stated in the question, [pic] the absolute value of z is less than or equal to 1, includes both positive and negative values of z. For example, both [pic] one half and negative one half are possible values of z. Keep this in mind as you evaluate each of the inequalities in the answer choices to see whether the inequality must be true.

Choice A: [pic] z squared is less than or equal to 1. First look at what happens for a positive and a negative value of z for which [pic] the absolute value of z is less than or equal to 1, say, [pic] z = one half and z = negative one half. If [pic] z = one half, then z squared = one quarter.

If [pic] z = negative one half, then z squared = one quarter. So in both these cases it is true that [pic] z squared is less than or equal to 1.

Since the inequality [pic] z squared is less than or equal to 1 is true for a positive and a negative value of z, try to prove that it is true for all values of z such that [pic]

the absolute value of z is less than or equal to 1.

Recall that if [pic] 0 is less than or equal to c, which is less than or equal to 1, then c squared is less than or equal to 1.

Since [pic]

0 is less than or equal to the absolute value of z, which is less than or equal to 1, letting c be equal to the absolute value of z, yields the inequality, the absolute value of z, end absolute value, squared, is less than or equal to one.

Also, it is always true that [pic] the absolute value of z, end absolute value, squared, is equal to z squared, and so z squared is less than or equal to 1.

Choice B: [pic] z squared is less than or equal to z. As before, look at what happens when [pic] z = one half and when z = negative one half.

If [pic] z = to one half, then z squared = one quarter.

If [pic] z = negative one half, then z squared = one quarter.

So when [pic] z = one half, the inequality, z squared is less than or equal to z is true, and when [pic] z = negative one half, the inequality, z squared is less than or equal to z, is false. Therefore you can conclude that if [pic] the absolute value of z is less than or equal to 1, it is not necessarily true that [pic] z squared is less than or equal to z.

Choice C: [pic] z cubed is less than or equal to z. As before, look at what happens when [pic] z = one half and when z = negative one half.

If [pic] z = one half, then z cubed is equal to one eighth.

If [pic] z = negative one half, then z cubed is equal to negative one eighth. So when [pic] z = one half, the inequality [pic] z cubed is less than or equal to z is true, and when [pic] z = negative one half, the inequality [pic] z cubed is less than or equal to z is false. Therefore, you can conclude that if [pic] the absolute value of z is less than or equal to 1, it is not necessarily true that [pic] z cubed is less than or equal to z.

Thus when [pic] the absolute value of z is less than or equal to 1, Choice A, [pic] z squared is less than or equal to 1, must be true, but the other two choices are not necessarily true. The correct answer consists of one choice, A; that is, [pic] z squared is less than or equal to 1.

This explanation uses the following strategies.

Strategy 8: Search for a Mathematical Relationship

Strategy 10: Trial and Error

Strategy 13: Determine Whether a Conclusion Follows from the Information Given

Question 16.

This question has eight answer choices, labeled A through H. Select all the answer choices that apply.

In a certain medical group, Dr. Schwartz schedules appointments to begin 30 minutes apart, Dr. Ramirez schedules appointments to begin 25 minutes apart, and Dr. Wu schedules appointments to begin 50 minutes apart. All three doctors schedule their first appointments to begin at 8:00 in the morning, which are followed by their successive appointments throughout the day without breaks. Other than at 8:00 in the morning, at what times before 1:30 in the afternoon do all three doctors schedule their appointments to begin at the same time?

Indicate all such times.

A. 9:30 in the morning

B. 10:00 in the morning

C. 10:30 in the morning

D. 11:00 in the morning

E. 11:30 in the morning

F. 12:00 noon

G. 12:30 in the afternoon

H. 1:00 in the afternoon

Select and indicate all the answer choices that apply. The correct answer to a question of this type could consist of as few as one or as many as all three of the answer choices.

Explanation for Question 16.

By examining the pattern of beginning times for the three types of appointments, you can see that the times will coincide when the number of minutes after 8:00 in the morning is a common multiple of 30, 25, and 50. The least common multiple of 30, 25, and 50 is 150, which represents 150 minutes, or 2.5 hours. So the times coincide every 2.5 hours after 8:00 in the morning, that is, at 10:30 in the morning, at 1:00 in the afternoon, and so on.

The correct answer consists of two choices, C and H; that is, 10:30 in the morning, and 1:00 in the afternoon.

This explanation uses the following strategy.

Strategy 7: Find a Pattern

Question 17.

This question does not have any answer choices; it is a numeric entry question. To answer this question, enter a number in the answer space provided.

The integers x and y are greater than 1. If [pic] 4 x times 7 y = 756, what is the value of x + y ?

The answer space is preceded by the label “x + y =.”

To answer this question, enter a number in the answer space provided. The number can include a decimal point, and can be positive, negative, or zero. The number entered cannot be a fraction.

Explanation for Question 17.

You can solve the given equation, [pic] 4 x times 7 y = 756, for the product [pic] x y, as follows.

Simplifying the left-hand side of the equation [pic] 4 x times 7 y = 756,

yields the equation [pic]. 28 x y equals 756. Then dividing both sides by 28 yields the equation [pic] x y equals 27.

By trial and error, you find that 3 and 9 are the only two integers greater than 1 whose product is 27. So x + y = 12 and the correct answer is 12.

This explanation uses the following strategy.

Strategy 10: Trial and Error

Question 18.

This question does not have any answer choices; it is a numeric entry question. To answer this question, enter a number in the answer space provided.

In the sequence [pic] 1, negative 3, 4, 1, negative 3, 4, 1, negative 3, 4, dot, dot, dot, the first 3 terms repeat without end. What is the sum of the terms of the sequence from the 150th term to the 154th term?

To answer this question, enter a number in the answer space provided. The number can include a decimal point, and can be positive, negative, or zero. The number entered cannot be a fraction.

Explanation for Question 18.

Examining the repeating pattern, you see that the 3rd term is 4, and every 3rd term after that, in other words, the 6th, 9th, 12th, 15th, and so on, is 4. Since 150 is a multiple of 3, the 150th term is 4. Therefore the 150th to the 154th terms are 4, 1, [pic] negative 3, 4, 1. The sum of these 5 terms is 7, so the correct answer is 7.

This explanation uses the following strategy.

Strategy 7: Find a Pattern

Question 19.

This question does not have any answer choices; it is a numeric entry question. To answer this question, enter a number in the answer space provided.

A manufacturing company has plants in three locations: Indonesia, Mexico, and Pakistan. The company has 6,000 employees, and each of the employees works at only one of the plants. If [pic] three eighths of the employees work at the plant in Indonesia and if twice as many employees work at the plant in Mexico as work at the plant in Pakistan, how many employees work at the plant in Mexico?

The answer space is followed by the word “employees.”

To answer this question, enter a number in the answer space provided. The number can include a decimal point, and can be positive, negative, or zero. The number entered cannot be a fraction.

Explanation for Question 19.

Three-eighths of the company’s 6,000 employees work in Indonesia, so the number of employees that do not work in Indonesia is [pic] 5 eighths times 6,000, or 3,750. Of those employees, twice as many work in Mexico as work in Pakistan, so the number working in Mexico is [pic] 2 thirds times 3,750, or 2,500. Thus the correct answer is 2,500 employees.

This explanation uses the following strategy.

Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation

This is the end of Chapter 3 – Arithmetic Answer Key with Answers and Explanations.

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