Arithmetic Reasoning (AR)

Which of the following is an integer? A) -9 B) 3/4 C) 0.5 D) √42

A) -9 An integer is any positive or negative whole number or zero. Therefore, -9 is an integer. ¾ and 0.5 are not integers because they are not whole numbers. The square root of 42 is approximately 6.48 and therefore not an integer.

All of the following are examples of composite numbers except which one? A) 2 B) 6 C) 9 D) 12

A) 2

How many prime numbers are there between 25 and 35, inclusive? A) 2 B) 3 C) 4 D) 5

A) 2 Prime numbers are not divisible by anything other than themselves and 1. The only prime numbers in this set are 29 and 31. 25, 30, and 35 can be excluded because they are divisible by 5. 26, 28, 30, 32, and 34 are divisible by 2. 27, 30, and 33 are divisible by 3.

Which of the following is equivalent to 2 times the total of x plus y? A) 2x + 2y B) 2x(2y) C) 2x/2y D) 2xy

A) 2x + 2y 2 times the total of x plus y is 2(x + y). From there, use the Distributive Property to multiply the 2 by each term inside the parenthesis. 2(x + y) = 2x + 2y

Dave is on a kayaking trip. On the first day, he travels 15 miles. On the second day, he travels 35 miles and on the third day he rests. On the fourth day, he travels 57 miles and on the fifth day, he travels 43 miles. What is the average number of miles that he travels per day? A) 32 B) 30 C) 27 D) 25

B) 30 number of miles divided by the days = average (15+35+0+57+43)/5 =30

Laura goes to the grocery store every 5 days and Tim goes to the same grocery store every 6 days. If Laura and Tim both went to the grocery store today, when is the next time they will both go to the grocery store on the same day? A) 11 days B) 30 days C) 60 days D) there is not enough information

B) 30 days To solve this problem, you must find the least common multiple of 5 and 6, which is the smallest multiple common to both numbers. To do this, make a list of multiples for each number until at least two multiples are on both lists. 5: 5, 10, 15, 20, 25, 30... 6: 6, 12, 18, 24, 30... The lowest common multiple of both numbers is 30.

A math class has 32 students. Fourteen are females. What percent of the class is female? A) 24.22% B) 43.75% C) 37.25% D) 52.75%

B) 43.75% Divide the number of females students by total number of students. Then change decimal to a percent 14/32= .4375 = 43.75%

Which of the following is equivalent to 4 × 4 × 4 × 4? A) √4 x 4 B) 4^4 C) 4 ÷ 4 D) 4,000

B) 4^4 An exponent is a method of indicating repeated multiplication. For example, 4 × 4 × 4 × 4 can also be expressed as 44, which is also known as "4 to the fourth power." The small number written slightly above and to the right of a number is the exponent, and it indicates the number of times you multiply the number it accompanies by itself.

Solve the following equation: |7 - (24 ÷ | 3-6 |)| A) 15 B) -12 C) 1 D) -1

C) 1 Solve the problem from the inside out. |7 - (24 ÷ | 3-6 |)| = |7 - (24 ÷ | -3 |)| = |7 - (24 ÷ 3)| = |7 - 8| = |-1| = 1

Five years ago, Ruth made a deposit of $500 into a savings account that pays simple interest. She made no further deposits, and now her account is worth $750. What was the rate of interest per year? A) 4% B) 2% C) 10% D) 9%

C) 10% I=prt $250=$500(r)5 $250=$2500r .10=r

A meteor made a circular crater with a circumference of 56.52 meters. What is the diameter of the crater? A) 12m B) 15m C) 18m D) 9m

C) 18m C = 2(3.14)r or C=(3.14)d d = 56.52/3.14 d = 18m

Which of the following is a prime number? A) 27 B) 9 C) 2 D) 12

C) 2 A prime number is a whole number that can be divided evenly by itself and by 1 but not by any other number. 2 is a prime number because its only factors are 1 and 2.

Convert 0.023 to a fraction. A) .023/100 B) 23/100 C) 23/1,000 D) 2 2/67

C) 23/1,000 When a number is divided by a multiple of 10, simply move the decimal one position to the left for every zero. We can take each answer to find out which one is correct. 23/100 = 0.23 (move decimal 2 positions to the left) 23/1,000 = 0.023 (move decimal 3 positions to the left) 23/10,000 = 0.0023 (move decimal 4 positions to the left) 23/100,000 = 0.00023 (move decimal 5 positions to the left) Therefore, 0.023 converted to a fraction is 23/1,000.

Every day, Bert spends an hour commuting to and from his office, driving at an average speed of 50 mph and taking the same route each way. How far does Bert live from his office? A) 50 miles B) 30 miles C) 25 miles D) 15 miles

C) 25 miles Use the distance formula, where d stands for distance, r stands for the (constant or average) rate of speed, and t stands for time. Remember that his total commute is 1 hour, so one-way, it will be .5 hours. d=rt d = 50(.5) d = 25

Which of the following numbers is divisible by 3? A) 49,763,296 B) 32,832,988 C) 85,019,457 D) 18,067,871

C) 85,019,457 If the sum of the digits of a number is divisible by 3, then the number itself is divisible by 3. 8 + 5 + 0 + 1 + 9 + 4 + 5 + 7 = 39 39 divided by 3 is 13 with no remainders, so the number is divisible by 3.

What is the result when 7 is added to the product of 2 and 3? A) 20 B) 17 C) 35 D) 13

D) 13 7+ (2 * 3) = 7+ (6) 13

Jenny is 34-years-old. Two years ago she was twice as old as her cousin. How old her cousin now? A) 15 B) 17 C) 21 D) 18

D) 18 2c = 32 c = 16 16 + 2 = 18

What is the absolute value of the quantity two minus seven? A) -5 B) 9 C) 0 D) 5

D) 5 The absolute value of the quantity two minus seven" should be written as |2 - 7|. Absolute value is the distance of a number from zero, and since distances cannot be negative, absolute values are always positive numbers. To take the absolute value, simplify the expression between the absolute value bars and then take the positive value of it. |2 - 7| = |-5| = 5.

Which of the following is true? A) If a number is divisible by 5, it is also divisible by 10. B) If a number is divisible by 1, it is also divisible by 2. C) If the last 3 digits of a number are divisible by 2, then the number is divisible by 4. D) If a number is divisible by 2 and 3, it is also divisible by 6.

D) If a number is divisible by 2 and 3, it is also divisible by 6. It is true that if a number is divisible by both 2 and 3, it is also divisible by 6. For example, 108 is divisible by 2 (108 ÷ 2 = 54) and by 3 (1 + 0 + 8 = 9 ÷ 3 = 3), and therefore is also divisible by 6.

The absolute value of the quantity of 5 plus a number equals 10. Which of the following options is the correct solution set for the above equation? A) {-5, 5} B) {10, -10} C) {-5, 15} D) {-15, 5}

D) {-15, 5} The absolute value of 5 plus a number equals 10 should be written as |5 + x| = 10. Absolute value means the distance of a number from zero, so whenever you solve for the number inside absolute value bars, you must consider both the positive and negative values. Take away the bars and set the expression equal to both 10 and -10. 5 + x = 10 gives you x = 5, and 5 + x = -10 gives you x = -15. The solution set is x = {-15, 5}.