Arithmetic Reasoning Questions

1. If x, y, and z are integers with x≤y and yz, which of the following could x, y, and z represent (respectively)? A ‾3, ‾2, ‾3 B. 3, 2, 3 C. 1, 2, 3 D. 3, 2, 1 Answer: A-¬x=¬‾3, y=¬¬¬¬¬‾2, z=¬‾3.‾3 is less than or equal to ¬‾2, and¬¬‾2 is greater than ¬‾3 2: The number ½ is a __________. A. Whole number B. Rational number C. Decimal D. Percentage Answer: B - ½ is a rational number. A fraction is a rational number in regards to a/b if a and b are both positive integers and b is not equal to 0. Whole numbers, mixed numbers, and decimals are also rational numbers. 3:Which of the following uses the doubling method of informal counting to solve the following:3+4= A. (1+1+1) + (1+1+1+1) = 7 B. (3+4) + (3+4) - (3+4) = 7 C. 3+4 = (3+3) +1 = 6+1 = 7 D. 2+2+2+1=7 Answer: C -The doubling method would be 3 + 4 = (3 + 3) +1 = 6 + 1 = 7. Using the doubling method of informal counting involves taking apart a number so that it is the same number as the one being added to it and then adding the difference. It is a way to do mental math easily in one’s head. 4:Solve the following equation: 1 3/8 ÷ 2/3 = A. 1/3 B. 1 1/3 C. 33/16 D. 1 5/8 Answer: C- 1 3/8 ÷ 2/3 = 33/16. 1 3/8 is equal to 11/8. Multiply 11/8 by the reciprocal of 2/3 when dividing. By multiplying 11/8 by 3/2, you get 33/16. 5:Solve the following equation:3/6 + 2/5 + 1/3 = A. 70/64 B. 37/30 C. 1/3 D. 16/3 Answer: B - 3/6 + 2/5 + 1/3 = 37/30. By finding the least common denominator , you can add all 3 fractions. 6: What is the greatest common factor of 30 and 60? A. 30 B. 60 C.90 D. 10 Answer: A-The greatest common factor of 30 and 60 is 30. Factors are numbers you multiply together to get another number. The shared factors of 30 and 60 are [1, 2, 3, 5, 6, 10, 15, 30], the largest of which is 30. 7:Which of the following is a prime number? A. 50 B. 25 C.23 D. 6 Answer: C - 23 is a prime number. A prime number is a number that can only be divided by itself and by the number 1, without a remainder. 50, 25, and 6 can all be divided by numbers other than itself and 1. Even numbers greater than 2 are never prime.1 8:Which of the following is a composite number? A. 14 B. 31 C.7 D. 11 Answer: A - 14 is a composite number. A composite number is the opposite of a prime number. A composite number can be divided by more than just 1 and itself. 14 can be divided also by 7 and 2. 9:Which of the following is NOT a prime factor of 204? A. 5 B. 3 C.17 D. 2 Answer: A- 5 is not a prime factor of 204. 5 cannot be multiplied by any whole number to equal 204 without a remainder. 10: Round 567.342 to the nearest hundredth. What is the answer? A.600 B. 560 C.567.34 D. 567.3 Answer: C -567.342 rounded to the nearest hundredth is 567.34. The 4 is in the hundredths place. Since it is followed by the number 2, which is less than 5, you would round down and keep the 4. 11: 34.55 + 6 + 19.8 + 23.53What is the sum of the numbers rounded to the nearest tenths place? A.600 B. 560 C.567.34 D. 567.3 Answer: C - The sum of the numbers rounded to the nearest tenths place is 83.9. Before rounding the numbers, the answer is 83.88. Since the 8 in the hundredths place is greater than 5, you would round up, changing the 8 in the tenths place to a 9. 12: 34.55 + 6 + 19.8 + 23.53What is the difference between the exact sum and the sum rounded to the nearest tenths place?