Free Texas Civil Service Arithmetic Reasoning Question and Answers — Questions and Answers
Question 1: Ben enjoys collecting sports cards, and his collection features football, baseball, and basketball. What is the ratio of football cards to basketball cards if the ratio of football cards to baseball cards is 5 to 2 and the ratio of baseball cards to basketball cards is 5 to 1?
- 20:3
- 15:3
- 5:3
- 25:2 (Correct answer)
Correct answer: 25:2
To find the ratio of football cards to basketball cards, we combine the given ratios. The ratio of football (F) to baseball (B) is 5:2 (F/B = 5/2), and baseball (B) to basketball (K) is 5:1 (B/K = 5/1). From B/K = 5/1, we know B = 5K. Substituting this into F/B = 5/2 gives F/(5K) = 5/2, which simplifies to F = (5/2)(5K) = 25/2 K. Therefore, the ratio of football cards to basketball cards is 25:2.
Question 2: What's the quotient of 0.808 ÷ 0.29?
- 27.86
- 2.786 (Correct answer)
- 278.6
- 0.279
Correct answer: 2.786
To find the quotient of 0.808 ÷ 0.29, perform the division. It's often helpful to eliminate the decimal in the divisor by multiplying both numbers by 100, transforming the problem into 80.8 ÷ 29. Performing this division yields approximately 2.7862, which, when rounded to three decimal places, is 2.786.
Question 3: Mary received a loan from Sarah in the amount of $2,000, with a 4% interest rate per year. What will the total amount of interest that is due on this loan be after a year has passed?
- $48
- $4
- $80 (Correct answer)
- $2,080
Correct answer: $80
To calculate the total amount of simple interest due after one year, use the formula I = PRT, where I is interest, P is the principal amount, R is the annual interest rate, and T is the time in years. Given P = $2,000, R = 4% (or 0.04), and T = 1 year, the interest is $2,000 × 0.04 × 1 = $80.
Question 4: A truck that weighs one ton is subject to a tax of $0.11 per pound. What is the total amount of tax money that is due?
- $110
- $330
- $220 (Correct answer)
- $0.11
Correct answer: $220
First, convert the truck's weight from tons to pounds, knowing that one ton equals 2,000 pounds. So, a one-ton truck weighs 2,000 pounds. Then, multiply the total weight in pounds by the tax rate per pound: 2,000 pounds × $0.11/pound = $220. This is the total amount of tax due.
Question 5: If you drive a car at an average speed of 28.5 miles per hour, how many hours will it take you to travel a distance of 91.2 miles?
- 3.5 hours
- 2.6 hours
- 1.6 hours
- 3.2 hours (Correct answer)
Correct answer: 3.2 hours
To determine the time it will take to travel a certain distance at a given average speed, use the formula Time = Distance ÷ Speed. In this case, the distance is 91.2 miles and the average speed is 28.5 miles per hour. Dividing 91.2 by 28.5 yields 3.2 hours.
Question 6: Find the average of the following numbers: 32, 31
- 63
- 31.1
- 32.3
- 31.5 (Correct answer)
Correct answer: 31.5
To find the average of a set of numbers, sum all the numbers and then divide by the total count of the numbers. For the numbers 32 and 31, their sum is 32 + 31 = 63. Since there are two numbers, divide the sum by 2: 63 ÷ 2 = 31.5.
Question 7: There is a sale at a women's clothing store. Get a second dress shirt for 15% less when you purchase one at full price. What will Selena have to pay for the second shirt if she purchases two shirts, each of which has a regular price of $32.59?
- $70.07
- $27.70 (Correct answer)
- $60.29
- $9.78
Correct answer: $27.70
Selena purchases a second dress shirt at a 15% discount from its regular price of $32.59. First, calculate the discount amount: 15% of $32.59 is 0.15 × $32.59 = $4.8885. Then, subtract this discount from the regular price to find the cost of the second shirt: $32.59 - $4.8885 = $27.7015. Rounded to the nearest cent, Selena will pay $27.70 for the second shirt.
