# Arithmetic Reasoning Shortcuts, Tutorials

The two words, “arithmetic reasoning,” strike terror into the hearts of people who have been out of school for a while or who have concentrated their studies in the humanities. The phrase “quantitative reasoning” is probably equally as terrifying as it is puzzling. The quantitative reasoning test includes arithmetic problems as well as questions asking test takers to evaluate a set of facts and conclusions to determine if the conclusions are true or false. Not all exams for special agent include this section, but it is very similar to the logical reasoning test. Practice this section in the short exercise below.

For the straight arithmetic reasoning test, you do not need to understand intricate mathematical operations or to memorize complicated formulas. You can solve the problems arithmetically or by using some simple algebra.
Each problem is presented as a short verbal description of a situation that includes some numerical facts. You must read the problem to determine what the question is, if a series of calculations will be required, you do not want to stop short of the answer because you misinterpreted the question. Likewise, you do not waste time going beyond what is asked.

Once you have determined what the question asks, you must settle on the best route for arriving at the answer and set the problem up accordingly. Finally, you must perform the calculations. Some special agent exams will give you “none of these” as the fifth (E) choice, but the TEA has a fifth numerical choice. It is important that you perform all calculations carefully because an estimate or an approximation may lead you to choose the wrong answer.

Reminder: Do all the practice exercise questions with pencil on scratch paper. You will not be permitted to use a calculator at the exam, so get used to doing arithmetic without one. Answer questions in the practice exercise by circling the letter of your choice.

## Solved Examples - Arithmetic Reasoning

Example 1) A police department purchases badges at 16$each for all the graduates of the police training academy. The last training class graduated 10 new officers. What is the total amount of money the department will spend for badges for these new officers? (A)$70
(B) $116 (C)$160
(D) $180 (E)$200

Solution: The correct answer is (C). It can be obtained by computing the following:
$16\times 10\:=\:160$
The badges are priced at 16$each. The department must purchase 10 of them for the new officers. Multiplying the price of one badge (16$) by the number of graduates (10) gives the total price for all of the badges.
Choice (A), (B), and (D) are the result of erroneous computations.

Example 2) An investigator rented a car for six days and was charged 450$. The car rental company charged 35$ per day plus 0.30$per mile driven. How many miles did the investigator drive the car? Solution: The correct answer is (A). It can be obtained by computing the following: 6(35) + 0.30x = 450 The investigator rented the car for six days at 35$ per day, which is 210$; 210$ subtracted from the total charge of 450$leaves 240$, the portion of the total charge which was expended for the miles driven. This amount divided by charge per mile $(240\div 0.30)$ gives the number of miles (800) driven by the investigator.
Choices (B), (C), and (D) are the result of erroneous computations.

## Arithmetic Reasoning Questions from Previous Year Exams

Verbal Reasoning : Arithmetic Reasoning