Mastering Arithmetic Reasoning for the AFCT

If a person deposits $300 into an account and then withdraws 60% of his account after one month which yields him a withdrawal of $264, how much originally was in his account?

• A. $140
• B. $360
• C. $300
• D. $264

Answer: (A)

To find the original amount in the account before the withdrawal, we need to understand how the withdrawal amount relates to the percentage withdrawn. The person initially deposits $300 into the account. After one month, he withdraws 60% of the total amount in the account. The problem states that this withdrawal amounts to $264. To determine the total amount in the account after the deposit and before the withdrawal, we set up the equation based on the withdrawal percentage. If the total amount in the account is represented as \( x \), then: \[ 0.60x = 264 \] To find \( x \), we divide both sides of the equation by 0.60: \[ x = \frac{264}{0.60} \] \[ x = 440 \] Therefore, the total amount in the account before the withdrawal was $440. The original deposit is $300, and the account must have gained an additional amount to reach $440 before the withdrawal. To find how much was gained, we subtract the original deposit from the total amount: \[ 440 - 300 = 140 \] Thus, the question asks for the original amount in the account, which is $440

When preparing for the Armed Forces Classification Test (AFCT), one topic that often raises eyebrows is arithmetic reasoning. It sounds technical, doesn't it? But guess what? You encounter arithmetic reasoning daily without realizing it. Think of it as your brain's gym; it helps flex those mental muscles needed for math-based problem-solving!

Let’s tackle a common type of problem you might see in practice tests. Imagine a person deposits $300 into an account. Fast forward a month, and they withdrawal 60% of the total in the account, netting them $264. Now, here’s a question for you—how much was originally in the account? Was it $140, $360, $300, or $264? If you went with $140, you're in the right ballpark, but let’s break this down.

First off, a crucial step in arithmetic reasoning is understanding how percentages work within a context. The person withdrew 60% of the total account balance post-deposit, which equals $264. So, if we denote the total amount in the account as ( x ), we get this little equation:

[

0.60x = 264

]

To solve for ( x ), just divide both sides by 0.60, leading us to:

[

x = \frac{264}{0.60}

]

[

x = 440

]

Voilà! The account held $440 before the withdrawal swooped in. But wait, where do we derive that $440 from? Since the person initially deposited $300, we need to consider the additional amount earned, which is a key aspect in arithmetic reasoning. By subtracting the original deposit from the total amount, we find:

[

440 - 300 = 140

]

And thus, the original amount in the account before any withdrawals were made is indeed $440!

Isn’t it interesting how a seemingly simple question can lead to a deeper understanding of financial mathematics? This methodology isn’t just useful for test-taking; it applies broadly in real life when managing finances or making investment decisions.

As you prepare for the arithmetic reasoning section of the AFCT, practice similar problems to sharpen your skills. Think of it as addressing a puzzle: each piece contributes to the bigger picture, just like every math problem reinforces your overall proficiency. Moreover, the ability to decipher financial scenarios is crucial, not only for tests but also in navigating your future.

So, as you continue your studies, remember: arithmetic reasoning isn't merely a box to check off in your preparation plan; it is a vital skill that will benefit you long after the test is finished. Embrace the intricacies of numbers, and let them guide you toward greater confidence and clarity in your financial decision-making. Here’s the thing—you’ve got this!