Unveiling The Math: Solving The IFSC Question 03

Hey there, math enthusiasts! Let's dive headfirst into a fascinating problem from the IFSC exam. This question, a real brain-teaser, tests your understanding of fundamental math concepts. We'll break it down step by step, making sure you grasp every single detail. Get ready to flex those math muscles and sharpen your problem-solving skills! In this guide, we'll dissect the IFSC exam question 03. We'll explore the given mathematical statements and determine their truthfulness. We will ensure that you are well-prepared to tackle similar problems in the future. The ability to solve this kind of problem is crucial for success in any mathematics-related field. Let's make sure you're ready to ace it! We'll start with the initial expression, then, delve into the given statements and how to assess their validity, helping you to understand the logic behind the mathematical operations involved. Now, let’s get started and unravel the mystery of this intriguing question.

Deciphering the First Statement

Alright, guys, let's start with the first statement: -5^2 - sqrt(16) * (-10) + (sqrt(5))^2 = -17. This looks a bit intimidating at first glance, but trust me, we'll break it down into easy-to-manage parts. Remember, when dealing with exponents, the order of operations (PEMDAS/BODMAS) is our best friend. So, first, we'll handle the exponent. -5^2 is actually -(5*5), which equals -25. Not 100% sure why people get this wrong, but it’s a super common mistake. Now, let’s look at the square root of 16, which is 4. Multiplying this by -10 gives us -40. Finally, the square root of 5, squared, is just 5. Now, putting it all together, we have: -25 - (-40) + 5. Simplifying this gives us -25 + 40 + 5. And guess what? That adds up to 20, not -17! This means the first statement is false. Keep in mind the order of operations to avoid making common errors. It’s always best to be very careful with the signs and how they interact with each other. This is a very common type of question, so understanding this will help you answer similar ones in the future. Always double-check your work to ensure accuracy and to minimize any mistakes. Now that we've carefully evaluated this step, we'll move on to the next. The best thing is to practice as many examples as possible to reinforce your skills.

Cracking the Second Statement

Moving on to statement number two: 35 + (3 + sqrt(81) - 23 + 1) * 2 = 10. Time to simplify, yeah? Let's take it piece by piece! The square root of 81 is 9, so inside the parentheses we have: 3 + 9 - 23 + 1. That simplifies to -10. Now, we multiply -10 by 2, which gives us -20. Finally, we add 35 to -20, and the result is 15. So, the second statement also appears to be false since the result isn’t 10. Again, this highlights the importance of keeping the order of operations in mind. Always do the operations within parentheses first. This part is a little less tricky, but we should always be careful. The key here is not to rush through the calculations. Taking your time can prevent mistakes. Remember, you're not in a race. Also, remember to double-check your answer to see if it makes sense. If you got something weird, it’s probably wrong, and you should go back and check the previous steps. By practicing consistently, you can improve your speed and accuracy. Remember, in math, it’s not just about getting the right answer; it's about understanding why the answer is correct. Let's move on to the final statement, but first, take a moment to reflect on what you've learned. Think about any areas that you find challenging and then focus on them. And most importantly, keep practicing!

Analyzing the Third Statement

Finally, let's take a look at the third statement: (3 + sqrt(5))(3 - sqrt(5)) - is a multiple of 2. This looks like a perfect opportunity to use the difference of squares formula, right? If we multiply this out, we'll get 3^2 - (sqrt(5))^2. That simplifies to 9 - 5, which equals 4. And hey, 4 is a multiple of 2! Therefore, the third statement is true. This is an example of an elegant mathematical solution. The difference of squares is your friend in these situations. This kind of problem often appears in exams and tests. It can be particularly useful when dealing with square roots and other radicals. Notice how the use of the formula made the calculations much simpler. Now, you should review the steps you took. Always make sure to be super precise when simplifying expressions. The best way to master this is by practicing different examples. You will start to recognize patterns and become faster at solving these types of problems. When you master these principles, you will be well-equipped to tackle more challenging mathematical concepts. After this practice, you'll be well on your way to math mastery. Let's recap what we've discovered.

Determining the Correct Answer

So, after careful evaluation, we’ve found that the first statement is false, the second statement is false, and the third statement is true. Going back to the options: A) all are true, obviously wrong. B) only one statement is true, wrong. C) only II is false, nope. D) only I and III are true, wrong. E) only III is true, that’s right! That's our correct answer. Always double-check your final answer to confirm it aligns with your calculations. Make sure to review the key concepts covered in this question. Practice solving similar problems to enhance your skills and build confidence. You've successfully navigated a challenging math problem! Congratulations! Keep up the awesome work, and remember, practice makes perfect. Keep up with the questions, and you will learn the necessary content to solve any type of question related to mathematics. Each problem you solve is a step forward in your journey. Don't be afraid to take on new challenges. Always remember that learning math can be an enjoyable and rewarding experience. This type of practice will help you excel in mathematics.

Final Thoughts and Next Steps

Awesome work, guys! We've successfully dissected this IFSC question, breaking it down into manageable parts and figuring out the correct answer. Remember the key takeaways: the order of operations is crucial, and knowing your formulas (like the difference of squares) can make your life a whole lot easier. Practice is your best friend. Keep working through problems, review your mistakes, and don't be afraid to ask for help when you need it. There are tons of resources available online and in textbooks. The more you practice, the more confident and skilled you will become. I hope you found this guide helpful. If you have any questions or want to dive deeper into any of these concepts, feel free to ask! Keep up the great work, and happy calculating!