The RMS CET Mathematics section isn't just about getting the right answer. It's about getting it quickly. You already know how to add, subtract, multiply, and divide. Now, we'll focus on the strategies that turn slow, step-by-step calculations into fast, efficient problem-solving.

The key is learning to see the patterns behind the numbers. Let's start with two tools you're familiar with, but we'll use them in more complex situations: LCM and HCF.

You've learned how to find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of a set of numbers. The real test is knowing when to use them, especially in word problems. Here's a simple rule to remember:

• Use LCM when you're looking for a future point in time or a total quantity where different cycles align. Think about bells ringing together, runners meeting at a starting point, or buying items in different-sized packs to get an equal number of each.
• Use HCF when you need to divide or distribute things into the largest possible equal groups. This applies to problems about arranging students in rows, cutting materials into equal lengths, or finding the largest size of tile to cover a floor without waste.

Let's try one. Three bells ring at intervals of 12, 15, and 18 minutes respectively. If they ring together at 9:00 AM, when will they next ring together? This is a classic LCM problem. We need to find the smallest number of minutes that is a multiple of all three intervals. The LCM of 12, 15, and 18 is 180. So, they will ring together again after 180 minutes, or 3 hours. That means the next time is 12:00 PM.

Now, let's consider an HCF problem. A rectangular courtyard is 20 meters 16 cm long and 15 meters 60 cm wide. It is to be paved with square tiles of the same size. What is the least possible number of such tiles?

First, convert everything to the same unit. Length = 2016 cm, Width = 1560 cm. We need the largest possible square tile that can fit perfectly into both dimensions. This is the HCF of 2016 and 1560. Using the division method for HCF, we find that the HCF is 24. So, the side of the largest possible tile is 24 cm.

To find the number of tiles, we divide the area of the courtyard by the area of one tile:

Number of tiles = (Area of courtyard) / (Area of one tile)

After calculation, we get 5460 tiles. By using HCF, we found the most efficient tile size and solved the problem.

Fractions, decimals, and percentages are just different ways of saying the same thing. Being able to switch between them instantly is a superpower in a timed exam. You should know the common conversions by heart, but here are some patterns to speed up the rest.

To convert a fraction to a percentage, you multiply by 100. But instead of always doing the full calculation, look for shortcuts. For example, to find $3/8$ as a percentage, you could calculate $(3 \div 8) \times 100$. Or, you can remember that $1/8 = 12.5\%$. So, $3/8$ is just $3 \times 12.5\% = 37.5\%$. Memorizing the percentage equivalents of unit fractions like $1/2, 1/3, 1/4, 1/5, 1/6, 1/8,$ and $1/9$ will save you critical seconds. Another powerful tool is the unitary method which helps in solving problems involving proportions.

This table is your new best friend. For profit and loss problems, percentages are key. For instance, if the cost price of an item is $80 and it's sold at a 25% profit, don't multiply $80$ by $25/100$. Instead, think: 25% is $1/4$. What is $1/4$ of $80? It's $20. The selling price is $80 + 20 = \text{\textdollar}100$. Simple and fast.

The relationship between speed, distance, and time is fundamental. All problems in this category come down to three variations of one formula.

One of the most important aspects of these problems is unit consistency. If speed is in km/h, time must be in hours and distance in kilometers. The most common conversion you'll need is changing km/h to m/s and vice versa.

• To convert from km/h to m/s, multiply by $5/18$.
• To convert from m/s to km/h, multiply by $18/5$.

Why this specific fraction? Let's break it down. 1 km = 1000 meters, and 1 hour = 3600 seconds. So, 1 km/h = $1000m / 3600s$, which simplifies to $5/18$ m/s. Knowing this conversion factor saves you from calculating it from scratch every time.

Let's apply this. A train travels at 90 km/h. How many meters will it cover in 10 seconds? First, convert the speed: $90 \times (5/18) = 25$ m/s. Now, use the formula: Distance = Speed × Time. Distance = $25 \text{ m/s} \times 10 \text{ s} = 250$ meters. Easy.

Finally, let's touch on averages. The formula for the average of a set of numbers is the sum of the items divided by the number of items. For average speed, however, it's not always the average of the speeds. The correct formula is always:

Average Speed = Total Distance / Total Time

If a car goes from A to B at 40 km/h and returns from B to A at 60 km/h, what is the average speed? You might be tempted to average 40 and 60 to get 50 km/h. That's wrong. Let the distance be $d$. Time to go from A to B is $d/40$. Time to return is $d/60$. Total distance is $2d$. Total time is $(d/40) + (d/60)$. After some algebra, the average speed comes out to be 48 km/h, regardless of the actual distance.

Mastering these shortcuts and understanding when to apply each formula is the key to succeeding in the mathematics section. It's all about practice and recognizing the type of problem you're facing.