TGAT2 Summary: Quantitative Reasoning — "Numerical Ability" Chapter

Hello, future TCAS students! Welcome to the summary of the "Numerical Ability" chapter, a crucial component of the TGAT2 Quantitative Reasoning test. Many of you might feel anxious when you hear "numbers" or "math," but I want to tell you: If it feels difficult at first, don't worry! This section doesn't focus on complex calculations like an applied mathematics exam; instead, it emphasizes "observation" and "quick thinking."

In this chapter, we will practice visualizing numbers and spotting the patterns within them to maximize your score!

1. Numerical Series

This involves finding the "rule" or "relationship" in a given set of numbers to determine the next number in the sequence.

Common Types of Series:

  • Simple Series: Increases or decreases by a constant value, or changes in a consistent rhythm, e.g., \( 2, 4, 6, 8, ... \) (adds 2 each time).
  • Multi-layered Series: If you don't find a pattern in the first difference, find the difference of the differences.
  • Alternating (Mixed) Series: Two or more sets of numbers are interleaved together.
  • Cumulative Series: The next number is the result of adding the preceding numbers, e.g., \( 1, 2, 3, 5, 8, ... \) (derived from \( 1+2=3 \), \( 2+3=5 \)).

Key Tip: If the numbers in the sequence grow rapidly, think about multiplication or exponents. If they increase slowly, think about addition.

Try it out:

Find the next number in \( 3, 6, 12, 24, ... \)
Logic: You can see the numbers are doubling each time (\( \times 2 \)). Therefore, the next number is \( 24 \times 2 = \mathbf{48} \).

Common Mistake: Jumping to conclusions based on only the first two numbers. I recommend checking the relationship against the 3rd and 4th numbers to be certain.

2. Quantitative Comparison

In this section, you are given two columns (Column A and Column B) and asked to determine which value is greater.

Response Criteria:

  • Choose 1: If the value in Column A is greater than Column B.
  • Choose 2: If the value in Column B is greater than Column A.
  • Choose 3: If both columns are equal.
  • Choose 4: If the provided information is insufficient to conclude.

Time-saving Technique: You don't need to calculate the exact value down to the last digit. Simply estimate or simplify the expressions to clearly see which side is larger.

Did you know? This type of question loves to trick you with "negative numbers" and "zero." For example, if the problem states \( x^2 = 4 \), don't forget that \( x \) could be both \( 2 \) and \( -2 \), which might change your answer to "insufficient info" (Choice 4) immediately!

3. Data Interpretation

This involves reading data from tables, pictographs, bar charts, or line graphs and performing minor calculations to find the answer.

Things to Observe Carefully:

  • Data Units: Check if it's in Baht, Millions of Baht, or Percentages (%).
  • Table/Graph Title: It tells you what the data is about and the time frame it covers.
  • Common Question: Finding the "percentage change" (how much of a percentage increase/decrease).

The Golden Formula:
Percentage Increase/Decrease = \( \frac{New Value - Old Value}{Old Value} \times 100 \)

Key Tip: When dealing with tables filled with large numbers, use "rounding" to speed up your calculations. For instance, treat \( 9,985 \) as \( 10,000 \).

4. Word Problems

These turn everyday scenarios into numerical equations. Most cover foundational topics:

Frequently Tested Topics:

  • Percentages: e.g., discounts, profit-loss.
  • Ratio and Proportion: e.g., distributing money by ratio, mixing solutions.
  • Average: \( Average = \frac{Total Sum}{Number of Data Points} \).
  • Age Equations: Comparing ages in the past, present, and future.
  • Work and Time: e.g., 5 people finish a job in 2 days; what happens if you add more people?
"Draw it out" Technique:

For problems that sound confusing, drawing a simple number line or a quick sketch can help you see the relationship between the numbers much more clearly.

Common Mistake: Not reading carefully, especially the distinction between "how many times" and "how many times more." These two phrases have very different meanings. Be careful!

Key Takeaways (Things to remember before the exam)

1. Stay composed: The TGAT2 test emphasizes speed. If you get stuck on a question for more than 2 minutes, skip it and come back later.
2. Look at the big picture: Before calculating, try to estimate where the answer should fall. This helps eliminate wrong choices faster.
3. Practice spotting patterns: For series, try looking for various relationships: addition, subtraction, multiplication, division, and exponents.
4. Watch out for conditions: In quantitative comparison, don't forget to check critical values like \( 0, 1, -1 \), or fractions.

Good luck, everyone! "Numerical Ability" doesn't depend on how naturally "good at math" you are; it depends on how much you practice until you are "accustomed" to numbers and can see patterns quickly. Keep practicing, and the score you're aiming for won't be out of reach!