TGAT2 Summary: Quantitative Reasoning — "Numerical Ability" Chapter

Hello, future TCAS students! Welcome to the summary of the "Numerical Ability" (ความสามารถทางจำนวน / ทางตัวเลข) chapter, an essential component of the TGAT2 Critical & Logical Thinking exam. Many of you might feel anxious when you hear "numbers" or "math," but remember: TGAT2 does not test advanced school mathematics! It focuses on everyday quantitative reasoning, pattern recognition, and logical deduction.

According to the official blueprint, Numerical Ability covers four distinct sub-types: Number Series, Quantitative Comparison, Data Sufficiency, and Word Problems. Let's master each one!

1. Number Series (อนุกรมมิติ)

This sub-type involves identifying the rule or pattern governing a sequence of numbers to deduce the missing value. The sequence may be presented in a linear list, a grid, or a geometric figure.

Common Series Patterns:

  • Arithmetic / Constant Step: Increases or decreases by a fixed difference, e.g., \( 3, 7, 11, 15, \dots \) (adds \( 4 \) each step).
  • Multi-level (Difference of Differences): If the first differences do not reveal a constant pattern, take the difference of those differences.
  • Geometric / Factor Scaling: Values grow by multiplication or division, e.g., \( 3, 6, 12, 24, \dots \) (multiplies by \( 2 \)).
  • Alternating (Interleaved) Series: Two distinct sub-sequences woven together into one sequence.
  • Cumulative / Fibonacci-style: Each term is the sum or product of preceding terms, e.g., \( 1, 2, 3, 5, 8, \dots \) where \( 1 + 2 = 3 \) and \( 2 + 3 = 5 \).
  • Grids and Figures: Numbers placed in matrices, triangles, or circles where row, column, or perimeter operations yield a central value.

Key Tip: If the numbers grow rapidly, test for multiplication or exponents (\( n^2, n^3 \)). If they grow steadily, test for addition.

Try it out:

Find the missing number in \( 2, 5, 10, 17, 26, ? \)
Logic: Examine the differences: \( +3, +5, +7, +9 \). The next difference must be \( +11 \). Thus, the missing number is \( 26 + 11 = \mathbf{37} \).

2. Quantitative Comparison (การเปรียบเทียบเชิงปริมาณ)

In TGAT2, quantitative comparison items present three quantities in three separate columns: สดมภ์ ก. (Column A), สดมภ์ ข. (Column B), and สดมภ์ ค. (Column C). All items have 5 multiple-choice options.

Standard Comparison Formats:

  • Column A (สดมภ์ ก.) is the greatest.
  • Column B (สดมภ์ ข.) is the greatest.
  • Column C (สดมภ์ ค.) is the greatest.
  • All three columns are equal.
  • The provided information is insufficient to determine the relationship.

Time-saving Technique: You do not always need an exact decimal value. Simplify, cancel identical terms across columns, or estimate boundaries to see which quantity is largest.

Watch Out for Pitfalls: Watch out for conditions involving negative numbers, zero, and fractions. If a variable is only given as \( x^2 = 9 \), remember that \( x \) could be \( 3 \) or \( -3 \), which might make the relative ordering change and require choosing "insufficient information."

3. Data Sufficiency (ความเพียงพอของข้อมูล)

Data sufficiency tests whether the provided statements provide enough information to answer a target question. A problem consists of an initial question followed by two conditions: Statement ก and Statement ข.

Typical 5-Choice Evaluation Structure:

  • Statement ก alone suffices, but Statement ข alone does not.
  • Statement ข alone suffices, but Statement ก alone does not.
  • Both statements together suffice, but neither statement alone is sufficient.
  • Each statement alone suffices to answer the question independently.
  • Both statements together are still insufficient to answer the question.

Crucial Rule: Do not waste time computing the final numerical answer! Your only task is determining whether a unique, definitive answer can be found. As soon as you establish that a statement yields a single conclusive value or state, that statement is sufficient.

4. Word Problems (โจทย์ปัญหา)

Word problems translate practical, real-world situations into mathematical relationships. The mathematics remains strictly at everyday quantitative-reasoning level.

Frequently Tested Topics:

  • Percentages & Finances: Profit, loss, markups, discounts, and percentage change: \( \text{Percentage Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\% \).
  • Ratios and Proportions: Dividing quantities by parts, scaling recipes, and concentration mixtures.
  • Averages: \( \text{Average} = \frac{\text{Sum of values}}{\text{Number of values}} \).
  • Elementary Relations: Age problems across past/present/future, work rates, speed-distance-time, and perimeter/area of basic plane figures.
  • Tables & Charts: Extracting values accurately from tables, bar charts, or pie graphs and performing basic arithmetic on the data.
"Draw it out" Technique:

For word problems involving overlapping groups or multiple timelines, a quick sketch, timeline, or Venn diagram makes the numerical relations immediate.

Key Takeaways for Exam Day

1. Strict Time Budget: TGAT2 has 80 items in 60 minutes (45 seconds per question). If an item takes longer than a minute, make an educated guess and move on.
2. Remember the Format: Every question in TGAT2 is multiple choice with 5 options (1–5) and only one correct choice.
3. Check Boundary Values: In quantitative comparison and data sufficiency, always test \( 0 \), positive integers, negative integers, and fractions between \( 0 \) and \( 1 \).
4. Sufficient Doesn't Mean Solved: In data sufficiency, stop calculating the moment you know an exact answer is locked in.

"Numerical Ability" in TGAT2 is all about spotting patterns and evaluating logic quickly. Keep practicing consistent sets, and you will achieve your target score!