HEC Scholarship Aptitude Test (HAT) Guide

1. Factsheet: General Information

The HEC Scholarship Aptitude Test (HAT) is structured as follows:

• Test Duration: 120 minutes (2 hours).

• Total Number of Questions: 100 questions.

• Test Composition:

    ◦ Verbal Reasoning: 50% of the total questions.

    ◦ Quantitative Reasoning: 30% of the total questions.

    ◦ Analytical Reasoning: 20% of the total questions.

    ◦ Total: 100%.

2. Understanding the Test Components & Explainers

The HAT assesses a student’s aptitude across three main areas: Verbal Reasoning, Quantitative Reasoning, and Analytical Reasoning.

2.1. Verbal Reasoning

This section evaluates your English language proficiency, including vocabulary, grammar, and reading comprehension skills. It constitutes 50% of the test.

Key Concepts and Question Types:

• Synonyms (Similar Meaning): You will be asked to choose a word that is similar in meaning to a given word.

    ◦ Example: Choose the word that is similar in meaning to the word “DEBACLE”. a. Fiasco b. Conspiracy c. Arrogance d. Harmony

        ▪ Explainer: “Debacle” refers to a sudden and ignominious failure; a fiasco. Thus, “Fiasco” is the correct synonym.

• Vocabulary/Definitions (Fill in the Blank): You may need to define a word or complete a sentence using the correct word choice based on its meaning.

    ◦ Example: “Perfunctory means ______________:” a. Done with utmost care b. Occurring occasionally c. Done without care or interest d. Happening repeatedly

        ▪ Explainer: “Perfunctory” describes an action carried out with a minimum of effort or reflection, hence “Done without care or interest” is the correct definition.

• Antonyms (Opposite Meaning): You will choose a word that is most nearly opposite in meaning to a given word.

    ◦ Example: Choose the word that is most nearly opposite in meaning to the word “ADVERSITY”. a. Poverty b. Hardship c. Scarcity d. Prosperity

        ▪ Explainer: “Adversity” means difficulties or misfortune. The opposite is “Prosperity”.

• Sentence Completion: These questions require you to choose the correct word or combination of words to fill blanks in a statement, ensuring logical and grammatical coherence.

    ◦ Example: “Biological clocks are of such ___________ adaptive value to living organisms that we would expect most organisms to ____________ them.” a. clear . . . avoid b. meagre . . . evolve c. significant . . . eschew d. obvious . . . possess

        ▪ Explainer: The sentence implies a positive relationship between adaptive value and expectation of possession. “Obvious” and “possess” fit this context.

• Grammar/Usage (Fill in the Blank): Questions may test your understanding of correct grammatical structures or idiomatic expressions.

    ◦ Example 1: “It’s time she ________________ some work.” a. is doing b. would do c. did d. was to do

        ▪ Explainer: The phrase “It’s time she…” usually takes the simple past tense to express that something should be done now.

    ◦ Example 2: “Would you mind _____________ me that pencil.” a. to pass b. pass c. passing d. that you pass

        ▪ Explainer: The verb “mind” is typically followed by a gerund (-ing form).

Preparation Strategies for Verbal Reasoning:

• Extensive Reading: Read widely to encounter new vocabulary and improve comprehension.

• Vocabulary Building: Focus on learning synonyms, antonyms, and precise definitions. Utilize flashcards or vocabulary apps.

• Grammar Practice: Review fundamental English grammar rules, including verb tenses, sentence structure, and common idioms.

• Contextual Clues: Practice inferring the meaning of unknown words from the surrounding text in sentence completion exercises.

2.2. Quantitative Reasoning

This section assesses your ability to solve mathematical problems, covering topics such as algebra, arithmetic, and number properties. It constitutes 30% of the test.

Key Concepts and Question Types:

• Algebra (Exponents): Questions may involve solving equations with exponents.

    ◦ Example: If 8^n = 16^4 then n = a. 4 b. 16/4 c. 8 d. 4/3

        ▪ Explainer: Convert both bases to a common base (2). 8^n = (2^3)^n = 2^(3n). 16^4 = (2^4)^4 = 2^16. So, 3n = 16, which means n = 16/3. Note: The provided answer “16/4” for this question in the source is incorrect based on the problem statement; the correct answer should be 16/3. I will use the correct answer.

• Algebra (Inequalities): You will need to solve inequalities for a variable.

    ◦ Example: If p − 1 < 2p + 3 then, a. p > 4 b. p < −4 c. p > −4 d. p < 4

        ▪ Explainer: To solve p – 1 < 2p + 3, subtract p from both sides: -1 < p + 3. Then subtract 3 from both sides: -4 < p, or p > -4.

• Word Problems (Algebra): These involve translating a verbal description into an algebraic equation and solving it.

    ◦ Example: The sum of a number and its reciprocal is equal to four times the difference of the number and its reciprocal. The number is, e. f. g. ±2 h.

        ▪ Explainer: Let the number be ‘x’. The problem translates to x + (1/x) = 4 * (x – 1/x). Multiplying by x gives x^2 + 1 = 4x^2 – 4. Rearranging gives 3x^2 = 5, so x^2 = 5/3, and x = ±√(5/3). The option provided in the source is “±2”. This implies the sample question statement (or its solution) might have a slight discrepancy, but the type of question involves setting up and solving an equation.

• Complex Numbers: Operations with complex numbers, such as multiplication.

    ◦ Example: The product of complex numbers is (2−i)×(2+i) = i. 3+4𝑖 j. 3 k. 𝟓 l. 5+4𝑖

        ▪ Explainer: This is a difference of squares: (a-b)(a+b) = a^2 – b^2. Here, (2-i)(2+i) = 2^2 – i^2 = 4 – (-1) = 4 + 1 = 5.

• Number Properties (Repeating Decimals): Identify numbers that cannot be represented by a repeating decimal. This typically means identifying terminating decimals, which are rational numbers whose denominators (in simplest form) only have prime factors of 2 and 5.

    ◦ Example: Which of the following numbers cannot be represented by a repeating decimal? m. n. o. p. 10

        ▪ Explainer: A rational number (a fraction) results in a terminating decimal if its denominator has only 2 and/or 5 as prime factors. Otherwise, it’s a repeating decimal. Integers like 10 are terminating decimals (10.0).

• Simultaneous Equations: Solving for variables given multiple equations.

    ◦ Example: If 𝑥 + 2𝑦 = 𝑎 and 𝑥 − 2𝑦 = 𝑏 then the value 𝑥𝑦 equals to, q. r. s. t.

        ▪ Explainer: Add the two equations: (x+2y) + (x-2y) = a+b => 2x = a+b => x = (a+b)/2. Subtract the second from the first: (x+2y) – (x-2y) = a-b => 4y = a-b => y = (a-b)/4. Then xy = [(a+b)/2] * [(a-b)/4] = (a^2 – b^2)/8.

Preparation Strategies for Quantitative Reasoning:

• Master Basic Arithmetic: Ensure a strong foundation in addition, subtraction, multiplication, and division.

• Algebra Fundamentals: Practice solving linear equations, inequalities, working with exponents, and operations with complex numbers.

• Word Problem Conversion: Learn to translate written problems into mathematical expressions or equations.

• Number Theory: Understand properties of numbers, including prime numbers, factors, multiples, and types of decimals (terminating vs. repeating).

• Formula Recall: Memorize common algebraic formulas (e.g., difference of squares, quadratic formula if applicable).

2.3. Analytical Reasoning

Analytical reasoning questions, also known as analytical games, are designed to test your ability for conceptual learning and how you respond to solve complex situations. They do not require high-level knowledge of formal logic or mathematics, but rather basic general logic of daily life, along with vocabulary, skills, conceptual ability, and general math ability. This section accounts for 20% of the test.

Components of an Analytical Game:

Each analytical reasoning set typically consists of:

1. Situation: This part explains the actual problem or scenario, defining the circumstances, the objective, and the resources available.

2. Limitations or Rules: These are the most important component, outlining the constraints or conditions that must be followed to achieve the objective.

3. Questions: Usually three to seven questions that check your understanding of the complex situation and its implications.

Types of Rules:

• Basic Rules: These rules have the minimum possibility of occurrence and provide a fixed point or a very limited number of possibilities for an entity.

    ◦ Example: “N must be completed on Thursday” means task N has only one possible day. Even “N must be completed on Thursday or Friday” is a basic rule because it limits possibilities significantly.

• Relationship Rules: These rules describe a connection or relation between different entities.

    ◦ Example: “J must be completed sometime before L is completed” (J < L) or “M must be completed on the day immediately before or the day immediately after the day on which O is completed” (M = O ± 1).

• New Rules: These are deductions or further limitations that you can generate by combining the given basic and relationship rules.

Types of Analytical Games:

There are three major types of analytical games:

• Ordering Game: Requires you to place persons, tasks, or things in a particular sequence or order based on the given conditions.

    ◦ Example: Scheduling trains for departure at specific times.

• Grouping Game: Requires you to select a group of individuals or items according to a set of conditions.

    ◦ Example: Appointing members to a planning board from executives.

• Networking Game: Requires you to draw connections or links between entities (e.g., cities, computers) based on specified relations.

    ◦ Example: Message travel paths between computers.

Cheatsheet: Analytical Symbols

Using symbols and notations is crucial for solving analytical games efficiently.