Among four books, Book 1 is twice as heavy as Book 2. The weight of Book 3 is half of the weight of Book 2. Book 4 is 60 grams more than Book 2 but 60 grams less than Book 1. Which book is the heaviest?

Introduction / Context:
This arithmetic reasoning question involves comparing weights of four books based on given relationships rather than direct numerical values. You are told how each book weight relates to the others and asked to determine which book is heaviest. The problem tests your ability to convert verbal descriptions into algebraic relationships and then reason about relative sizes.

Given Data / Assumptions:

• Book 1 is twice as heavy as Book 2.
• The weight of Book 3 is half of the weight of Book 2.
• Book 4 is 60 grams more than Book 2.
• Book 4 is also 60 grams less than Book 1.
• All books have positive weights.
• We need to identify which book has the greatest weight.

Concept / Approach:
A convenient way to handle such problems is to assign a variable to one book and express all other weights in terms of that variable. Here, Book 2 is a natural choice. Using the given relationships, we can derive expressions for the weights of the other books. Even if we do not compute exact numbers, the relative sizes become clear. However, in this case, we can also find the exact weight of Book 2 by using the two conditions on Book 4 and solving a simple equation.

Step-by-Step Solution:
Step 1: Let the weight of Book 2 be x grams.Step 2: Book 1 is twice as heavy as Book 2, so its weight is 2x grams.Step 3: The weight of Book 3 is half of Book 2, so its weight is x / 2 grams.Step 4: Book 4 is 60 grams more than Book 2, so one expression for Book 4 weight is x + 60 grams.Step 5: Book 4 is also 60 grams less than Book 1. Since Book 1 weighs 2x, another expression for Book 4 weight is 2x - 60 grams.Step 6: Set the two expressions for Book 4 equal to each other: x + 60 = 2x - 60.Step 7: Solve this equation: bring x to one side and constants to the other. Subtract x from both sides to get 60 = x - 60. Add 60 to both sides to obtain x = 120.Step 8: Now substitute back. Book 2 weighs 120 grams, Book 1 weighs 2 * 120 = 240 grams, Book 3 weighs 120 / 2 = 60 grams and Book 4 weighs 120 + 60 = 180 grams.Step 9: Comparing 240, 120, 60 and 180, Book 1 has the largest weight.

Verification / Alternative check:
Even without solving for x, we can see that Book 1 is twice Book 2, whereas Book 4 is only 60 grams above Book 2 but still 60 grams below Book 1. This shows Book 1 must be heavier than both Book 2 and Book 4. Book 3 is half of Book 2, so it is clearly lighter than both Book 2 and Book 1. This reasoning also makes it clear that Book 1 is the heaviest book, consistent with the numeric calculation.

Why Other Options Are Wrong:
Book 2 cannot be the heaviest because Book 1 is twice its weight and Book 4 is even heavier than Book 2. Book 3 is explicitly half of Book 2, making it the lightest. Book 4, while heavier than Book 2, is still 60 grams lighter than Book 1. Therefore it cannot be the heaviest either. Only Book 1 has no heavier competitor.

Common Pitfalls:
Some learners might misinterpret the phrases “more than” and “less than” and reverse an inequality, for example thinking Book 4 is heavier than Book 1 instead of lighter by 60 grams. Others may try to guess without writing equations, leading to confusion. Writing all relationships in terms of a single variable keeps the reasoning clear and avoids mistakes.

Final Answer:
The heaviest book is Book 1.