Statements: 1. Elizabeth has four children. 2. Two of the children have blue eyes and two of the children have brown eyes. 3. Half of the children are girls. If the first three statements are taken as facts, which of the following additional statements must also be true?

Introduction / Context:
This logical reasoning question asks you to work with a small set of factual statements about Elizabeth's four children. You are given information about the number of children, their eye colours, and their genders. Based on these facts, you must decide which additional statement is guaranteed to be true, not merely possible. This type of question tests careful interpretation and elimination of possibilities.

Given Data / Assumptions:

Elizabeth has exactly four children.
Exactly two of the four children have blue eyes.
Exactly two of the four children have brown eyes.
Exactly half of the children are girls, so there are 2 girls and 2 boys.
We are testing three candidate statements: a. At least one girl has blue eyes. b. Two of the children are boys. c. The boys have brown eyes.

Concept / Approach:
The key idea is to treat the given information as fixed and then check whether each candidate statement must hold in every possible arrangement that satisfies the facts. If a statement fails in even one valid arrangement, then it is not a necessary fact. Only a statement that holds in all possible distributions of eye colour and gender can be accepted as a fact that “must also be true”.

Step-by-Step Solution:
From “half of the children are girls”, we know there are 2 girls and 2 boys. So statement b, “Two of the children are boys”, follows directly and must be true. Now test statement a: “At least one girl has blue eyes.” This is not forced. It is possible that both boys have blue eyes and both girls have brown eyes. In that scenario, a is false. Since such a distribution (boys: blue, girls: brown) still satisfies all the original facts, statement a cannot be said to “must” be true. Test statement c: “The boys have brown eyes.” This is also not necessary. We can construct a valid case where at least one boy has blue eyes, or even both boys have blue eyes. Therefore c is not guaranteed. Hence, among a, b and c, only b is logically forced by the given information.

Verification / Alternative check:
List a few extreme valid cases. Case 1: both boys blue, both girls brown. Case 2: both boys brown, both girls blue. Case 3: one boy blue, one boy brown, one girl blue, one girl brown. All these respect the given data but make a and c change truth value, while b stays true in all of them. This confirms that only b must be true.

Why Other Options Are Wrong:
Options that include statement a assume at least one girl must have blue eyes, which can be violated by a simple counterexample. Options that include statement c wrongly assume both boys must share brown eyes, which is also not forced. Any option omitting b misses a clear direct consequence of the “half are girls” statement.

Common Pitfalls:
A frequent mistake is to confuse “possible” with “must be true”. Many test-takers quickly imagine one scenario and then assume all statements true in that scenario are necessary. Always try to find a counterexample; if you can, the statement is not guaranteed. Here, experimenting with different colour–gender assignments is crucial.

Final Answer:
The only statement that must be a fact is that two of the children are boys. So the correct choice is b only.