Aptitude Test Score Comparison Problem

This problem requires us to determine the highest score among five children based on the given relational statements about their scores. We will deduce the order of scores by combining the provided information.

Analyzing the Given Score Relationships

Let's represent the scores of the five children A, B, C, D, and E. We are given the following comparisons:

• Child A scored less marks than child B. Mathematically, this is \(\text{Score}(A) < \text{Score}(B)\).
• Child C scored less marks than child D. Mathematically, this is \(\text{Score}(C) < \text{Score}(D)\).
• Child B scored less marks than child C. Mathematically, this is \(\text{Score}(B) < \text{Score}(C)\).
• Child A scored more marks than child E. Mathematically, this is \(\text{Score}(A) > \text{Score}(E)\), or \(\text{Score}(E) < \text{Score}(A)\).

Combining the Score Inequalities

Now, let's chain these inequalities together to establish a complete or partial order of the children's scores.

1. We know \(\text{Score}(A) < \text{Score}(B)\) and \(\text{Score}(B) < \text{Score}(C)\). Combining these gives us \(\text{Score}(A) < \text{Score}(B) < \text{Score}(C)\).
2. Next, we have \(\text{Score}(B) < \text{Score}(C)\) and \(\text{Score}(C) < \text{Score}(D)\). Combining these extends the chain: \(\text{Score}(B) < \text{Score}(C) < \text{Score}(D)\).
3. Putting the results from step 1 and step 2 together, we get a clear order for children A, B, C, and D: \(\text{Score}(A) < \text{Score}(B) < \text{Score}(C) < \text{Score}(D)\).
4. Finally, we have the relationship \(\text{Score}(E) < \text{Score}(A)\). Since A's score is already established as the lowest among A, B, C, and D in the chain \(\text{Score}(A) < \text{Score}(B) < \text{Score}(C) < \text{Score}(D)\), and E scored even less than A, E's score is the lowest of all five children.

The complete order of scores from lowest to highest is \(\text{Score}(E) < \text{Score}(A) < \text{Score}(B) < \text{Score}(C) < \text{Score}(D)\).

Identifying the Highest Score

From the combined inequality \(\text{Score}(E) < \text{Score}(A) < \text{Score}(B) < \text{Score}(C) < \text{Score}(D)\), it is clear that Child D has the highest score among the five children.

Conclusion on Highest Score

Based on the step-by-step deduction of the score relationships, Child D scored the highest marks in the aptitude test.

Revision Table: Aptitude Test Score Comparison

Additional Information: Logical Deduction and Ranking

Problems like this one are common in aptitude tests and involve logical deduction. They require you to piece together several pieces of information to arrive at a conclusion about the relative positions (ranking) of items or individuals. These questions test your ability to follow logical steps and manage multiple constraints simultaneously. Practicing such problems helps improve analytical and reasoning skills.

• Logical Deduction: Using given premises to infer a conclusion that must be true if the premises are true.
• Ranking Problems: Arranging elements in a specific order based on given comparisons (e.g., height, weight, scores).
• Transitivity: The principle used here (if A < B and B < C, then A < C) is called transitivity.

Being systematic in listing and combining the given facts is crucial for solving these logical deduction problems accurately.