Analyzing the Relationships

We are given information about the relative height and intelligence of four people: A, B, C, and D. We need to determine who is the shortest and who is the least smart based on these clues.

Let's break down the information for both height and intelligence separately.

Height Relationships

Here are the clues related to height:

• C is shorter than D: \(C < D\)
• B is taller than D: \(B > D\)
• A is not taller than C: \(A \le C\) (This means A is shorter than or equal to C in height)

Let's combine these relationships to find the order of heights:

• We know \(B > D\) and \(C < D\). This tells us B is taller than D, and C is shorter than D. So, D is in between B and C in height, or B is taller than D, which is taller than C: \(B > D > C\).
• We also know \(A \le C\). This means A is either shorter than C or has the same height as C.

Combining \(B > D > C\) with \(A \le C\), we get the overall height order:

\(B > D > C \ge A\)

From this combined relationship, it is clear that A is the shortest person among A, B, C, and D because A is shorter than or equal to C, and C is shorter than both D and B.

Intelligence Relationships

Here are the clues related to intelligence:

• C is smarter than D: \(C > D\)
• B is not smarter than D: \(B \le D\) (This means B is less smart than or equal to D in intelligence)
• A is smarter than C: \(A > C\)

Let's combine these relationships to find the order of intelligence:

• We know \(A > C\) and \(C > D\). This tells us A is smarter than C, and C is smarter than D. So, A is smarter than both C and D, and C is smarter than D: \(A > C > D\).
• We also know \(B \le D\). This means B is either less smart than D or has the same intelligence as D.

Combining \(A > C > D\) with \(B \le D\), we get the overall intelligence order:

\(A > C > D \ge B\)

From this combined relationship, it is clear that B is the least smart person among A, B, C, and D because B is less smart than or equal to D, and D is less smart than both C and A.

Summary of Findings

Based on our analysis:

• The shortest person is A.
• The least smart person is B.

Let's compare these findings with the given options.

The statement "A is the shortest and B is the least smart" matches our conclusions.